List of algebras and topological zeta functions. Created 2016-02-02 09:27:35.162831 using Zeta 0.3. ------------------------------------------------------------------------ ALGEBRA #0 ------------------------------------------------------------------------ names: 'L(1,1)', '(ZZ,0)', 'C(1,1)' id: 0 Lie: True commutative: True nilpotency class: 1 nilpotent: True (u,v): (0, 0) cocentral dim: 0 rank: 1 soluble: True derived dim: 0 derived length: 1 associative: True description: ZZ with zero multiplication Topological subalgebra zeta function: poles: 0.0000 order@zero: -1 degree: -1 ess. value@zero: 1 zeta: 1/s complex roots: None ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000 order@zero: -1 degree: -1 ess. value@zero: 1 zeta: 1/s complex roots: None ess. value@infinity: 1 Topological representation zeta function: ess. value@zero: 1 zeta: 1 order@zero: 0 degree: 0 ------------------------------------------------------------------------ ALGEBRA #1 ------------------------------------------------------------------------ names: 'L(2,1)', '(ZZ^2,0)', 'C(2,1)' id: 1 Lie: True commutative: True nilpotency class: 1 nilpotent: True (u,v): (0, 0) cocentral dim: 0 rank: 2 soluble: True derived dim: 0 derived length: 1 associative: True description: ZZ^2 with zero multiplication Topological subalgebra zeta function: poles: 0.0000, 1.0000 order@zero: -1 degree: -2 ess. value@zero: -1 zeta: 1/((s - 1)*s) complex roots: None ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -1 degree: -2 ess. value@zero: -1 zeta: 1/((s - 1)*s) complex roots: None ess. value@infinity: 1 ------------------------------------------------------------------------ ALGEBRA #2 ------------------------------------------------------------------------ names: 'L(3,1)', '(ZZ^3,0)', 'C(3,1)', 'L^1' id: 2 Lie: True commutative: True nilpotency class: 1 nilpotent: True (u,v): (0, 0) cocentral dim: 0 rank: 3 soluble: True derived dim: 0 derived length: 1 associative: True description: ZZ^3 with zero multiplication Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/((s - 1)*(s - 2)*s) complex roots: None ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/((s - 1)*(s - 2)*s) complex roots: None ess. value@infinity: 1 ------------------------------------------------------------------------ ALGEBRA #3 ------------------------------------------------------------------------ names: 'L(3,2)', 'Heisenberg', 'h(ZZ)', 'H(2)', 'L^4(0)', 'n(3,ZZ)', 'A(3,5)' id: 3 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (1, 0) cocentral dim: 2 rank: 3 soluble: True derived dim: 1 derived length: 2 associative: True description: Heisenberg Lie ring over ZZ Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 3/2/((2*s - 3)*(s - 1)*s) complex roots: None ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 0.6667, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/((3*s - 2)*(s - 1)*s) complex roots: None ess. value@infinity: 1/3 Topological representation zeta function: degree: 0 ess. value@zero: -1 complex roots: 0.0000 (zeta-1)@infinity: 1 zeta: s/(s - 1) fixed points: 0.0000, 2.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #4 ------------------------------------------------------------------------ names: 'L(4,1)', '(ZZ^4,0)', 'C(4,1)', 'M^1' id: 4 Lie: True commutative: True nilpotency class: 1 nilpotent: True (u,v): (0, 0) cocentral dim: 0 rank: 4 soluble: True derived dim: 0 derived length: 1 associative: True description: ZZ^4 with zero multiplication Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/((s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/((s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 1 ------------------------------------------------------------------------ ALGEBRA #5 ------------------------------------------------------------------------ names: 'L(4,2)', 'L(3,2) (+) (ZZ,0)', 'h(ZZ) (+) (ZZ,0)', 'H(2) (+) (ZZ,0)', 'M^5' id: 5 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (1, 0) cocentral dim: 2 rank: 4 soluble: True derived dim: 1 derived length: 2 associative: True description: Direct sum of the Heisenberg Lie ring and (ZZ,0) Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 2.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(3*s - 4)/((2*s - 3)*(s - 1)*(s - 2)^2*s) complex roots: 1.3333 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/3/((s - 1)^2*(s - 2)*s) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #6 ------------------------------------------------------------------------ names: 'L(4,3)', 'M3', 'nb(sp(4,ZZ))', 'M^7(0,0)' id: 6 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (1, 1) cocentral dim: 3 rank: 4 soluble: True derived dim: 2 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 1.6667 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(13*s - 15)/((3*s - 5)*(2*s - 3)^2*(s - 1)*s) complex roots: 1.1538 ess. value@infinity: 13/24 Topological ideal zeta function: poles: 0.0000, 0.5000, 0.6000, 0.6667, 1.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(5*s - 2)/((5*s - 3)*(3*s - 2)*(2*s - 1)*(s - 1)*s) complex roots: 0.4000 ess. value@infinity: 1/12 Topological representation zeta function: degree: 0 ess. value@zero: 1 complex roots: 0.0000 (zeta-1)@infinity: 2 zeta: s^2/(s - 1)^2 fixed points: 0.0000, 0.3820, 2.6180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #7 ------------------------------------------------------------------------ names: 'L(5,1)', '(ZZ^5,0)', 'C(5,1)' id: 7 Lie: True commutative: True nilpotency class: 1 nilpotent: True (u,v): (0, 0) cocentral dim: 0 rank: 5 soluble: True derived dim: 0 derived length: 1 associative: True description: ZZ^5 with zero multiplication Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/((s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: None ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/((s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: None ess. value@infinity: 1 ------------------------------------------------------------------------ ALGEBRA #8 ------------------------------------------------------------------------ names: 'L(5,2)', 'h(ZZ) (+) (ZZ^2,0)' id: 8 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (1, 0) cocentral dim: 2 rank: 5 soluble: True derived dim: 1 derived length: 2 associative: True description: Direct sum of the Heisenberg Lie ring and (ZZ^2,0) Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 3.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/2*(3*s - 5)/((2*s - 5)*(s - 1)*(s - 2)^2*(s - 3)*s) complex roots: 1.6667 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/((3*s - 4)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #9 ------------------------------------------------------------------------ names: 'L(5,3)', 'M3 (+) (ZZ,0)' id: 9 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (1, 1) cocentral dim: 3 rank: 5 soluble: True derived dim: 2 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/24*(13*s^2 - 41*s + 32)/((s - 1)*(s - 2)^5*s) complex roots: 1.4183, 1.7355 ess. value@infinity: 13/24 Topological ideal zeta function: poles: 0.0000, 0.7500, 0.8000, 1.0000, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/3*(5*s - 3)/((5*s - 4)*(4*s - 3)*(s - 1)^2*(s - 2)*s) complex roots: 0.6000 ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #10 ------------------------------------------------------------------------ names: 'L(5,4)', 'h(ZZ) curlyvee h(ZZ)' id: 10 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 5 soluble: True derived dim: 1 derived length: 2 associative: True description: Central product of two copies of the Heisenberg Lie ring Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.3333, 2.0000, 2.3333, 3.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/3*(17*s - 21)/((3*s - 4)*(3*s - 7)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: 1.2353 ess. value@infinity: 17/27 Topological ideal zeta function: poles: 0.0000, 0.8000, 1.0000, 2.0000, 3.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/((5*s - 4)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 1/5 Topological representation zeta function: degree: 0 ess. value@zero: -2 complex roots: 0.0000 (zeta-1)@infinity: 1/2 zeta: 2*s/(2*s - 1) fixed points: 0.0000, 1.5000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #11 ------------------------------------------------------------------------ names: 'L(5,5)', 'Q5' id: 11 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 4 rank: 5 soluble: True derived dim: 2 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.3333, 1.8333, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/18*(153*s^3 - 704*s^2 + 1064*s - 528)/((6*s - 11)*(3*s - 4)*(s - 1)*(s - 2)^4*s) complex roots: 1.2176, 1.5241, 1.8596 ess. value@infinity: 17/36 Topological ideal zeta function: poles: 0.0000, 0.8000, 1.0000, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/3/((5*s - 4)*(s - 1)^2*(s - 2)*s) complex roots: None ess. value@infinity: 1/15 Topological representation zeta function: degree: 0 ess. value@zero: -1/2 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 3/2 zeta: 1/2*(2*s - 1)*s/(s - 1)^2 fixed points: 0.0000, 0.6340, 2.3660 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #12 ------------------------------------------------------------------------ names: 'L(5,6)', 'Fil4' id: 12 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 4 rank: 5 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.3333, 1.5000, 1.6000, 1.7143, 1.7333, 1.7500, 1.8000, 1.8333, 1.8571 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/3*(392031360*s^9 - 5741480808*s^8 + 37286908278*s^7 - 140917681751*s^6 + 341501393670*s^5 - 550262853249*s^4 + 589429290044*s^3 - 404678115300*s^2 + 161557332768*s - 28569052512)/((15*s - 26)*(7*s - 12)*(7*s - 13)*(6*s - 11)^3*(5*s - 8)*(5*s - 9)*(4*s - 7)^2*(3*s - 4)*(2*s - 3)*(s - 1)*s) complex roots: 1.1440, 1.3545, 1.5862, 1.6758, 1.7243 - 0.0162*i, 1.7243 + 0.0162*i, 1.7892, 1.8236 - 0.0134*i, 1.8236 + 0.0134*i ess. value@infinity: 463/1350 Topological ideal zeta function: poles: 0.0000, 0.4000, 0.5714, 0.5833, 0.6000, 0.6250, 0.6667, 1.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/2*(5040*s^4 - 10157*s^3 + 7522*s^2 - 2412*s + 280)/((12*s - 7)*(8*s - 5)*(7*s - 4)*(5*s - 2)*(5*s - 3)*(3*s - 2)^2*(s - 1)*s) complex roots: 0.2996, 0.5120, 0.5939, 0.6098 ess. value@infinity: 1/60 Topological representation zeta function: degree: 0 ess. value@zero: 2/3 complex roots: 0.0000 (zeta-1)@infinity: 5/2 zeta: 2*s^2/((2*s - 3)*(s - 1)) fixed points: 0.0000, 0.5000, 3.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #13 ------------------------------------------------------------------------ names: 'L(5,7)', 'M4' id: 13 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (1, 1) cocentral dim: 4 rank: 5 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 1.7143, 1.7500, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/2*(46*s^3 - 216*s^2 + 333*s - 168)/((7*s - 12)*(4*s - 7)*(2*s - 3)*(s - 1)*(s - 2)^3*s) complex roots: 1.1964, 1.6569, 1.8423 ess. value@infinity: 23/56 Topological ideal zeta function: poles: 0.0000, 0.4000, 0.5455, 0.5714, 0.5833, 0.6250, 0.6667, 1.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 2*(1386*s^3 - 2023*s^2 + 948*s - 140)*(2*s - 1)/((12*s - 7)*(11*s - 6)*(8*s - 5)*(7*s - 4)*(5*s - 2)*(3*s - 2)^2*(s - 1)*s) complex roots: 0.3023, 0.5000, 0.5520, 0.6053 ess. value@infinity: 1/60 Topological representation zeta function: degree: 0 ess. value@zero: 1/2 complex roots: 0.0000 (zeta-1)@infinity: 3 zeta: s^2/((s - 1)*(s - 2)) fixed points: 0.0000, 0.5858, 3.4142 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #14 ------------------------------------------------------------------------ names: 'L(5,8)', 'G3' id: 14 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (1, 0) cocentral dim: 3 rank: 5 soluble: True derived dim: 2 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/6*(7*s - 10)/((2*s - 5)*(s - 1)*(s - 2)^3*s) complex roots: 1.4286 ess. value@infinity: 7/12 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 1.3333, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 2/((5*s - 6)*(3*s - 4)*(s - 1)*(s - 2)*s) complex roots: None ess. value@infinity: 2/15 Topological representation zeta function: degree: 0 ess. value@zero: -1/2 complex roots: 0.0000 (zeta-1)@infinity: 2 zeta: s/(s - 2) fixed points: 0.0000, 3.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #15 ------------------------------------------------------------------------ names: 'L(5,9)', 'F(3,2)' id: 15 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (1, 1) cocentral dim: 3 rank: 5 soluble: True derived dim: 3 derived length: 2 associative: False description: Free nilpotent Lie ring of class 3 on 2 generators Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 1.6000, 1.8000, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/6*(121*s^3 - 565*s^2 + 864*s - 432)/((5*s - 8)*(5*s - 9)*(2*s - 3)*(s - 1)*(s - 2)^3*s) complex roots: 1.1910, 1.5745, 1.9040 ess. value@infinity: 121/300 Topological ideal zeta function: poles: 0.0000, 0.6667, 0.7500, 0.8000, 0.8571, 1.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 2*(35*s^2 - 42*s + 12)/((7*s - 6)*(5*s - 4)^2*(4*s - 3)*(3*s - 2)*(s - 1)*s) complex roots: 0.4691, 0.7309 ess. value@infinity: 1/30 Topological representation zeta function: degree: 0 ess. value@zero: 1/2 complex roots: 0.0000 (zeta-1)@infinity: 3 zeta: s^2/((s - 1)*(s - 2)) fixed points: 0.0000, 0.5858, 3.4142 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #16 ------------------------------------------------------------------------ names: 'L(6,1)', '(ZZ^6,0)', 'C(6,1)' id: 16 Lie: True commutative: True nilpotency class: 1 nilpotent: True (u,v): (0, 0) cocentral dim: 0 rank: 6 soluble: True derived dim: 0 derived length: 1 associative: True description: ZZ^6 with zero multiplication Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 4.0000, 5.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/((s - 1)*(s - 2)*(s - 3)*(s - 4)*(s - 5)*s) complex roots: None ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 4.0000, 5.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/((s - 1)*(s - 2)*(s - 3)*(s - 4)*(s - 5)*s) complex roots: None ess. value@infinity: 1 ------------------------------------------------------------------------ ALGEBRA #17 ------------------------------------------------------------------------ names: 'L(6,2)', 'h(ZZ) (+) (ZZ^3,0)' id: 17 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (1, 0) cocentral dim: 2 rank: 6 soluble: True derived dim: 1 derived length: 2 associative: True description: Direct sum of the Heisenberg Lie ring and (ZZ^3,0) Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.5000, 3.0000, 4.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 3/2/((2*s - 5)*(s - 1)*(s - 3)^2*(s - 4)*s) complex roots: None ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/((3*s - 5)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #18 ------------------------------------------------------------------------ names: 'L(6,3)', 'M3 (+) (ZZ^2,0)' id: 18 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (1, 1) cocentral dim: 3 rank: 6 soluble: True derived dim: 2 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.3333, 2.5000, 2.6667, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/2*(13*s - 28)*(3*s - 5)/((3*s - 7)*(3*s - 8)*(2*s - 5)^2*(s - 1)*(s - 2)*(s - 3)*s) complex roots: 1.6667, 2.1538 ess. value@infinity: 13/24 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/20*(5*s - 4)/((3*s - 4)*(s - 1)^3*(s - 2)*(s - 3)*s) complex roots: 0.8000 ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #19 ------------------------------------------------------------------------ names: 'L(6,4)', 'h(ZZ) curlyvee h(ZZ) (+) (ZZ,0)' id: 19 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 6 soluble: True derived dim: 1 derived length: 2 associative: True description: Direct sum of (ZZ,0) and the central product of two Heisenberg Lie rings Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 2.3333, 2.6667, 3.0000, 4.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: (17*s^2 - 63*s + 56)/((3*s - 5)*(3*s - 7)*(3*s - 8)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: 1.4797, 2.2261 ess. value@infinity: 17/27 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/5/((s - 1)^2*(s - 2)*(s - 3)*(s - 4)*s) complex roots: None ess. value@infinity: 1/5 ------------------------------------------------------------------------ ALGEBRA #20 ------------------------------------------------------------------------ names: 'L(6,5)', 'Q5 (+) (ZZ,0)' id: 20 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 4 rank: 6 soluble: True derived dim: 2 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.1667, 2.2500, 2.3333, 2.4000, 2.5000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/2*(12240*s^5 - 126784*s^4 + 521522*s^3 - 1063913*s^2 + 1075150*s - 429975)/((6*s - 13)*(5*s - 12)*(4*s - 9)*(3*s - 5)*(3*s - 7)^2*(2*s - 5)^2*(s - 1)*(s - 3)*s) complex roots: 1.4385, 1.9370, 2.2668, 2.3579 - 0.0423*i, 2.3579 + 0.0423*i ess. value@infinity: 17/36 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/5/((3*s - 4)*(s - 1)^2*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 1/15 ------------------------------------------------------------------------ ALGEBRA #21 ------------------------------------------------------------------------ names: 'L(6,6)', 'Fil4 (+) (ZZ,0)' id: 21 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 4 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 2.0667, 2.0833, 2.1429, 2.1538, 2.1667, 2.2000, 2.2222, 2.2500, 2.2667, 2.2857 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/48*(52839554826240*s^15 - 1612571385729024*s^14 + 22945067840268288*s^13 - 201917310138409536*s^12 + 1228942670032455984*s^11 - 5479610770178424720*s^10 + 18489925054934205732*s^9 - 48077179247205683304*s^8 + 97118269735864324559*s^7 - 152405042677332499112*s^6 + 184268407184801648476*s^5 - 168562287295854189878*s^4 + 112921211241642321545*s^3 - 52295417007047312650*s^2 + 14969814525806597400*s - 1996549752637440000)/((15*s - 31)*(15*s - 34)*(13*s - 28)*(12*s - 25)*(9*s - 20)*(7*s - 15)*(7*s - 16)*(6*s - 13)^3*(5*s - 11)*(4*s - 9)^3*(3*s - 5)*(s - 1)*(s - 2)^4*s) complex roots: 1.3327, 1.7194, 1.9249 - 0.0829*i, 1.9249 + 0.0829*i, 2.0383 - 0.0104*i, 2.0383 + 0.0104*i, 2.0858, 2.1173, 2.1482, 2.1539, 2.1766 - 0.0174*i, 2.1766 + 0.0174*i, 2.1855, 2.2338, 2.2621 ess. value@infinity: 463/1350 Topological ideal zeta function: poles: 0.0000, 0.6000, 0.7143, 0.7500, 0.8000, 0.8750, 0.8889, 1.0000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/6*(5040*s^4 - 13845*s^3 + 14044*s^2 - 6215*s + 1008)/((9*s - 8)*(8*s - 7)*(7*s - 5)*(5*s - 3)*(5*s - 4)*(4*s - 3)*(s - 1)^2*(s - 2)*s) complex roots: 0.4514, 0.6770, 0.7863, 0.8324 ess. value@infinity: 1/60 ------------------------------------------------------------------------ ALGEBRA #22 ------------------------------------------------------------------------ names: 'L(6,7)', 'M4 (+) (ZZ,0)' id: 22 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (1, 1) cocentral dim: 4 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.1429, 2.4000, 2.5000, 2.6667 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/48*(8280*s^5 - 81688*s^4 + 320237*s^3 - 623254*s^2 + 601785*s - 230400)/((7*s - 15)*(5*s - 12)*(3*s - 8)*(2*s - 5)^2*(s - 1)*(s - 2)^4*s) complex roots: 1.4152, 1.9615 - 0.0874*i, 1.9615 + 0.0874*i, 2.1080, 2.4195 ess. value@infinity: 23/56 Topological ideal zeta function: poles: 0.0000, 0.6000, 0.7143, 0.7273, 0.7500, 0.8750, 0.8889, 1.0000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 4*(154*s^3 - 309*s^2 + 201*s - 42)*(3*s - 2)/((11*s - 8)*(9*s - 8)*(8*s - 7)*(7*s - 5)*(5*s - 3)*(4*s - 3)*(s - 1)^2*(s - 2)*s) complex roots: 0.4556, 0.6667, 0.7233, 0.8275 ess. value@infinity: 1/60 ------------------------------------------------------------------------ ALGEBRA #23 ------------------------------------------------------------------------ names: 'L(6,8)', 'G3 (+) (ZZ,0)' id: 23 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (1, 0) cocentral dim: 3 rank: 6 soluble: True derived dim: 2 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6667, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/2*(7*s - 12)/((3*s - 8)*(2*s - 5)*(s - 1)*(s - 2)*(s - 3)^2*s) complex roots: 1.7143 ess. value@infinity: 7/12 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.6000, 1.6667, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 2/((5*s - 8)*(3*s - 5)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 2/15 ------------------------------------------------------------------------ ALGEBRA #24 ------------------------------------------------------------------------ names: 'L(6,9)', 'F(3,2) (+) (ZZ,0)' id: 24 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (1, 1) cocentral dim: 3 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.2000, 2.3333, 2.4000, 2.5000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/6*(726*s^4 - 5575*s^3 + 15887*s^2 - 19900*s + 9240)/((5*s - 11)*(5*s - 12)*(3*s - 7)*(2*s - 5)^2*(s - 1)*(s - 2)^3*s) complex roots: 1.4546, 1.7604, 2.1240, 2.3401 ess. value@infinity: 121/300 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.1429, 1.2000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/30*(35*s - 24)/((7*s - 8)*(5*s - 6)*(s - 1)^3*(s - 2)*s) complex roots: 0.6857 ess. value@infinity: 1/30 ------------------------------------------------------------------------ ALGEBRA #25 ------------------------------------------------------------------------ names: 'L(6,10)', 'g(6,12)', 'M3 curlyvee h(ZZ)' id: 25 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 6 soluble: True derived dim: 2 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 2.1667, 2.2500, 2.2857, 2.4000, 2.5000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/72*(166530*s^6 - 1931987*s^5 + 9294564*s^4 - 23731443*s^3 + 33913892*s^2 - 25719216*s + 8087040)/((7*s - 16)*(6*s - 13)*(5*s - 12)*(4*s - 9)*(3*s - 5)*(2*s - 5)*(s - 1)*(s - 2)^3*(s - 3)*s) complex roots: 1.5237 - 0.1287*i, 1.5237 + 0.1287*i, 1.9653, 2.1197, 2.1479, 2.3212 ess. value@infinity: 793/1728 Topological ideal zeta function: poles: 0.0000, 0.6667, 0.7143, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/2*(7*s - 4)/((7*s - 5)*(3*s - 2)*(3*s - 4)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: 0.5714 ess. value@infinity: 1/18 Topological representation zeta function: degree: 0 ess. value@zero: 2 complex roots: 0.0000 (zeta-1)@infinity: 3/2 zeta: 2*s^2/((2*s - 1)*(s - 1)) fixed points: 0.0000, 0.2192, 2.2808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 1.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #26 ------------------------------------------------------------------------ names: 'L(6,11)' id: 26 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.6667, 0.7143, 0.7500, 0.8889, 1.0000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/6*(63*s^2 - 79*s + 24)/((9*s - 8)*(7*s - 5)*(4*s - 3)*(3*s - 2)*(s - 1)^2*(s - 2)*s) complex roots: 0.5167, 0.7372 ess. value@infinity: 1/72 Topological representation zeta function: degree: 0 ess. value@zero: 1/8 complex roots: -0.1667, 0.0000 (zeta-1)@infinity: 5/2 zeta: 1/2*(6*s + 1)*s/((3*s - 4)*(s - 1)) fixed points: 0.0000, 0.3974, 2.9360 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.3333 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #27 ------------------------------------------------------------------------ names: 'L(6,12)' id: 27 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.6667, 0.7143, 0.7500, 0.8889, 1.0000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/6*(63*s^2 - 79*s + 24)/((9*s - 8)*(7*s - 5)*(4*s - 3)*(3*s - 2)*(s - 1)^2*(s - 2)*s) complex roots: 0.5167, 0.7372 ess. value@infinity: 1/72 Topological representation zeta function: degree: 0 ess. value@zero: 2/3 complex roots: 0.0000 (zeta-1)@infinity: 5/2 zeta: 2*s^2/((2*s - 3)*(s - 1)) fixed points: 0.0000, 0.5000, 3.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #28 ------------------------------------------------------------------------ names: 'L(6,13)' id: 28 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.5000, 0.7143, 0.8000, 1.0000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/9*(7*s - 3)/((7*s - 5)*(5*s - 4)*(2*s - 1)*(s - 1)^2*(s - 2)*s) complex roots: 0.4286 ess. value@infinity: 1/90 Topological representation zeta function: degree: 0 ess. value@zero: 7/6 complex roots: 0.0000, 0.7500 - 0.1443*i, 0.7500 + 0.1443*i (zeta-1)@infinity: 2 zeta: 1/6*(12*s^2 - 18*s + 7)*s^2/((2*s - 1)*(s - 1)^3) fixed points: 0.0000, 0.3027, 0.7758 - 0.1496*i, 0.7758 + 0.1496*i, 2.6456 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 1.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #29 ------------------------------------------------------------------------ names: 'L(6,14)' id: 29 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 3) cocentral dim: 5 rank: 6 soluble: True derived dim: 4 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/9 complex roots: 0.0000, 0.0918, 0.9082 (zeta-1)@infinity: 3 zeta: 1/3*(12*s^2 - 12*s + 1)*s^2/((2*s - 1)*(2*s - 3)*(s - 1)^2) fixed points: 0.0000, 0.4310 - 0.2655*i, 0.4310 + 0.2655*i, 0.9053, 3.2326 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 1.0000, 1.5000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #30 ------------------------------------------------------------------------ names: 'L(6,15)' id: 30 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 6 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 7/15 complex roots: 0.0000, 1.1667 (zeta-1)@infinity: 3 zeta: (6*s - 7)*s^2/((3*s - 5)*(2*s - 3)*(s - 1)) fixed points: 0.0000, 0.6271, 1.1903, 3.3493 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000, 1.6667 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #31 ------------------------------------------------------------------------ names: 'L(6,16)' id: 31 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 3) cocentral dim: 5 rank: 6 soluble: True derived dim: 4 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1 complex roots: 0.0000 (zeta-1)@infinity: 7/2 zeta: 2*s^3/((2*s - 1)*(s - 1)*(s - 2)) fixed points: 0.0000, 0.4468 - 0.2787*i, 0.4468 + 0.2787*i, 3.6064 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 1.0000, 2.0000 order@zero: 3 ------------------------------------------------------------------------ ALGEBRA #32 ------------------------------------------------------------------------ names: 'L(6,17)' id: 32 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 6 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 3/8 complex roots: 0.0000, 1.5000 (zeta-1)@infinity: 7/2 zeta: 1/2*(2*s - 3)*s^2/((s - 1)*(s - 2)^2) fixed points: 0.0000, 0.6800, 1.5677, 3.7523 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #33 ------------------------------------------------------------------------ names: 'L(6,18)', 'M5' id: 33 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (1, 1) cocentral dim: 5 rank: 6 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/3 complex roots: 0.0000 (zeta-1)@infinity: 4 zeta: s^2/((s - 1)*(s - 3)) fixed points: 0.0000, 0.6972, 4.3028 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 3.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #34 ------------------------------------------------------------------------ names: 'L(6,19;0)', 'g(6,7)' id: 34 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 4 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 2.1667, 2.2857, 2.3333, 2.5000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/48*(45927*s^5 - 413991*s^4 + 1480593*s^3 - 2628249*s^2 + 2318984*s - 815360)/((7*s - 16)*(6*s - 13)*(3*s - 5)*(3*s - 7)^2*(2*s - 5)*(s - 1)*(s - 2)^3*s) complex roots: 1.4011 - 0.2584*i, 1.4011 + 0.2584*i, 1.7925, 2.1504, 2.2689 ess. value@infinity: 27/64 Topological ideal zeta function: poles: 0.0000, 0.7500, 1.0000, 1.2000, 1.3333, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/210*(455*s^3 - 1144*s^2 + 942*s - 252)/((5*s - 6)*(4*s - 3)*(3*s - 4)*(s - 1)^4*(s - 2)*s) complex roots: 0.6061, 0.9541 - 0.0589*i, 0.9541 + 0.0589*i ess. value@infinity: 13/360 Topological representation zeta function: degree: 0 ess. value@zero: 1/2 complex roots: 0.0000 (zeta-1)@infinity: 3 zeta: s^2/((s - 1)*(s - 2)) fixed points: 0.0000, 0.5858, 3.4142 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #35 ------------------------------------------------------------------------ names: 'L(6,19;1)', 'n(4,ZZ)' id: 35 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.5000, 0.7143, 1.0000, 1.2000, 1.3333, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 2/3*(7*s - 3)/((7*s - 5)*(5*s - 6)*(3*s - 4)*(2*s - 1)*(s - 1)*(s - 2)*s) complex roots: 0.4286 ess. value@infinity: 1/45 Topological representation zeta function: degree: 0 ess. value@zero: 1 complex roots: 0.0000 (zeta-1)@infinity: 5/2 zeta: 2*s^2/((2*s - 1)*(s - 2)) fixed points: 0.0000, 0.3139, 3.1861 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #36 ------------------------------------------------------------------------ names: 'L(6,20)' id: 36 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 2.0556, 2.1000, 2.1250, 2.1429, 2.1500, 2.1818, 2.2000, 2.2222, 2.2500, 2.5000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/144*(124640208000*s^10 - 2450257567200*s^9 + 21632784382760*s^8 - 112945139244690*s^7 + 386146453844181*s^6 - 903233150980483*s^5 + 1463738811463999*s^4 - 1622577592730987*s^3 + 1177352866364580*s^2 - 504902635502400*s + 97166672064000)/((20*s - 43)*(18*s - 37)*(11*s - 24)*(10*s - 21)*(9*s - 20)*(8*s - 17)*(7*s - 15)*(5*s - 11)*(4*s - 9)*(3*s - 5)*(2*s - 5)*(s - 1)*(s - 2)^3*s) complex roots: 1.4566, 1.5113, 1.7940, 2.0542, 2.0981 - 0.0165*i, 2.0981 + 0.0165*i, 2.1397, 2.1439, 2.1814 - 0.0093*i, 2.1814 + 0.0093*i ess. value@infinity: 1249/3456 Topological ideal zeta function: poles: 0.0000, 0.6667, 0.7143, 0.8889, 1.0000, 1.2000, 1.3333, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/2*(126*s^2 - 183*s + 64)/((9*s - 8)*(7*s - 5)*(5*s - 6)*(3*s - 2)*(3*s - 4)*(s - 1)*(s - 2)*s) complex roots: 0.5868, 0.8655 ess. value@infinity: 1/45 Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 5/2 zeta: 1/2*(2*s - 1)*s/((s - 1)*(s - 2)) fixed points: 0.0000, 0.7753, 3.2247 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #37 ------------------------------------------------------------------------ names: 'L(6,21;0)' id: 37 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 4 rank: 6 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/4 complex roots: 0.0000 (zeta-1)@infinity: 4 zeta: s^2/(s - 2)^2 fixed points: 0.0000, 1.0000, 4.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #38 ------------------------------------------------------------------------ names: 'L(6,21;1)' id: 38 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 6 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/3 complex roots: 0.0000 (zeta-1)@infinity: 7/2 zeta: 2*s^2/((2*s - 3)*(s - 2)) fixed points: 0.0000, 0.8139, 3.6861 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #39 ------------------------------------------------------------------------ names: 'L(6,22;0)', 'L(3,2)[eps]', 'h(ZZ[X]/X^2)', 'g(6,4)' id: 39 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 6 soluble: True derived dim: 2 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 2.2500, 2.3333, 2.4000, 2.5000, 2.6667, 2.7500, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: (2144*s^5 - 22726*s^4 + 95508*s^3 - 198735*s^2 + 204519*s - 83160)/((5*s - 12)*(4*s - 9)*(4*s - 11)*(3*s - 5)*(3*s - 7)*(3*s - 8)*(2*s - 5)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: 1.4473, 1.9181, 2.3086, 2.3453, 2.5804 ess. value@infinity: 67/135 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.3333, 1.5000, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/15*(8*s - 9)/((3*s - 4)*(2*s - 3)*(s - 1)^2*(s - 2)*(s - 3)*s) complex roots: 1.1250 ess. value@infinity: 4/45 Topological representation zeta function: degree: 0 ess. value@zero: -2/3 complex roots: 0.0000 (zeta-1)@infinity: 3/2 zeta: 2*s/(2*s - 3) fixed points: 0.0000, 2.5000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #40 ------------------------------------------------------------------------ names: 'L(6,22;1)' id: 40 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 6 soluble: True derived dim: 2 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: 1 complex roots: 0.0000 (zeta-1)@infinity: 2 zeta: s^2/(s - 1)^2 fixed points: 0.0000, 0.3820, 2.6180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #41 ------------------------------------------------------------------------ names: 'L(6,22;1) [alternative basis]', 'h(ZZ)^2', 'h(ZZ) (+) h(ZZ)', 'H(2)^2', 'H(2) (+) H(2)' id: 41 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 6 soluble: True derived dim: 2 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 2.3333, 2.5000, 2.6667, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/4*(243*s^4 - 1819*s^3 + 5041*s^2 - 6145*s + 2800)/((3*s - 5)*(3*s - 7)*(3*s - 8)*(2*s - 5)^2*(s - 1)*(s - 2)^2*(s - 3)*s) complex roots: 1.4398 - 0.3098*i, 1.4398 + 0.3098*i, 2.3030 - 0.0929*i, 2.3030 + 0.0929*i ess. value@infinity: 9/16 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/5*(5*s - 4)/((3*s - 4)^2*(s - 1)^2*(s - 2)*(s - 3)*s) complex roots: 0.8000 ess. value@infinity: 1/9 ------------------------------------------------------------------------ ALGEBRA #42 ------------------------------------------------------------------------ names: 'L(6,23)' id: 42 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 4 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 2.1667, 2.2500, 2.3333, 2.4000, 2.4444, 2.5000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/12*(1073952*s^8 - 18184536*s^7 + 134166390*s^6 - 563193911*s^5 + 1470653304*s^4 - 2445276177*s^3 + 2527052978*s^2 - 1483294080*s + 378378000)/((9*s - 22)*(6*s - 13)*(5*s - 12)*(4*s - 9)*(3*s - 5)*(3*s - 7)^2*(2*s - 5)^3*(s - 1)*(s - 2)^2*s) complex roots: 1.3595, 1.7268, 2.1590 - 0.0584*i, 2.1590 + 0.0584*i, 2.3116, 2.3778 - 0.0436*i, 2.3778 + 0.0436*i, 2.4609 ess. value@infinity: 1243/3240 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.1429, 1.2000, 1.2222, 1.3333, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/30*(63*s^2 - 130*s + 66)*(15*s - 16)/((9*s - 11)*(7*s - 8)*(5*s - 6)*(3*s - 4)*(s - 1)^3*(s - 2)*s) complex roots: 0.9018, 1.0667, 1.1617 ess. value@infinity: 1/30 Topological representation zeta function: degree: 0 ess. value@zero: -3/8 complex roots: 0.0000, 1.5000 (zeta-1)@infinity: 5/2 zeta: 1/2*(2*s - 3)*s/(s - 2)^2 fixed points: 0.0000, 1.6340, 3.3660 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #43 ------------------------------------------------------------------------ names: 'L(6,24;0)', 'g(6,9)' id: 43 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 4 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 2.1667, 2.2000, 2.2222, 2.2500, 2.2857, 2.3333 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/6*(7060608*s^9 - 127146024*s^8 + 1015050156*s^7 - 4714488399*s^6 + 14037015009*s^5 - 27779768957*s^4 + 36535455587*s^3 - 30785573604*s^2 + 15077423544*s - 3269185920)/((9*s - 20)*(7*s - 16)*(6*s - 13)*(5*s - 11)*(4*s - 9)^3*(3*s - 5)*(3*s - 7)^2*(s - 1)*(s - 2)^3*s) complex roots: 1.3575, 1.7736 - 0.0471*i, 1.7736 + 0.0471*i, 2.1026, 2.1652, 2.1655 - 0.0591*i, 2.1655 + 0.0591*i, 2.2276, 2.2768 ess. value@infinity: 227/630 Topological ideal zeta function: poles: 0.0000, 0.8750, 1.0000, 1.0714, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/60*(168*s^2 - 268*s + 105)/((14*s - 15)*(8*s - 7)*(s - 1)^4*(s - 2)*s) complex roots: 0.6918, 0.9034 ess. value@infinity: 1/40 Topological representation zeta function: degree: 0 ess. value@zero: -1/9 complex roots: 0.0000, 0.1910, 1.3090 (zeta-1)@infinity: 5/2 zeta: (4*s^2 - 6*s + 1)*s/((2*s - 3)^2*(s - 1)) fixed points: 0.0000, 0.6192, 1.3183, 3.0624 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #44 ------------------------------------------------------------------------ names: 'L(6,24;1)' id: 44 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 4 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/3 complex roots: -0.5000, 0.0000 (zeta-1)@infinity: 3 zeta: (2*s + 1)*s/((2*s - 3)*(s - 1)) fixed points: 0.0000, 0.3139, 3.1861 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #45 ------------------------------------------------------------------------ names: 'L(6,25)', 'L_W' id: 45 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (1, 1) cocentral dim: 4 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.3333, 2.4000, 2.5000, 2.6667 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/2*(318*s^4 - 2654*s^3 + 8219*s^2 - 11168*s + 5600)/((5*s - 12)*(3*s - 7)*(3*s - 8)*(2*s - 5)^3*(s - 1)*(s - 2)^2*s) complex roots: 1.4580, 2.2334 - 0.0251*i, 2.2334 + 0.0251*i, 2.4211 ess. value@infinity: 53/120 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 1.2222, 1.3333, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/120*(585*s^2 - 1130*s + 528)/((9*s - 11)*(5*s - 6)*(3*s - 4)*(s - 1)^3*(s - 2)*s) complex roots: 0.7919, 1.1397 ess. value@infinity: 13/360 Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 3 zeta: (s - 1)*s/(s - 2)^2 fixed points: 0.0000, 1.3820, 3.6180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #46 ------------------------------------------------------------------------ names: 'L(6,26)', 'F(2,3)' id: 46 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (1, 0) cocentral dim: 3 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: True description: Free nilpotent Lie ring of class 2 on 3 generators Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.3333, 2.5000, 2.6667, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/3*(25*s^2 - 94*s + 84)/((3*s - 7)*(3*s - 8)*(2*s - 5)*(s - 1)*(s - 2)^2*(s - 3)*s) complex roots: 1.4624, 2.2976 ess. value@infinity: 25/54 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.5000, 1.6000, 1.6667, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 2/((5*s - 8)*(3*s - 5)*(2*s - 3)*(s - 1)*(s - 2)*s) complex roots: None ess. value@infinity: 1/15 Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000 (zeta-1)@infinity: 3 zeta: s/(s - 3) fixed points: 0.0000, 4.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #47 ------------------------------------------------------------------------ names: 'L(7,1)', '(ZZ^7,0)', 'C(7,1)', 'L(6,1) (+) (ZZ,0)' id: 47 Lie: True commutative: True nilpotency class: 1 nilpotent: True (u,v): (0, 0) cocentral dim: 0 rank: 7 soluble: True derived dim: 0 derived length: 1 associative: True description: ZZ^7 with zero multiplication Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 4.0000, 5.0000, 6.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/((s - 1)*(s - 2)*(s - 3)*(s - 4)*(s - 5)*(s - 6)*s) complex roots: None ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 4.0000, 5.0000, 6.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/((s - 1)*(s - 2)*(s - 3)*(s - 4)*(s - 5)*(s - 6)*s) complex roots: None ess. value@infinity: 1 ------------------------------------------------------------------------ ALGEBRA #48 ------------------------------------------------------------------------ names: 'L(7,2)', 'L(6,2) (+) (ZZ,0)', 'h(ZZ) (+) (ZZ^4,0)' id: 48 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (1, 0) cocentral dim: 2 rank: 7 soluble: True derived dim: 1 derived length: 2 associative: True description: Direct sum of the Heisenberg Lie ring and (ZZ^4,0) Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 3.5000, 4.0000, 5.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/2*(3*s - 7)/((2*s - 7)*(s - 1)*(s - 2)*(s - 3)^2*(s - 4)*(s - 5)*s) complex roots: 2.3333 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 4.0000, 5.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/3/((s - 1)*(s - 2)^2*(s - 3)*(s - 4)*(s - 5)*s) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #49 ------------------------------------------------------------------------ names: 'L(7,3)', 'L(6,3) (+) (ZZ,0)', 'M3 (+) (ZZ^3,0)' id: 49 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (1, 1) cocentral dim: 3 rank: 7 soluble: True derived dim: 2 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.6667, 3.0000, 3.3333, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/8*(39*s^2 - 175*s + 192)/((3*s - 8)*(3*s - 10)*(s - 1)*(s - 2)*(s - 3)^3*(s - 4)*s) complex roots: 1.9110, 2.5762 ess. value@infinity: 13/24 Topological ideal zeta function: poles: 0.0000, 1.2000, 1.2500, 1.6667, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 5/((5*s - 6)*(4*s - 5)*(3*s - 5)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: None ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #50 ------------------------------------------------------------------------ names: 'L(7,4)', 'L(6,4) (+) (ZZ,0)', 'h(ZZ) curlyvee h(ZZ) (+) (ZZ^2,0)' id: 50 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 7 soluble: True derived dim: 1 derived length: 2 associative: True description: Direct sum of (ZZ^2,0) and the central product of two Heisenberg Lie rings Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.6667, 3.0000, 4.0000, 5.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/9*(17*s^2 - 71*s + 72)/((3*s - 8)*(s - 1)*(s - 2)^2*(s - 3)^2*(s - 4)*(s - 5)*s) complex roots: 1.7341, 2.4424 ess. value@infinity: 17/27 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 2.0000, 3.0000, 4.0000, 5.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/((5*s - 6)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*(s - 5)*s) complex roots: None ess. value@infinity: 1/5 ------------------------------------------------------------------------ ALGEBRA #51 ------------------------------------------------------------------------ names: 'L(7,5)', 'L(6,5) (+) (ZZ,0)', 'Q5 (+) (ZZ^2,0)' id: 51 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 4 rank: 7 soluble: True derived dim: 2 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6667, 2.7500, 3.0000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/180*(1530*s^5 - 18842*s^4 + 92105*s^3 - 223131*s^2 + 267498*s - 126720)*(4*s - 9)/((4*s - 11)*(3*s - 8)^2*(2*s - 5)*(s - 1)*(s - 2)^2*(s - 3)^4*(s - 4)*s) complex roots: 1.6639, 2.2500, 2.3339, 2.7679 - 0.0813*i, 2.7679 + 0.0813*i, 2.7814 ess. value@infinity: 17/36 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 1.6667, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/((5*s - 6)*(3*s - 5)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: None ess. value@infinity: 1/15 ------------------------------------------------------------------------ ALGEBRA #52 ------------------------------------------------------------------------ names: 'L(7,6)', 'L(6,6) (+) (ZZ,0)', 'Fil4 (+) (ZZ^2,0)' id: 52 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 4 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.8000, 0.8571, 0.9167, 1.0000, 1.1111, 1.1250, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/10*(15120*s^4 - 52599*s^3 + 67714*s^2 - 38156*s + 7920)/((12*s - 11)*(9*s - 10)*(8*s - 9)*(7*s - 6)*(5*s - 4)*(3*s - 4)*(s - 1)^2*(s - 2)*(s - 3)*s) complex roots: 0.6026, 0.8388, 0.9815, 1.0559 ess. value@infinity: 1/60 ------------------------------------------------------------------------ ALGEBRA #53 ------------------------------------------------------------------------ names: 'L(7,7)', 'L(6,7) (+) (ZZ,0)', 'M4 (+) (ZZ^2,0)' id: 53 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (1, 1) cocentral dim: 4 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.2500, 2.3333, 2.5000, 2.5714, 3.0000, 3.3333 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/20*(4140*s^5 - 47896*s^4 + 220249*s^3 - 502784*s^2 + 569121*s - 255150)/((7*s - 18)*(4*s - 9)*(3*s - 7)*(3*s - 10)*(2*s - 5)*(s - 1)*(s - 2)*(s - 3)^4*s) complex roots: 1.6093, 2.3382 - 0.1619*i, 2.3382 + 0.1619*i, 2.5572, 2.7262 ess. value@infinity: 23/56 Topological ideal zeta function: poles: 0.0000, 0.8000, 0.8571, 0.9091, 0.9167, 1.0000, 1.1111, 1.1250, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 2*(1386*s^3 - 3539*s^2 + 2942*s - 792)*(6*s - 5)/((12*s - 11)*(11*s - 10)*(9*s - 10)*(8*s - 9)*(7*s - 6)*(5*s - 4)*(3*s - 4)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: 0.6080, 0.8333, 0.8936, 1.0519 ess. value@infinity: 1/60 ------------------------------------------------------------------------ ALGEBRA #54 ------------------------------------------------------------------------ names: 'L(7,8)', 'L(6,8) (+) (ZZ,0)', 'G3 (+) (ZZ^2,0)' id: 54 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (1, 0) cocentral dim: 3 rank: 7 soluble: True derived dim: 2 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 3.0000, 3.3333, 3.5000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 7/2/((3*s - 10)*(2*s - 7)*(s - 1)*(s - 3)^2*(s - 4)*s) complex roots: None ess. value@infinity: 7/12 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 2/15/((s - 1)*(s - 2)^3*(s - 3)*(s - 4)*s) complex roots: None ess. value@infinity: 2/15 ------------------------------------------------------------------------ ALGEBRA #55 ------------------------------------------------------------------------ names: 'L(7,9)', 'L(6,9) (+) (ZZ,0)', 'F(3,2) (+) (ZZ^2,0)' id: 55 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (1, 1) cocentral dim: 3 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6667, 2.8000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/30*(363*s^4 - 3517*s^3 + 12590*s^2 - 19696*s + 11340)/((5*s - 14)*(3*s - 8)*(2*s - 5)*(s - 1)*(s - 2)*(s - 3)^5*s) complex roots: 1.6802, 2.2121, 2.8982 - 0.0744*i, 2.8982 + 0.0744*i ess. value@infinity: 121/300 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 1.2500, 1.3333, 1.4286, 1.6000, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 2*(35*s^2 - 76*s + 40)/((7*s - 10)*(5*s - 6)*(5*s - 8)*(4*s - 5)*(3*s - 4)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: 0.8962, 1.2752 ess. value@infinity: 1/30 ------------------------------------------------------------------------ ALGEBRA #56 ------------------------------------------------------------------------ names: 'L(7,10)', 'L(6,10) (+) (ZZ,0)' id: 56 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 2 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.2500, 2.3333, 2.5000, 2.5714, 2.7500, 2.8000, 3.0000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/12*(111020*s^8 - 2017301*s^7 + 15998618*s^6 - 72326536*s^5 + 203850500*s^4 - 366777333*s^3 + 411384618*s^2 - 262971954*s + 73347120)/((7*s - 18)*(5*s - 14)*(4*s - 9)*(4*s - 11)*(3*s - 7)^2*(2*s - 5)^2*(s - 1)*(s - 2)^2*(s - 3)^2*(s - 4)*s) complex roots: 1.8288 - 0.0549*i, 1.8288 + 0.0549*i, 2.1945 - 0.0859*i, 2.1945 + 0.0859*i, 2.4213 - 0.0067*i, 2.4213 + 0.0067*i, 2.6407 - 0.0783*i, 2.6407 + 0.0783*i ess. value@infinity: 793/1728 Topological ideal zeta function: poles: 0.0000, 0.8333, 0.8571, 1.0000, 1.6667, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: (7*s - 5)/((7*s - 6)*(6*s - 5)*(3*s - 5)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: 0.7143 ess. value@infinity: 1/18 ------------------------------------------------------------------------ ALGEBRA #57 ------------------------------------------------------------------------ names: 'L(7,22;0)', 'L(6,22;0) (+) (ZZ,0)' id: 57 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 7 soluble: True derived dim: 2 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.6667, 2.7500, 3.0000, 3.2500, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/45*(1072*s^4 - 10127*s^3 + 35461*s^2 - 54459*s + 30888)/((4*s - 11)*(4*s - 13)*(3*s - 8)*(s - 1)*(s - 2)^2*(s - 3)^3*(s - 4)*s) complex roots: 1.6842, 2.2641, 2.7027, 2.7958 ess. value@infinity: 67/135 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 1.6667, 1.8333, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: (8*s - 11)/((6*s - 11)*(5*s - 6)*(3*s - 5)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: 1.3750 ess. value@infinity: 4/45 ------------------------------------------------------------------------ ALGEBRA #58 ------------------------------------------------------------------------ names: 'L(7,23)', 'L(6,23) (+) (ZZ,0)' id: 58 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 4 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6667, 2.7500, 2.8333, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/4320*(715968*s^8 - 14509008*s^7 + 128070788*s^6 - 642918600*s^5 + 2006747659*s^4 - 3986143783*s^3 + 4918094196*s^2 - 3443712260*s + 1046960640)/((6*s - 17)*(4*s - 11)*(3*s - 8)^2*(2*s - 5)*(s - 1)*(s - 2)^2*(s - 3)^6*s) complex roots: 1.5728, 2.0871, 2.4951, 2.6928 - 0.0445*i, 2.6928 + 0.0445*i, 2.9081 - 0.0860*i, 2.9081 + 0.0860*i, 2.9082 ess. value@infinity: 1243/3240 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 1.4286, 1.5556, 1.6000, 1.6667, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 5/2*(63*s^2 - 169*s + 112)/((9*s - 14)*(7*s - 10)*(5*s - 6)*(5*s - 8)*(3*s - 5)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: 1.1956, 1.4870 ess. value@infinity: 1/30 ------------------------------------------------------------------------ ALGEBRA #59 ------------------------------------------------------------------------ names: 'L(7,24;0)', 'L(6,24;0) (+) (ZZ,0)' id: 59 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 4 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6667, 2.7143, 2.7500, 2.7778, 2.8000, 2.8333, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/9*(35303040*s^9 - 780720552*s^8 + 7650294828*s^7 - 43587972890*s^6 + 159094465631*s^5 - 385674173909*s^4 + 620769083108*s^3 - 639494815616*s^2 + 382443949880*s - 101115537600)/((9*s - 25)*(7*s - 19)*(6*s - 17)*(5*s - 14)^2*(4*s - 11)^3*(3*s - 8)^2*(2*s - 5)*(s - 1)*(s - 2)^2*(s - 3)*s) complex roots: 1.5589, 2.1068, 2.2615, 2.6089, 2.6424 - 0.1174*i, 2.6424 + 0.1174*i, 2.7306, 2.7686, 2.7947 ess. value@infinity: 227/630 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.1250, 1.2000, 1.2500, 1.3333, 1.3571, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 2*(252*s^3 - 845*s^2 + 936*s - 342)/((14*s - 19)*(8*s - 9)*(5*s - 6)*(4*s - 5)*(3*s - 4)^2*(s - 1)*(s - 2)*(s - 3)*s) complex roots: 0.9136, 1.1709, 1.2686 ess. value@infinity: 1/40 ------------------------------------------------------------------------ ALGEBRA #60 ------------------------------------------------------------------------ names: 'L(7,25)', 'L(6,25) (+) (ZZ,0)' id: 60 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (1, 1) cocentral dim: 4 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6667, 3.0000, 3.3333 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/80*(636*s^4 - 6258*s^3 + 22847*s^2 - 36585*s + 21600)/((3*s - 8)*(3*s - 10)*(2*s - 5)*(s - 1)*(s - 2)*(s - 3)^5*s) complex roots: 1.6996, 2.6500 - 0.1166*i, 2.6500 + 0.1166*i, 2.8401 ess. value@infinity: 53/120 Topological ideal zeta function: poles: 0.0000, 1.2000, 1.2500, 1.3333, 1.5556, 1.6000, 1.6667, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/2*(585*s^2 - 1622*s + 1120)/((9*s - 14)*(5*s - 6)*(5*s - 8)*(4*s - 5)*(3*s - 4)*(3*s - 5)*(s - 2)*(s - 3)*s) complex roots: 1.3005, 1.4722 ess. value@infinity: 13/360 ------------------------------------------------------------------------ ALGEBRA #61 ------------------------------------------------------------------------ names: 'L(7,26)', 'L(6,26) (+) (ZZ,0)', 'F(2,3) (+) (ZZ,0)' id: 61 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (1, 0) cocentral dim: 3 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.6667, 3.0000, 3.3333, 3.5000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/3*(25*s^2 - 116*s + 126)/((3*s - 8)*(3*s - 10)*(2*s - 7)*(s - 1)*(s - 2)*(s - 3)^3*s) complex roots: 1.7349, 2.9051 ess. value@infinity: 25/54 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/15/((s - 1)*(s - 2)^4*(s - 3)*s) complex roots: None ess. value@infinity: 1/15 ------------------------------------------------------------------------ ALGEBRA #62 ------------------------------------------------------------------------ names: 'g(37A)' id: 62 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (1, 0) cocentral dim: 4 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: True Topological ideal zeta function: poles: 0.0000, 1.0000, 1.7143, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 2/5/((7*s - 12)*(s - 1)*(s - 2)^3*(s - 3)*s) complex roots: None ess. value@infinity: 2/35 Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000 (zeta-1)@infinity: 3 zeta: s/(s - 3) fixed points: 0.0000, 4.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #63 ------------------------------------------------------------------------ names: 'g(37B)', 'T4' id: 63 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6667, 2.8000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/144*(11700*s^7 - 193524*s^6 + 1365106*s^5 - 5323213*s^4 + 12394047*s^3 - 17233680*s^2 + 13256364*s - 4354560)/((5*s - 14)*(3*s - 8)^2*(2*s - 5)^2*(s - 1)*(s - 2)^2*(s - 3)^5*s) complex roots: 1.7218 - 0.3205*i, 1.7218 + 0.3205*i, 2.2418, 2.5565, 2.7576 - 0.0455*i, 2.7576 + 0.0455*i, 2.7834 ess. value@infinity: 65/144 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 1.6000, 1.6667, 1.7143, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: (255*s^3 - 1031*s^2 + 1373*s - 600)/((7*s - 12)*(5*s - 6)*(5*s - 8)*(3*s - 5)^3*(s - 1)*(s - 2)*(s - 3)*s) complex roots: 1.0468, 1.4982 - 0.0569*i, 1.4982 + 0.0569*i ess. value@infinity: 17/315 Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 3 zeta: (s - 1)*s/(s - 2)^2 fixed points: 0.0000, 1.3820, 3.6180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #64 ------------------------------------------------------------------------ names: 'g(37C)' id: 64 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6667, 2.7500, 2.8333, 3.0000, 3.2500 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/180*(41532*s^6 - 609721*s^5 + 3703235*s^4 - 11901991*s^3 + 21330141*s^2 - 20190156*s + 7876440)/((6*s - 17)*(4*s - 11)*(4*s - 13)*(3*s - 8)*(2*s - 5)*(s - 1)*(s - 2)^2*(s - 3)^4*s) complex roots: 1.5920, 2.1008, 2.5483, 2.7221, 2.8587 - 0.0432*i, 2.8587 + 0.0432*i ess. value@infinity: 3461/8640 Topological representation zeta function: degree: 0 ess. value@zero: -2/5 complex roots: 0.0000 (zeta-1)@infinity: 5/2 zeta: 2*s/(2*s - 5) fixed points: 0.0000, 3.5000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #65 ------------------------------------------------------------------------ names: 'g(37D)' id: 65 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 5/2 zeta: 2*(s - 1)*s/((2*s - 3)*(s - 2)) fixed points: 0.0000, 1.2192, 3.2808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #66 ------------------------------------------------------------------------ names: 'g(357A)' id: 66 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 4 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/6 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 4 zeta: (s - 1)*s/((s - 2)*(s - 3)) fixed points: 0.0000, 1.5858, 4.4142 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #67 ------------------------------------------------------------------------ names: 'g(357B)' id: 67 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 4 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/8 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 4 zeta: (s - 1)^2*s/(s - 2)^3 fixed points: 0.0000, 1.4261 - 0.3690*i, 1.4261 + 0.3690*i, 4.1479 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #68 ------------------------------------------------------------------------ names: 'g(357C)' id: 68 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 4 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -3/16 complex roots: 0.0000, 1.0000, 1.5000 (zeta-1)@infinity: 7/2 zeta: 1/2*(2*s - 3)*(s - 1)*s/(s - 2)^3 fixed points: 0.0000, 1.5410 - 0.2236*i, 1.5410 + 0.2236*i, 3.9180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #69 ------------------------------------------------------------------------ names: 'g(27A)' id: 69 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 7 soluble: True derived dim: 2 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6667, 2.7500, 3.0000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/36*(839*s^4 - 7830*s^3 + 27217*s^2 - 41718*s + 23760)/((4*s - 11)*(3*s - 8)*(2*s - 5)^2*(s - 1)*(s - 2)*(s - 3)^3*(s - 4)*s) complex roots: 1.7787, 2.3617, 2.5961 - 0.0444*i, 2.5961 + 0.0444*i ess. value@infinity: 839/1728 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 1.4286, 1.6667, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 2*(4*s - 5)/((7*s - 10)*(5*s - 6)*(3*s - 5)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: 1.2500 ess. value@infinity: 8/105 Topological representation zeta function: degree: 0 ess. value@zero: -1/2 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 3/2 zeta: 1/2*(2*s - 1)*s/(s - 1)^2 fixed points: 0.0000, 0.6340, 2.3660 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #70 ------------------------------------------------------------------------ names: 'g(27B)' id: 70 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 7 soluble: True derived dim: 2 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6667, 2.7143, 2.8000, 3.0000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/9*(793*s^4 - 7182*s^3 + 24093*s^2 - 35398*s + 19152)/((7*s - 19)*(5*s - 14)*(3*s - 8)*(2*s - 5)*(s - 1)*(s - 2)^2*(s - 3)^2*(s - 4)*s) complex roots: 1.5513, 2.3793 - 0.0815*i, 2.3793 + 0.0815*i, 2.7468 ess. value@infinity: 793/1890 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 1.4286, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 2/((7*s - 10)*(5*s - 6)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: None ess. value@infinity: 2/35 Topological representation zeta function: degree: 0 ess. value@zero: -1 complex roots: 0.0000 (zeta-1)@infinity: 1 zeta: s/(s - 1) fixed points: 0.0000, 2.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #71 ------------------------------------------------------------------------ names: 'g(257A)' id: 71 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6667, 2.7143, 2.7500, 2.8000, 2.8571, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/36*(16879275*s^8 - 335882855*s^7 + 2915881445*s^6 - 14419964396*s^5 + 44417109503*s^4 - 87230055182*s^3 + 106615575230*s^2 - 74108459340*s + 22415500800)/((7*s - 19)^2*(7*s - 20)*(5*s - 14)^2*(4*s - 11)*(3*s - 8)^2*(2*s - 5)^2*(s - 1)*(s - 2)*(s - 3)^2*s) complex roots: 1.6152, 2.2920, 2.5518, 2.6139, 2.6745 - 0.1313*i, 2.6745 + 0.1313*i, 2.7386 - 0.0197*i, 2.7386 + 0.0197*i ess. value@infinity: 1531/4032 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2857, 1.6000, 1.6667, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 3/((7*s - 9)*(5*s - 8)*(3*s - 5)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 1/35 Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 5/2 zeta: 2*(s - 1)*s/((2*s - 3)*(s - 2)) fixed points: 0.0000, 1.2192, 3.2808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #72 ------------------------------------------------------------------------ names: 'g(257B)' id: 72 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6000, 2.6667, 2.7143, 2.7500, 2.8000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/288*(9066960000*s^11 - 248494313760*s^10 + 3090910452008*s^9 - 23030782078062*s^8 + 114208844521753*s^7 - 395733704421642*s^6 + 977554548042132*s^5 - 1721295328640052*s^4 + 2116927954575871*s^3 - 1731521948910612*s^2 + 847571544397964*s - 188051108044800)/((7*s - 19)^2*(5*s - 13)*(5*s - 14)^2*(4*s - 11)^3*(3*s - 8)^3*(2*s - 5)^3*(s - 1)*(s - 2)*(s - 3)*s) complex roots: 1.6142, 2.2785 - 0.1938*i, 2.2785 + 0.1938*i, 2.5333, 2.5499, 2.6169, 2.6651 - 0.0309*i, 2.6651 + 0.0309*i, 2.7321, 2.7366 - 0.0342*i, 2.7366 + 0.0342*i ess. value@infinity: 1285/3456 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 1.2500, 1.2857, 1.3333, 1.5000, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/36*(2976*s^4 - 13674*s^3 + 23344*s^2 - 17515*s + 4860)/((7*s - 9)*(5*s - 6)*(4*s - 5)^2*(3*s - 4)*(2*s - 3)*(s - 1)^2*(s - 2)*(s - 3)*s) complex roots: 0.8213, 1.2279 - 0.0363*i, 1.2279 + 0.0363*i, 1.3177 ess. value@infinity: 31/1260 Topological representation zeta function: degree: 0 ess. value@zero: -1/9 complex roots: 0.0000, 0.1910, 1.3090 (zeta-1)@infinity: 5/2 zeta: (4*s^2 - 6*s + 1)*s/((2*s - 3)^2*(s - 1)) fixed points: 0.0000, 0.6192, 1.3183, 3.0624 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #73 ------------------------------------------------------------------------ names: 'g(257C)' id: 73 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6250, 2.6667, 2.7143, 2.7500, 2.8000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/72*(6562080*s^8 - 127086360*s^7 + 1073900260*s^6 - 5170500064*s^5 + 15510346136*s^4 - 29676516593*s^3 + 35356447047*s^2 - 23972124906*s + 7078579200)/((8*s - 21)*(7*s - 19)*(5*s - 14)*(4*s - 11)*(3*s - 8)^3*(2*s - 5)^3*(s - 1)*(s - 2)*(s - 3)^2*s) complex roots: 1.6270, 2.2865 - 0.1316*i, 2.2865 + 0.1316*i, 2.5340, 2.5808, 2.6259, 2.6979, 2.7282 ess. value@infinity: 217/576 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2857, 1.6000, 1.6667, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 3/((7*s - 9)*(5*s - 8)*(3*s - 5)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 1/35 Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 5/2 zeta: 2*(s - 1)*s/((2*s - 3)*(s - 2)) fixed points: 0.0000, 1.2192, 3.2808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #74 ------------------------------------------------------------------------ names: 'g(257D)' id: 74 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -4/9 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 2 zeta: 4*(s - 1)*s/(2*s - 3)^2 fixed points: 0.0000, 1.1340, 2.8660 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #75 ------------------------------------------------------------------------ names: 'g(257E)' id: 75 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 5/2 zeta: 1/2*(2*s - 1)*s/((s - 1)*(s - 2)) fixed points: 0.0000, 0.7753, 3.2247 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #76 ------------------------------------------------------------------------ names: 'g(257F)' id: 76 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 5/2 zeta: 2*(s - 1)*s/((2*s - 3)*(s - 2)) fixed points: 0.0000, 1.2192, 3.2808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #77 ------------------------------------------------------------------------ names: 'g(257G)' id: 77 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -3/8 complex roots: 0.0000, 0.6162, 1.2171 (zeta-1)@infinity: 2 zeta: 1/2*(12*s^2 - 22*s + 9)*s/((3*s - 4)*(2*s - 3)*(s - 1)) fixed points: 0.0000, 0.7977, 1.2278, 2.8078 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.3333, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #78 ------------------------------------------------------------------------ names: 'g(257H)' id: 78 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 0.2500 - 0.4330*i, 0.2500 + 0.4330*i (zeta-1)@infinity: 5/2 zeta: 1/4*(4*s^2 - 2*s + 1)*s/(s - 1)^3 fixed points: 0.0000, 0.5198 - 0.3899*i, 0.5198 + 0.3899*i, 2.9603 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #79 ------------------------------------------------------------------------ names: 'g(257I)' id: 79 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 2/3 complex roots: 0.0000 (zeta-1)@infinity: 5/2 zeta: 2*s^2/((2*s - 3)*(s - 1)) fixed points: 0.0000, 0.5000, 3.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #80 ------------------------------------------------------------------------ names: 'g(257J)' id: 80 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 2 zeta: (2*s - 1)*s/((2*s - 3)*(s - 1)) fixed points: 0.0000, 0.7192, 2.7808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #81 ------------------------------------------------------------------------ names: 'g(257K)' id: 81 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.8333, 0.8571, 1.0000, 1.1111, 1.1429, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/10*(1575*s^3 - 3762*s^2 + 3000*s - 800)/((9*s - 10)*(7*s - 6)*(7*s - 8)*(6*s - 5)*(3*s - 4)*(s - 1)^2*(s - 2)*(s - 3)*s) complex roots: 0.7546 - 0.0905*i, 0.7546 + 0.0905*i, 0.8793 ess. value@infinity: 5/252 Topological representation zeta function: degree: 0 ess. value@zero: 1/2 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 5/2 zeta: 1/2*(2*s - 1)*s^2/(s - 1)^3 fixed points: 0.0000, 0.5410 - 0.2236*i, 0.5410 + 0.2236*i, 2.9180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #82 ------------------------------------------------------------------------ names: 'g(257L)' id: 82 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 2 zeta: 1/4*(2*s - 1)^2*s/(s - 1)^3 fixed points: 0.0000, 0.6587 - 0.1791*i, 0.6587 + 0.1791*i, 2.6826 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #83 ------------------------------------------------------------------------ names: 'g(247A)' id: 83 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (1, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/6 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 4 zeta: (s - 1)*s/((s - 2)*(s - 3)) fixed points: 0.0000, 1.5858, 4.4142 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #84 ------------------------------------------------------------------------ names: 'g(247B)' id: 84 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/4 complex roots: 0.0000 (zeta-1)@infinity: 4 zeta: s^2/(s - 2)^2 fixed points: 0.0000, 1.0000, 4.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #85 ------------------------------------------------------------------------ names: 'g(247C)' id: 85 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -3/16 complex roots: 0.0000, 1.0000, 1.5000 (zeta-1)@infinity: 7/2 zeta: 1/2*(2*s - 3)*(s - 1)*s/(s - 2)^3 fixed points: 0.0000, 1.5410 - 0.2236*i, 1.5410 + 0.2236*i, 3.9180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #86 ------------------------------------------------------------------------ names: 'g(247D)' id: 86 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/8 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 7/2 zeta: 1/2*(2*s - 1)*s/(s - 2)^2 fixed points: 0.0000, 1.1771, 3.8229 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #87 ------------------------------------------------------------------------ names: 'g(247E)' id: 87 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/8 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 7/2 zeta: 1/2*(2*s - 1)*s/(s - 2)^2 fixed points: 0.0000, 1.1771, 3.8229 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #88 ------------------------------------------------------------------------ names: 'g(247F)' id: 88 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/2 complex roots: 0.0000 (zeta-1)@infinity: 4 zeta: s^3/((s - 1)^2*(s - 2)) fixed points: 0.0000, 0.5844 - 0.4248*i, 0.5844 + 0.4248*i, 3.8312 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 3 ------------------------------------------------------------------------ ALGEBRA #89 ------------------------------------------------------------------------ names: 'g(247G)' id: 89 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/8 complex roots: 0.0000, 0.2500 - 0.4330*i, 0.2500 + 0.4330*i (zeta-1)@infinity: 7/2 zeta: 1/4*(4*s^2 - 2*s + 1)*s/((s - 1)^2*(s - 2)) fixed points: 0.0000, 0.6662 - 0.4119*i, 0.6662 + 0.4119*i, 3.6677 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #90 ------------------------------------------------------------------------ names: 'g(247H)' id: 90 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 0.5000 - 0.5000*i, 0.5000 + 0.5000*i (zeta-1)@infinity: 3 zeta: 1/2*(2*s^2 - 2*s + 1)*s/((s - 1)^2*(s - 2)) fixed points: 0.0000, 0.7582 - 0.3779*i, 0.7582 + 0.3779*i, 3.4837 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #91 ------------------------------------------------------------------------ names: 'g(247I)' id: 91 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/3 complex roots: 0.0000 (zeta-1)@infinity: 7/2 zeta: 2*s^2/((2*s - 3)*(s - 2)) fixed points: 0.0000, 0.8139, 3.6861 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #92 ------------------------------------------------------------------------ names: 'g(247J)' id: 92 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/16 complex roots: -0.1667, 0.0000 (zeta-1)@infinity: 7/2 zeta: 1/2*(6*s + 1)*s/((3*s - 4)*(s - 2)) fixed points: 0.0000, 0.6853, 3.6480 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #93 ------------------------------------------------------------------------ names: 'g(247K)' id: 93 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/10 complex roots: 0.0000, 0.2500 (zeta-1)@infinity: 3 zeta: (4*s - 1)*s/((4*s - 5)*(s - 2)) fixed points: 0.0000, 0.7962, 3.4538 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.2500, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #94 ------------------------------------------------------------------------ names: 'g(247L)' id: 94 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/5 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 7/2 zeta: 2*(s - 1)*s/((2*s - 5)*(s - 2)) fixed points: 0.0000, 1.5000, 4.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 2.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #95 ------------------------------------------------------------------------ names: 'g(247M)' id: 95 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/12 complex roots: 0.0000, 0.2929, 1.7071 (zeta-1)@infinity: 7/2 zeta: (2*s^2 - 4*s + 1)*s/((2*s - 3)*(s - 2)^2) fixed points: 0.0000, 1.0000, 1.7192, 3.7808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #96 ------------------------------------------------------------------------ names: 'g(247N)' id: 96 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -2/9 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 7/2 zeta: 2*(s - 1)*s/((2*s - 3)*(s - 3)) fixed points: 0.0000, 1.3139, 4.1861 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #97 ------------------------------------------------------------------------ names: 'g(247O)' id: 97 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -37/144 complex roots: 0.0000, 1.0000, 1.7500 - 0.1443*i, 1.7500 + 0.1443*i (zeta-1)@infinity: 3 zeta: 1/6*(12*s^2 - 42*s + 37)*(s - 1)*s/((2*s - 3)*(s - 2)^3) fixed points: 0.0000, 1.3027, 1.7758 - 0.1496*i, 1.7758 + 0.1496*i, 3.6456 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #98 ------------------------------------------------------------------------ names: 'g(247P)' id: 98 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -2/9 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 7/2 zeta: 2*(s - 1)*s/((2*s - 3)*(s - 3)) fixed points: 0.0000, 1.3139, 4.1861 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #99 ------------------------------------------------------------------------ names: 'g(247Q)' id: 99 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -7/32 complex roots: 0.0000, 0.7257, 1.6076 (zeta-1)@infinity: 3 zeta: 1/2*(6*s^2 - 14*s + 7)*s/((3*s - 4)*(s - 2)^2) fixed points: 0.0000, 1.0993, 1.6496, 3.5844 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #100 ------------------------------------------------------------------------ names: 'g(247R)' id: 100 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -7/32 complex roots: 0.0000, 0.7257, 1.6076 (zeta-1)@infinity: 3 zeta: 1/2*(6*s^2 - 14*s + 7)*s/((3*s - 4)*(s - 2)^2) fixed points: 0.0000, 1.0993, 1.6496, 3.5844 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #101 ------------------------------------------------------------------------ names: 'g(2457A)' id: 101 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (1, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/6 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 4 zeta: (s - 1)*s/((s - 2)*(s - 3)) fixed points: 0.0000, 1.5858, 4.4142 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #102 ------------------------------------------------------------------------ names: 'g(2457B)' id: 102 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/4 complex roots: 0.0000 (zeta-1)@infinity: 4 zeta: s^2/(s - 2)^2 fixed points: 0.0000, 1.0000, 4.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #103 ------------------------------------------------------------------------ names: 'g(2457C)' id: 103 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/5 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 7/2 zeta: 2*(s - 1)*s/((2*s - 5)*(s - 2)) fixed points: 0.0000, 1.5000, 4.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 2.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #104 ------------------------------------------------------------------------ names: 'g(2457D)' id: 104 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -3/16 complex roots: 0.0000, 1.0000, 1.5000 (zeta-1)@infinity: 7/2 zeta: 1/2*(2*s - 3)*(s - 1)*s/(s - 2)^3 fixed points: 0.0000, 1.5410 - 0.2236*i, 1.5410 + 0.2236*i, 3.9180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #105 ------------------------------------------------------------------------ names: 'g(2457E)' id: 105 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/6 complex roots: -0.5000, 0.0000 (zeta-1)@infinity: 4 zeta: (2*s + 1)*s/((2*s - 3)*(s - 2)) fixed points: 0.0000, 0.6492, 3.8508 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #106 ------------------------------------------------------------------------ names: 'g(2457F)' id: 106 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -3/16 complex roots: 0.0000, 1.0000, 1.5000 (zeta-1)@infinity: 7/2 zeta: 1/2*(2*s - 3)*(s - 1)*s/(s - 2)^3 fixed points: 0.0000, 1.5410 - 0.2236*i, 1.5410 + 0.2236*i, 3.9180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #107 ------------------------------------------------------------------------ names: 'g(2457G)' id: 107 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/12 complex roots: 0.0000, 0.2929, 1.7071 (zeta-1)@infinity: 7/2 zeta: (2*s^2 - 4*s + 1)*s/((2*s - 3)*(s - 2)^2) fixed points: 0.0000, 1.0000, 1.7192, 3.7808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #108 ------------------------------------------------------------------------ names: 'g(2457H)' id: 108 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/18 complex roots: 0.0000, 0.1910, 1.3090 (zeta-1)@infinity: 7/2 zeta: (4*s^2 - 6*s + 1)*s/((2*s - 3)^2*(s - 2)) fixed points: 0.0000, 1.0000, 1.2753, 3.7247 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #109 ------------------------------------------------------------------------ names: 'g(2457I)' id: 109 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/18 complex roots: 0.0000, 0.1910, 1.3090 (zeta-1)@infinity: 7/2 zeta: (4*s^2 - 6*s + 1)*s/((2*s - 3)^2*(s - 2)) fixed points: 0.0000, 1.0000, 1.2753, 3.7247 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #110 ------------------------------------------------------------------------ names: 'g(2457J)' id: 110 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 4/45 complex roots: -0.2374, 0.0000, 1.4041 (zeta-1)@infinity: 7/2 zeta: 2*(6*s^2 - 7*s - 2)*s/((3*s - 5)*(2*s - 3)^2) fixed points: 0.0000, 0.6796, 1.4025, 3.5845 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 1.6667 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #111 ------------------------------------------------------------------------ names: 'g(2457K)' id: 111 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -46/315 complex roots: 0.0000, 0.4350, 1.3506, 1.6310 (zeta-1)@infinity: 3 zeta: 2*(24*s^3 - 82*s^2 + 84*s - 23)*s/((4*s - 7)*(3*s - 5)*(2*s - 3)^2) fixed points: 0.0000, 1.0000, 1.3370, 1.6312, 3.4485 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 1.6667, 1.7500 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #112 ------------------------------------------------------------------------ names: 'g(2457L)' id: 112 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 5 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/8 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 5 zeta: (s - 1)*s^2/(s - 2)^3 fixed points: 0.0000, 1.2442 - 0.4745*i, 1.2442 + 0.4745*i, 4.5115 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #113 ------------------------------------------------------------------------ names: 'g(2457M)' id: 113 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 5 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/5 complex roots: 0.0000 (zeta-1)@infinity: 9/2 zeta: 2*s^2/((2*s - 5)*(s - 2)) fixed points: 0.0000, 1.1492, 4.3508 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 2.5000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #114 ------------------------------------------------------------------------ names: 'g(2357A)' id: 114 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/3 complex roots: 0.0000 (zeta-1)@infinity: 7/2 zeta: 2*s^2/((2*s - 3)*(s - 2)) fixed points: 0.0000, 0.8139, 3.6861 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #115 ------------------------------------------------------------------------ names: 'g(2357B)' id: 115 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -37/144 complex roots: 0.0000, 1.0000, 1.7500 - 0.1443*i, 1.7500 + 0.1443*i (zeta-1)@infinity: 3 zeta: 1/6*(12*s^2 - 42*s + 37)*(s - 1)*s/((2*s - 3)*(s - 2)^3) fixed points: 0.0000, 1.3027, 1.7758 - 0.1496*i, 1.7758 + 0.1496*i, 3.6456 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #116 ------------------------------------------------------------------------ names: 'g(2357C)' id: 116 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/32 complex roots: 0.0000, 0.0750, 1.1843, 1.4074 (zeta-1)@infinity: 3 zeta: 1/2*(72*s^3 - 192*s^2 + 134*s - 9)*s/((3*s - 4)^2*(2*s - 3)^2) fixed points: 0.0000, 0.7482, 1.1737, 1.4075, 3.3372 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #117 ------------------------------------------------------------------------ names: 'g(2357D)' id: 117 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 29/96 complex roots: -0.6241, 0.0000, 1.2908 (zeta-1)@infinity: 7/2 zeta: 1/2*(36*s^2 - 24*s - 29)*s/((3*s - 4)^2*(2*s - 3)) fixed points: 0.0000, 0.4169, 1.2906, 3.4592 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #118 ------------------------------------------------------------------------ names: 'g(23457A)' id: 118 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 5 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/6 complex roots: 0.0000 (zeta-1)@infinity: 5 zeta: s^2/((s - 2)*(s - 3)) fixed points: 0.0000, 1.2679, 4.7321 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 3.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #119 ------------------------------------------------------------------------ names: 'g(23457B)' id: 119 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 3) cocentral dim: 5 rank: 7 soluble: True derived dim: 5 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/6 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 9/2 zeta: 2*(s - 1)*s^2/((2*s - 3)*(s - 2)^2) fixed points: 0.0000, 1.1305 - 0.3706*i, 1.1305 + 0.3706*i, 4.2389 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #120 ------------------------------------------------------------------------ names: 'g(23457C)' id: 120 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 3) cocentral dim: 5 rank: 7 soluble: True derived dim: 5 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/6 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 9/2 zeta: 1/2*(2*s - 1)*s^2/((s - 1)^2*(s - 3)) fixed points: 0.0000, 0.7633 - 0.2966*i, 0.7633 + 0.2966*i, 4.4733 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 3.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #121 ------------------------------------------------------------------------ names: 'g(23457D)' id: 121 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 3) cocentral dim: 5 rank: 7 soluble: True derived dim: 5 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/5 complex roots: 0.0000, 0.5355, 1.5656 - 0.1972*i, 1.5656 + 0.1972*i (zeta-1)@infinity: 4 zeta: 1/2*(6*s^3 - 22*s^2 + 25*s - 8)*s^2/((3*s - 5)*(s - 1)^2*(s - 2)^2) fixed points: 0.0000, 0.7540 - 0.2906*i, 0.7540 + 0.2906*i, 1.5901 - 0.1944*i, 1.5901 + 0.1944*i, 3.9785 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.6667, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #122 ------------------------------------------------------------------------ names: 'g(23457E)' id: 122 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 5 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/5 complex roots: 0.0000 (zeta-1)@infinity: 9/2 zeta: 2*s^2/((2*s - 5)*(s - 2)) fixed points: 0.0000, 1.1492, 4.3508 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 2.5000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #123 ------------------------------------------------------------------------ names: 'g(17)' id: 125 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (3, 0) cocentral dim: 6 rank: 7 soluble: True derived dim: 1 derived length: 2 associative: True Topological ideal zeta function: poles: 0.0000, 0.8571, 1.0000, 2.0000, 3.0000, 4.0000, 5.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/((7*s - 6)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*(s - 5)*s) complex roots: None ess. value@infinity: 1/7 Topological representation zeta function: degree: 0 ess. value@zero: -3 complex roots: 0.0000 (zeta-1)@infinity: 1/3 zeta: 3*s/(3*s - 1) fixed points: 0.0000, 1.3333 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.3333 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #124 ------------------------------------------------------------------------ names: 'g(157)' id: 126 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (3, 1) cocentral dim: 6 rank: 7 soluble: True derived dim: 2 derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.8571, 1.0000, 1.6667, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/((7*s - 6)*(3*s - 5)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: None ess. value@infinity: 1/21 Topological representation zeta function: degree: 0 ess. value@zero: -1/2 complex roots: 0.0000, 0.3333 (zeta-1)@infinity: 4/3 zeta: (3*s - 1)*s/((3*s - 2)*(s - 1)) fixed points: 0.0000, 0.4514, 2.2153 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.6667, 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #125 ------------------------------------------------------------------------ names: 'g(147A)' id: 127 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (3, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.8571, 1.0000, 1.6000, 1.6667, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 2/((7*s - 6)*(5*s - 8)*(3*s - 5)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 2/105 Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000, 0.6667 (zeta-1)@infinity: 7/3 zeta: 1/3*(3*s - 2)*s/((s - 1)*(s - 2)) fixed points: 0.0000, 0.8453, 3.1547 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #126 ------------------------------------------------------------------------ names: 'g(147B)' id: 128 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (3, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.8571, 1.0000, 1.6000, 1.6667, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 2/((7*s - 6)*(5*s - 8)*(3*s - 5)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 2/105 Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000, 0.6667 (zeta-1)@infinity: 7/3 zeta: 1/3*(3*s - 2)*s/((s - 1)*(s - 2)) fixed points: 0.0000, 0.8453, 3.1547 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #127 ------------------------------------------------------------------------ names: 'g(147C)' id: 129 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 10/3 zeta: 3*(s - 1)*s/((3*s - 4)*(s - 3)) fixed points: 0.0000, 1.2137, 4.1196 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #128 ------------------------------------------------------------------------ names: 'g(147D)' id: 130 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 10/3 zeta: 3*(s - 1)*s/((3*s - 4)*(s - 3)) fixed points: 0.0000, 1.2137, 4.1196 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #129 ------------------------------------------------------------------------ names: 'g(147E:0)' id: 131 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -2/9 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 7/2 zeta: 2*(s - 1)*s/((2*s - 3)*(s - 3)) fixed points: 0.0000, 1.3139, 4.1861 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #130 ------------------------------------------------------------------------ names: 'g(147E:1)' id: 132 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -2/9 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 7/2 zeta: 2*(s - 1)*s/((2*s - 3)*(s - 3)) fixed points: 0.0000, 1.3139, 4.1861 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #131 ------------------------------------------------------------------------ names: 'g(1457A)' id: 133 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 1) cocentral dim: 6 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/2 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 5/2 zeta: 1/2*(2*s - 1)*s^2/(s - 1)^3 fixed points: 0.0000, 0.5410 - 0.2236*i, 0.5410 + 0.2236*i, 2.9180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #132 ------------------------------------------------------------------------ names: 'g(1457B)' id: 134 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 2/3 complex roots: 0.0000, 0.6667 (zeta-1)@infinity: 7/3 zeta: 1/3*(3*s - 2)*s^2/(s - 1)^3 fixed points: 0.0000, 0.5856 - 0.1028*i, 0.5856 + 0.1028*i, 2.8288 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #133 ------------------------------------------------------------------------ names: 'g(137A)' id: 135 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -2 complex roots: 0.0000 (zeta-1)@infinity: 5/2 zeta: 2*s^3/((2*s - 1)*(s - 1)^2) fixed points: 0.0000, 0.3189 - 0.2702*i, 0.3189 + 0.2702*i, 2.8623 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 1.0000 order@zero: 3 ------------------------------------------------------------------------ ALGEBRA #134 ------------------------------------------------------------------------ names: 'g(137B)' id: 136 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (3, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.5714, 0.6250, 0.6667, 0.8333, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 2/15*(1080*s^4 - 2889*s^3 + 2858*s^2 - 1240*s + 200)/((8*s - 5)*(7*s - 4)*(6*s - 5)*(3*s - 2)*(3*s - 4)^2*(s - 1)^2*(s - 2)*(s - 3)*s) complex roots: 0.5150 - 0.0858*i, 0.5150 + 0.0858*i, 0.8225 - 0.0533*i, 0.8225 + 0.0533*i ess. value@infinity: 1/63 Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 0.1233 - 0.3637*i, 0.1233 + 0.3637*i, 0.7533 (zeta-1)@infinity: 7/3 zeta: (9*s^3 - 9*s^2 + 3*s - 1)*s/((3*s - 2)^2*(s - 1)^2) fixed points: 0.0000, 0.3818 - 0.3403*i, 0.3818 + 0.3403*i, 0.7542, 2.8155 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.6667, 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #135 ------------------------------------------------------------------------ names: 'g(137C)' id: 137 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.5714, 0.6667, 0.6875, 0.8333, 0.9091, 1.0000, 1.3333, 1.5000, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/45*(76032*s^5 - 302247*s^4 + 471582*s^3 - 360697*s^2 + 135100*s - 19800)/((16*s - 11)*(11*s - 10)*(7*s - 4)*(6*s - 5)*(3*s - 2)*(3*s - 4)*(2*s - 3)*(s - 1)^2*(s - 2)*(s - 3)*s) complex roots: 0.4894, 0.6405, 0.8182, 0.9040, 1.1231 ess. value@infinity: 4/315 Topological representation zeta function: degree: 0 ess. value@zero: 4/3 complex roots: 0.0000 (zeta-1)@infinity: 2 zeta: 4*s^2/((2*s - 1)*(2*s - 3)) fixed points: 0.0000, 0.2753, 2.7247 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 1.5000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #136 ------------------------------------------------------------------------ names: 'g(137D)' id: 138 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (3, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.5714, 0.6667, 0.6875, 0.8333, 0.9091, 1.0000, 1.3333, 1.5000, 2.0000, 3.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/45*(76032*s^5 - 302247*s^4 + 471582*s^3 - 360697*s^2 + 135100*s - 19800)/((16*s - 11)*(11*s - 10)*(7*s - 4)*(6*s - 5)*(3*s - 2)*(3*s - 4)*(2*s - 3)*(s - 1)^2*(s - 2)*(s - 3)*s) complex roots: 0.4894, 0.6405, 0.8182, 0.9040, 1.1231 ess. value@infinity: 4/315 Topological representation zeta function: degree: 0 ess. value@zero: -2/5 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 11/6 zeta: 6*(2*s - 1)*s/((6*s - 5)*(2*s - 3)) fixed points: 0.0000, 0.6529, 2.6805 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.8333, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #137 ------------------------------------------------------------------------ names: 'g(1357A)' id: 139 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000, 0.5000, 0.6667 (zeta-1)@infinity: 11/6 zeta: 1/6*(3*s - 2)*(2*s - 1)*s/(s - 1)^3 fixed points: 0.0000, 0.7050 - 0.1334*i, 0.7050 + 0.1334*i, 2.5900 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #138 ------------------------------------------------------------------------ names: 'g(1357B)' id: 140 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/8 complex roots: -0.0957, 0.0000, 0.7979 - 0.1272*i, 0.7979 + 0.1272*i (zeta-1)@infinity: 2 zeta: 1/8*(16*s^3 - 24*s^2 + 8*s + 1)*s/((2*s - 1)*(s - 1)^3) fixed points: 0.0000, 0.2451, 0.8144 - 0.1283*i, 0.8144 + 0.1283*i, 2.6261 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #139 ------------------------------------------------------------------------ names: 'g(1357C)' id: 141 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -11/40 complex roots: 0.0000, 0.3244, 0.8378 - 0.0673*i, 0.8378 + 0.0673*i (zeta-1)@infinity: 11/6 zeta: 1/8*(48*s^3 - 96*s^2 + 60*s - 11)*s/((6*s - 5)*(s - 1)^3) fixed points: 0.0000, 0.5844, 0.8372 - 0.0730*i, 0.8372 + 0.0730*i, 2.5746 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.8333, 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #140 ------------------------------------------------------------------------ names: 'g(1357D)' id: 142 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -3/16 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 10/3 zeta: 3*(s - 1)^2*s/((3*s - 4)*(s - 2)^2) fixed points: 0.0000, 1.2785 - 0.2061*i, 1.2785 + 0.2061*i, 3.7763 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #141 ------------------------------------------------------------------------ names: 'g(1357E)' id: 143 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/6 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 7/2 zeta: 2*(s - 1)^2*s/((2*s - 3)*(s - 2)^2) fixed points: 0.0000, 1.3189 - 0.2702*i, 1.3189 + 0.2702*i, 3.8623 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #142 ------------------------------------------------------------------------ names: 'g(1357F)' id: 144 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -3/16 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 10/3 zeta: 3*(s - 1)^2*s/((3*s - 4)*(s - 2)^2) fixed points: 0.0000, 1.2785 - 0.2061*i, 1.2785 + 0.2061*i, 3.7763 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #143 ------------------------------------------------------------------------ names: 'g(1357G)' id: 145 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/3 complex roots: 0.0000 (zeta-1)@infinity: 7/2 zeta: 2*s^2/((2*s - 3)*(s - 2)) fixed points: 0.0000, 0.8139, 3.6861 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #144 ------------------------------------------------------------------------ names: 'g(1357H)' id: 146 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 3/8 complex roots: 0.0000 (zeta-1)@infinity: 10/3 zeta: 3*s^2/((3*s - 4)*(s - 2)) fixed points: 0.0000, 0.7427, 3.5907 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #145 ------------------------------------------------------------------------ names: 'g(1357I)' id: 147 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/4 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 7/2 zeta: 1/2*(2*s - 1)*s^2/((s - 1)^2*(s - 2)) fixed points: 0.0000, 0.6800 - 0.2950*i, 0.6800 + 0.2950*i, 3.6399 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #146 ------------------------------------------------------------------------ names: 'g(1357J)' id: 148 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/18 complex roots: 0.0000, 0.3333, 0.3333 (zeta-1)@infinity: 10/3 zeta: 1/9*(3*s - 1)^2*s/((s - 1)^2*(s - 2)) fixed points: 0.0000, 0.7086 - 0.2952*i, 0.7086 + 0.2952*i, 3.5828 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #147 ------------------------------------------------------------------------ names: 'g(1357K)' id: 149 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -9/32 complex roots: 0.0000, 1.0000, 1.5000 (zeta-1)@infinity: 17/6 zeta: 3/2*(2*s - 3)*(s - 1)*s/((3*s - 4)*(s - 2)^2) fixed points: 0.0000, 1.2290, 1.5758, 3.5286 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #148 ------------------------------------------------------------------------ names: 'g(1357L)' id: 150 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -9/32 complex roots: 0.0000, 1.0000, 1.5000 (zeta-1)@infinity: 17/6 zeta: 3/2*(2*s - 3)*(s - 1)*s/((3*s - 4)*(s - 2)^2) fixed points: 0.0000, 1.2290, 1.5758, 3.5286 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #149 ------------------------------------------------------------------------ names: 'g(1357M:0)' id: 151 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -37/144 complex roots: 0.0000, 1.0000, 1.7500 - 0.1443*i, 1.7500 + 0.1443*i (zeta-1)@infinity: 3 zeta: 1/6*(12*s^2 - 42*s + 37)*(s - 1)*s/((2*s - 3)*(s - 2)^3) fixed points: 0.0000, 1.3027, 1.7758 - 0.1496*i, 1.7758 + 0.1496*i, 3.6456 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #150 ------------------------------------------------------------------------ names: 'g(1357M:1)' id: 152 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 3 zeta: (s - 1)*s/(s - 2)^2 fixed points: 0.0000, 1.3820, 3.6180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #151 ------------------------------------------------------------------------ names: 'g(1357N:0)' id: 153 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 3 zeta: (s - 1)*s/(s - 2)^2 fixed points: 0.0000, 1.3820, 3.6180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #152 ------------------------------------------------------------------------ names: 'g(1357N:1)' id: 154 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -9/32 complex roots: 0.0000, 1.0000, 1.5000 (zeta-1)@infinity: 17/6 zeta: 3/2*(2*s - 3)*(s - 1)*s/((3*s - 4)*(s - 2)^2) fixed points: 0.0000, 1.2290, 1.5758, 3.5286 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #153 ------------------------------------------------------------------------ names: 'g(1357O)' id: 156 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -2/27 complex roots: 0.0000, 0.1910, 1.3090 (zeta-1)@infinity: 3 zeta: 2*(4*s^2 - 6*s + 1)*s/(2*s - 3)^3 fixed points: 0.0000, 0.8256, 1.3020, 3.3724 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #154 ------------------------------------------------------------------------ names: 'g(1357P)' id: 157 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/12 complex roots: 0.0000, 0.1910, 1.3090 (zeta-1)@infinity: 17/6 zeta: 3*(4*s^2 - 6*s + 1)*s/((3*s - 4)*(2*s - 3)^2) fixed points: 0.0000, 0.7611, 1.3082, 3.2640 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #155 ------------------------------------------------------------------------ names: 'g(1357Q)' id: 158 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 2/9 complex roots: -0.5000, 0.0000 (zeta-1)@infinity: 7/2 zeta: 2*(2*s + 1)*s/(2*s - 3)^2 fixed points: 0.0000, 0.5000, 3.5000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #156 ------------------------------------------------------------------------ names: 'g(1357R)' id: 159 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/4 complex roots: -0.5000, 0.0000 (zeta-1)@infinity: 10/3 zeta: 3*(2*s + 1)*s/((3*s - 4)*(2*s - 3)) fixed points: 0.0000, 0.4423, 3.3910 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #157 ------------------------------------------------------------------------ names: 'g(1357S:0)' id: 160 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/4 complex roots: -0.5000, 0.0000 (zeta-1)@infinity: 10/3 zeta: 3*(2*s + 1)*s/((3*s - 4)*(2*s - 3)) fixed points: 0.0000, 0.4423, 3.3910 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #158 ------------------------------------------------------------------------ names: 'g(1357S:1)' id: 161 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 29/96 complex roots: -0.6241, 0.0000, 1.2908 (zeta-1)@infinity: 7/2 zeta: 1/2*(36*s^2 - 24*s - 29)*s/((3*s - 4)^2*(2*s - 3)) fixed points: 0.0000, 0.4169, 1.2906, 3.4592 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #159 ------------------------------------------------------------------------ names: 'g(1357S:-1)' id: 162 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/4 complex roots: -0.5000, 0.0000 (zeta-1)@infinity: 10/3 zeta: 3*(2*s + 1)*s/((3*s - 4)*(2*s - 3)) fixed points: 0.0000, 0.4423, 3.3910 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #160 ------------------------------------------------------------------------ names: 'g(13457A)' id: 163 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 1) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 3/8 complex roots: 0.0000, 1.5000 (zeta-1)@infinity: 7/2 zeta: 1/2*(2*s - 3)*s^2/((s - 1)*(s - 2)^2) fixed points: 0.0000, 0.6800, 1.5677, 3.7523 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #161 ------------------------------------------------------------------------ names: 'g(13457B)' id: 164 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/30 complex roots: -0.0874, 0.0000, 1.3770 - 0.1055*i, 1.3770 + 0.1055*i (zeta-1)@infinity: 7/2 zeta: (6*s^3 - 16*s^2 + 10*s + 1)*s/((3*s - 5)*(2*s - 3)*(s - 1)*(s - 2)) fixed points: 0.0000, 0.6558, 1.4071 - 0.1176*i, 1.4071 + 0.1176*i, 3.6967 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000, 1.6667, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #162 ------------------------------------------------------------------------ names: 'g(13457C)' id: 165 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (1, 1) cocentral dim: 5 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/6 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 4 zeta: (s - 1)*s/((s - 2)*(s - 3)) fixed points: 0.0000, 1.5858, 4.4142 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #163 ------------------------------------------------------------------------ names: 'g(13457D)' id: 166 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/54 complex roots: -0.0391, 0.0000, 1.1577, 1.3814 (zeta-1)@infinity: 3 zeta: 1/2*(16*s^3 - 40*s^2 + 24*s + 1)*s/((2*s - 3)^3*(s - 1)) fixed points: 0.0000, 0.6106, 1.1818, 1.3792, 3.3284 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #164 ------------------------------------------------------------------------ names: 'g(13457E)' id: 167 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/6 complex roots: 0.0000, 0.2025 - 0.3722*i, 0.2025 + 0.3722*i, 0.9283 (zeta-1)@infinity: 17/6 zeta: 1/3*(18*s^3 - 24*s^2 + 10*s - 3)*s/((3*s - 2)*(2*s - 3)*(s - 1)^2) fixed points: 0.0000, 0.5234 - 0.3467*i, 0.5234 + 0.3467*i, 0.9271, 3.1928 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.6667, 1.0000, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #165 ------------------------------------------------------------------------ names: 'g(13457F)' id: 168 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 3/16 complex roots: 0.0000, 1.5000 (zeta-1)@infinity: 9/2 zeta: 1/2*(2*s - 3)*s^2/(s - 2)^3 fixed points: 0.0000, 1.3573 - 0.1566*i, 1.3573 + 0.1566*i, 4.2854 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #166 ------------------------------------------------------------------------ names: 'g(13457G)' id: 169 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (3, 4) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/5 complex roots: 0.0000, 1.3333 (zeta-1)@infinity: 13/3 zeta: (3*s - 4)*s^2/((3*s - 5)*(s - 2)^2) fixed points: 0.0000, 1.2460 - 0.2110*i, 1.2460 + 0.2110*i, 4.1748 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.6667, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #167 ------------------------------------------------------------------------ names: 'g(13457I)' id: 170 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (3, 4) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/5 complex roots: 0.0000, 1.3333 (zeta-1)@infinity: 13/3 zeta: (3*s - 4)*s^2/((3*s - 5)*(s - 2)^2) fixed points: 0.0000, 1.2460 - 0.2110*i, 1.2460 + 0.2110*i, 4.1748 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.6667, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #168 ------------------------------------------------------------------------ names: 'g(12457A)' id: 171 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 4/9 complex roots: 0.0000 (zeta-1)@infinity: 3 zeta: 4*s^2/(2*s - 3)^2 fixed points: 0.0000, 0.6771, 3.3229 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #169 ------------------------------------------------------------------------ names: 'g(12457B)' id: 172 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 4/9 complex roots: 0.0000 (zeta-1)@infinity: 3 zeta: 4*s^2/(2*s - 3)^2 fixed points: 0.0000, 0.6771, 3.3229 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #170 ------------------------------------------------------------------------ names: 'g(12457C)' id: 173 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -4/3 complex roots: 0.0000 (zeta-1)@infinity: 3 zeta: 4*s^3/((2*s - 1)*(2*s - 3)*(s - 1)) fixed points: 0.0000, 0.3911 - 0.2831*i, 0.3911 + 0.2831*i, 3.2178 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 1.0000, 1.5000 order@zero: 3 ------------------------------------------------------------------------ ALGEBRA #171 ------------------------------------------------------------------------ names: 'g(12457D)' id: 174 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/5 complex roots: 0.0000, 0.1451 - 0.4112*i, 0.1451 + 0.4112*i, 0.8765 (zeta-1)@infinity: 17/6 zeta: 2*(18*s^3 - 21*s^2 + 8*s - 3)*s/((6*s - 5)*(3*s - 2)*(2*s - 3)*(s - 1)) fixed points: 0.0000, 0.4711 - 0.3693*i, 0.4711 + 0.3693*i, 0.8776, 3.1803 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.6667, 0.8333, 1.0000, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #172 ------------------------------------------------------------------------ names: 'g(12457E)' id: 175 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 81/700 complex roots: -0.2010, 0.0000, 1.1392, 1.2284 (zeta-1)@infinity: 17/6 zeta: (288*s^3 - 624*s^2 + 266*s + 81)*s/((6*s - 7)*(4*s - 5)^2*(3*s - 4)) fixed points: 0.0000, 0.4887, 1.1387, 1.2284, 3.1442 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.1667, 1.2500, 1.3333 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #173 ------------------------------------------------------------------------ names: 'g(12457F)' id: 176 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 3/32 complex roots: -0.3166, 0.0000, 0.2100, 0.9399 (zeta-1)@infinity: 3 zeta: 1/8*(48*s^3 - 40*s^2 - 8*s + 3)*s/((3*s - 4)*(2*s - 1)*(s - 1)^2) fixed points: 0.0000, 0.3642 - 0.2656*i, 0.3642 + 0.2656*i, 0.9392, 3.1657 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 1.0000, 1.3333 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #174 ------------------------------------------------------------------------ names: 'g(12457G)' id: 177 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -17/160 complex roots: 0.0000, 0.0898 - 0.2949*i, 0.0898 + 0.2949*i, 0.8883, 0.9321 (zeta-1)@infinity: 17/6 zeta: 1/8*(432*s^4 - 864*s^3 + 540*s^2 - 139*s + 34)*s/((6*s - 5)*(3*s - 2)*(3*s - 4)*(s - 1)^2) fixed points: 0.0000, 0.4431 - 0.3463*i, 0.4431 + 0.3463*i, 0.8905, 0.9306, 3.1259 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.6667, 0.8333, 1.0000, 1.3333 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #175 ------------------------------------------------------------------------ names: 'g(12457H)' id: 178 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 2/9 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 4 zeta: 4*(s - 1)*s^2/((2*s - 3)^2*(s - 2)) fixed points: 0.0000, 1.0280 - 0.2901*i, 1.0280 + 0.2901*i, 3.9439 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #176 ------------------------------------------------------------------------ names: 'g(12457I)' id: 179 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (3, 4) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 7/27 complex roots: 0.0000, 1.1667 (zeta-1)@infinity: 23/6 zeta: 2/3*(6*s - 7)*s^2/((2*s - 3)^2*(s - 2)) fixed points: 0.0000, 1.0676 - 0.1566*i, 1.0676 + 0.1566*i, 3.8647 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #177 ------------------------------------------------------------------------ names: 'g(12457J)' id: 180 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (3, 4) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 7/27 complex roots: 0.0000, 1.1667 (zeta-1)@infinity: 23/6 zeta: 2/3*(6*s - 7)*s^2/((2*s - 3)^2*(s - 2)) fixed points: 0.0000, 1.0676 - 0.1566*i, 1.0676 + 0.1566*i, 3.8647 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #178 ------------------------------------------------------------------------ names: 'g(12457K)' id: 181 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 2/9 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 4 zeta: 4*(s - 1)*s^2/((2*s - 3)^2*(s - 2)) fixed points: 0.0000, 1.0280 - 0.2901*i, 1.0280 + 0.2901*i, 3.9439 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #179 ------------------------------------------------------------------------ names: 'g(12357A)' id: 186 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 5/8 complex roots: 0.0000, 0.7500 - 0.2500*i, 0.7500 + 0.2500*i (zeta-1)@infinity: 5/2 zeta: 1/8*(8*s^2 - 12*s + 5)*s^2/(s - 1)^4 fixed points: 0.0000, 0.5000, 0.7749 - 0.2784*i, 0.7749 + 0.2784*i, 2.9503 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #180 ------------------------------------------------------------------------ names: 'g(12357B)' id: 187 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 5/8 complex roots: 0.0000, 0.7500 - 0.2500*i, 0.7500 + 0.2500*i (zeta-1)@infinity: 5/2 zeta: 1/8*(8*s^2 - 12*s + 5)*s^2/(s - 1)^4 fixed points: 0.0000, 0.5000, 0.7749 - 0.2784*i, 0.7749 + 0.2784*i, 2.9503 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #181 ------------------------------------------------------------------------ names: 'g(12357C)' id: 188 Lie: True commutative: False nilpotency class: 5 nilpotent: True (u,v): (3, 3) cocentral dim: 6 rank: 7 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/35 complex roots: 0.0000, 0.0399, 0.8183 - 0.2369*i, 0.8183 + 0.2369*i, 0.8195, 0.8929 (zeta-1)@infinity: 7/3 zeta: 1/56*(3024*s^5 - 10248*s^4 + 13286*s^3 - 7893*s^2 + 1900*s - 64)*s/((9*s - 8)*(6*s - 5)*(s - 1)^4) fixed points: 0.0000, 0.4806, 0.8192, 0.8346 - 0.2471*i, 0.8346 + 0.2471*i, 0.8929, 2.8602 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.8333, 0.8889, 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #182 ------------------------------------------------------------------------ names: 'g(123457A)', 'M6' id: 189 Lie: True commutative: False nilpotency class: 6 nilpotent: True (u,v): (1, 1) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 1/4 complex roots: 0.0000 (zeta-1)@infinity: 5 zeta: s^2/((s - 1)*(s - 4)) fixed points: 0.0000, 0.7639, 5.2361 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 4.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #183 ------------------------------------------------------------------------ names: 'g(123457B)' id: 190 Lie: True commutative: False nilpotency class: 6 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 4/15 complex roots: 0.0000, 2.0000 (zeta-1)@infinity: 9/2 zeta: 2*(s - 2)*s^2/((2*s - 5)*(s - 1)*(s - 3)) fixed points: 0.0000, 0.7587, 2.1558, 4.5855 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.5000, 3.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #184 ------------------------------------------------------------------------ names: 'g(123457C)' id: 191 Lie: True commutative: False nilpotency class: 6 nilpotent: True (u,v): (3, 4) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 4/15 complex roots: 0.0000, 1.3333 (zeta-1)@infinity: 13/3 zeta: (3*s - 4)*s^2/((3*s - 5)*(s - 1)*(s - 3)) fixed points: 0.0000, 0.7806, 1.4410, 4.4451 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.6667, 3.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #185 ------------------------------------------------------------------------ names: 'g(123457D)' id: 192 Lie: True commutative: False nilpotency class: 6 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 3/10 complex roots: 0.0000, 1.5000 (zeta-1)@infinity: 4 zeta: (2*s - 3)*s^2/((2*s - 5)*(s - 1)*(s - 2)) fixed points: 0.0000, 0.7447, 1.6259, 4.1294 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000, 2.5000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #186 ------------------------------------------------------------------------ names: 'g(123457E)' id: 193 Lie: True commutative: False nilpotency class: 6 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 3/10 complex roots: 0.0000, 1.5000 (zeta-1)@infinity: 4 zeta: (2*s - 3)*s^2/((2*s - 5)*(s - 1)*(s - 2)) fixed points: 0.0000, 0.7447, 1.6259, 4.1294 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 2.0000, 2.5000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #187 ------------------------------------------------------------------------ names: 'g(123457F)' id: 194 Lie: True commutative: False nilpotency class: 6 nilpotent: True (u,v): (3, 4) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 3/10 complex roots: 0.0000, 1.3333, 1.5000 (zeta-1)@infinity: 23/6 zeta: 1/2*(3*s - 4)*(2*s - 3)*s^2/((3*s - 5)*(s - 1)*(s - 2)^2) fixed points: 0.0000, 0.7672, 1.4822 - 0.1066*i, 1.4822 + 0.1066*i, 3.9351 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.6667, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #188 ------------------------------------------------------------------------ names: 'g(123457G)' id: 195 Lie: True commutative: False nilpotency class: 6 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 5/14 complex roots: 0.0000, 1.2500 (zeta-1)@infinity: 7/2 zeta: (4*s - 5)*s^2/((4*s - 7)*(s - 1)*(s - 2)) fixed points: 0.0000, 0.7131, 1.3208, 3.7161 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.7500, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #189 ------------------------------------------------------------------------ names: 'g(123457H)' id: 196 Lie: True commutative: False nilpotency class: 6 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 5 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 5/14 complex roots: 0.0000, 1.2500 (zeta-1)@infinity: 7/2 zeta: (4*s - 5)*s^2/((4*s - 7)*(s - 1)*(s - 2)) fixed points: 0.0000, 0.7131, 1.3208, 3.7161 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.7500, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #190 ------------------------------------------------------------------------ names: 'N_1^(8,2)' id: 198 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (3, 0) cocentral dim: 6 rank: 8 soluble: True derived dim: 2 derived length: 2 associative: True description: See Ren, Zhu: `Classification of 2-step nilpotent Lie algebras of dimension 8 with 2-dimensional center (2011) Topological representation zeta function: degree: 0 ess. value@zero: 3 complex roots: 0.0000 (zeta-1)@infinity: 7/6 zeta: 6*s^2/((3*s - 2)*(2*s - 1)) fixed points: 0.0000, 0.1667, 2.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 0.6667 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #191 ------------------------------------------------------------------------ names: 'N_2^(8,2)' id: 199 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 6 rank: 8 soluble: True derived dim: 2 derived length: 2 associative: True description: See Ren, Zhu: `Classification of 2-step nilpotent Lie algebras of dimension 8 with 2-dimensional center (2011) Topological representation zeta function: degree: 0 ess. value@zero: -1 complex roots: 0.0000 (zeta-1)@infinity: 1 zeta: s/(s - 1) fixed points: 0.0000, 2.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #192 ------------------------------------------------------------------------ names: 'N_3^(8,2)' id: 200 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (3, 0) cocentral dim: 6 rank: 8 soluble: True derived dim: 2 derived length: 2 associative: True description: See Ren, Zhu: `Classification of 2-step nilpotent Lie algebras of dimension 8 with 2-dimensional center (2011) Topological representation zeta function: degree: 0 ess. value@zero: -2/3 complex roots: 0.0000, 0.2500 (zeta-1)@infinity: 1 zeta: 2*(4*s - 1)*s/((4*s - 3)*(2*s - 1)) fixed points: 0.0000, 0.3246, 1.9254 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 0.7500 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #193 ------------------------------------------------------------------------ names: 'N_4^(8,2)' id: 201 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (3, 0) cocentral dim: 6 rank: 8 soluble: True derived dim: 2 derived length: 2 associative: True description: See Ren, Zhu: `Classification of 2-step nilpotent Lie algebras of dimension 8 with 2-dimensional center (2011) Topological representation zeta function: degree: 0 ess. value@zero: -2/3 complex roots: 0.0000, 0.6667 (zeta-1)@infinity: 4/3 zeta: 1/3*(3*s - 2)*s/(s - 1)^2 fixed points: 0.0000, 0.7362, 2.2638 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #194 ------------------------------------------------------------------------ names: 'N_5^(8,2)' id: 202 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (3, 0) cocentral dim: 6 rank: 8 soluble: True derived dim: 2 derived length: 2 associative: True description: See Ren, Zhu: `Classification of 2-step nilpotent Lie algebras of dimension 8 with 2-dimensional center (2011) Topological representation zeta function: degree: 0 ess. value@zero: -6/5 complex roots: 0.0000 (zeta-1)@infinity: 5/6 zeta: 6*s/(6*s - 5) fixed points: 0.0000, 1.8333 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.8333 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #195 ------------------------------------------------------------------------ names: 'N_1^(8,3)' id: 203 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 8 soluble: True derived dim: 3 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 5/2 zeta: 2*(s - 1)*s/((2*s - 3)*(s - 2)) fixed points: 0.0000, 1.2192, 3.2808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #196 ------------------------------------------------------------------------ names: 'N_2^(8,3)' id: 204 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 8 soluble: True derived dim: 3 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 5/2 zeta: 2*(s - 1)*s/((2*s - 3)*(s - 2)) fixed points: 0.0000, 1.2192, 3.2808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #197 ------------------------------------------------------------------------ names: 'N_3^(8,3)' id: 205 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 8 soluble: True derived dim: 3 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: -1/9 complex roots: 0.0000, 0.1910, 1.3090 (zeta-1)@infinity: 5/2 zeta: (4*s^2 - 6*s + 1)*s/((2*s - 3)^2*(s - 1)) fixed points: 0.0000, 0.6192, 1.3183, 3.0624 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #198 ------------------------------------------------------------------------ names: 'N_4^(8,3)' id: 206 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 8 soluble: True derived dim: 3 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: -1/3 complex roots: 0.0000, 0.5000 (zeta-1)@infinity: 2 zeta: (2*s - 1)*s/((2*s - 3)*(s - 1)) fixed points: 0.0000, 0.7192, 2.7808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #199 ------------------------------------------------------------------------ names: 'N_5^(8,3)' id: 207 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 8 soluble: True derived dim: 3 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: -3/8 complex roots: 0.0000, 1.5000 (zeta-1)@infinity: 5/2 zeta: 1/2*(2*s - 3)*s/(s - 2)^2 fixed points: 0.0000, 1.6340, 3.3660 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #200 ------------------------------------------------------------------------ names: 'N_6^(8,3)' id: 208 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 8 soluble: True derived dim: 3 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: -4/9 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 2 zeta: 4*(s - 1)*s/(2*s - 3)^2 fixed points: 0.0000, 1.1340, 2.8660 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #201 ------------------------------------------------------------------------ names: 'N_7^(8,3)' id: 209 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 8 soluble: True derived dim: 3 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: -7/15 complex roots: 0.0000, 1.1667 (zeta-1)@infinity: 2 zeta: (6*s - 7)*s/((3*s - 5)*(2*s - 3)) fixed points: 0.0000, 1.2626, 2.9041 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 1.6667 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #202 ------------------------------------------------------------------------ names: 'N_8^(8,3)' id: 210 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 8 soluble: True derived dim: 3 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: -1/2 complex roots: 0.0000 (zeta-1)@infinity: 2 zeta: s/(s - 2) fixed points: 0.0000, 3.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #203 ------------------------------------------------------------------------ names: 'N_9^(8,3)' id: 211 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 8 soluble: True derived dim: 3 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: -2/3 complex roots: 0.0000 (zeta-1)@infinity: 3/2 zeta: 2*s/(2*s - 3) fixed points: 0.0000, 2.5000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #204 ------------------------------------------------------------------------ names: 'N_10^(8,3)' id: 212 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 8 soluble: True derived dim: 3 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: 1/3 complex roots: -0.5000, 0.0000 (zeta-1)@infinity: 3 zeta: (2*s + 1)*s/((2*s - 3)*(s - 1)) fixed points: 0.0000, 0.3139, 3.1861 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #205 ------------------------------------------------------------------------ names: 'N_11^(8,3)' id: 213 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 5 rank: 8 soluble: True derived dim: 3 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: 2/3 complex roots: 0.0000 (zeta-1)@infinity: 5/2 zeta: 2*s^2/((2*s - 3)*(s - 1)) fixed points: 0.0000, 0.5000, 3.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.0000, 1.5000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #206 ------------------------------------------------------------------------ names: 'N_1^(8,4)' id: 214 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 8 soluble: True derived dim: 4 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: -1/6 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 4 zeta: (s - 1)*s/((s - 2)*(s - 3)) fixed points: 0.0000, 1.5858, 4.4142 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #207 ------------------------------------------------------------------------ names: 'N_2^(8,4)' id: 215 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 8 soluble: True derived dim: 4 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: -2/9 complex roots: 0.0000, 2.0000 (zeta-1)@infinity: 4 zeta: (s - 2)*s/(s - 3)^2 fixed points: 0.0000, 2.3820, 4.6180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #208 ------------------------------------------------------------------------ names: 'N_3^(8,4)' id: 216 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 8 soluble: True derived dim: 4 derived length: 2 associative: True description: See Yan, Deng: `The classification of two step nilpotent complex Lie algebras of dimension 8' (2013) Topological representation zeta function: degree: 0 ess. value@zero: -4/15 complex roots: 0.0000, 2.0000 (zeta-1)@infinity: 7/2 zeta: 2*(s - 2)*s/((2*s - 5)*(s - 3)) fixed points: 0.0000, 2.2192, 4.2808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.5000, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #209 ------------------------------------------------------------------------ names: 'LL72_L1' id: 217 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (3, 3) cocentral dim: 7 rank: 9 soluble: True derived dim: 6 derived length: 2 associative: False description: See Leger and Luks: `On nilpotent groups of algebra automorphisms' (1972) Topological representation zeta function: degree: 0 ess. value@zero: -27/560 complex roots: 0.0000, 0.5246, 1.0000, 1.0000, 1.5654, 1.8267 (zeta-1)@infinity: 29/6 zeta: (36*s^3 - 141*s^2 + 167*s - 54)*(s - 1)^2*s/((4*s - 7)*(3*s - 4)*(3*s - 5)*(s - 2)^3) fixed points: 0.0000, 1.2452, 1.3110 - 0.5636*i, 1.3110 + 0.5636*i, 1.5692, 1.8266, 4.4870 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.3333, 1.6667, 1.7500, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #210 ------------------------------------------------------------------------ names: 'LL72_L3' id: 219 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 4 rank: 8 soluble: True derived dim: 3 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -1/4 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 3 zeta: (s - 1)*s/(s - 2)^2 fixed points: 0.0000, 1.3820, 3.6180 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #211 ------------------------------------------------------------------------ names: 'h(ZZ[X]/X^3)', 'L(3,2) otimes ZZ[X]/X^3' id: 221 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (3, 0) cocentral dim: 6 rank: 9 soluble: True derived dim: 3 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -8/15 complex roots: 0.0000, 1.3333 (zeta-1)@infinity: 11/6 zeta: 2*(3*s - 4)*s/((3*s - 5)*(2*s - 3)) fixed points: 0.0000, 1.3713, 2.7953 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 1.6667 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #212 ------------------------------------------------------------------------ names: 'M3 curlyvee M3' id: 223 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 7 soluble: True derived dim: 3 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -2 complex roots: 0.0000 (zeta-1)@infinity: 5/2 zeta: 2*s^3/((2*s - 1)*(s - 1)^2) fixed points: 0.0000, 0.3189 - 0.2702*i, 0.3189 + 0.2702*i, 2.8623 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000, 1.0000 order@zero: 3 ------------------------------------------------------------------------ ALGEBRA #213 ------------------------------------------------------------------------ names: 'n(5,ZZ)' id: 224 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (4, 4) cocentral dim: 9 rank: 10 soluble: True derived dim: 6 derived length: 3 associative: False Topological representation zeta function: degree: 0 ess. value@zero: 7/24 complex roots: 0.0000, 0.3991 - 0.3921*i, 0.3991 + 0.3921*i, 1.3509 - 0.1969*i, 1.3509 + 0.1969*i (zeta-1)@infinity: 13/3 zeta: 1/2*(12*s^4 - 42*s^3 + 52*s^2 - 28*s + 7)*s^2/((3*s - 1)*(2*s - 3)*(s - 1)^2*(s - 2)^2) fixed points: 0.0000, 0.3003, 0.8126 - 0.4055*i, 0.8126 + 0.4055*i, 1.3776 - 0.2161*i, 1.3776 + 0.2161*i, 4.1525 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.3333, 1.0000, 1.5000, 2.0000 order@zero: 2 ------------------------------------------------------------------------ ALGEBRA #214 ------------------------------------------------------------------------ names: 'Lie(2)' id: 226 Lie: True commutative: False nilpotent: False rank: 2 soluble: True derived length: 2 associative: False description: Non-abelian Lie ring of rank 2 Topological subalgebra zeta function: poles: 0.0000, 1.0000 order@zero: -1 degree: -2 ess. value@zero: -1 zeta: 1/((s - 1)*s) complex roots: None ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000 order@zero: -2 degree: -2 ess. value@zero: 1/2 zeta: 1/2/s^2 complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #215 ------------------------------------------------------------------------ names: 'L^2', 's(2)' id: 227 Lie: True commutative: False nilpotent: False rank: 3 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/((s - 1)*(s - 2)*s) complex roots: None ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 0.5000 order@zero: -2 degree: -3 ess. value@zero: -2/3 zeta: 2/3/((2*s - 1)*s^2) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #216 ------------------------------------------------------------------------ names: 'L^3(0)', 'Lie(2) (+) (ZZ,0)', 'tr(2,ZZ)' id: 228 Lie: True commutative: False nilpotent: False rank: 3 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/2*(2*s - 1)/((s - 1)^3*s) complex roots: 0.5000 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -2 degree: -3 ess. value@zero: -1/2 zeta: 1/2/((s - 1)*s^2) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #217 ------------------------------------------------------------------------ names: 'L^3(1)' id: 229 Lie: True commutative: False nilpotent: False rank: 3 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/2*(2*s - 1)/((s - 1)^3*s) complex roots: 0.5000 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000 order@zero: -3 degree: -3 ess. value@zero: 1/3 zeta: 1/3/s^3 complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #218 ------------------------------------------------------------------------ names: 'L^4(1)' id: 230 Lie: True commutative: False nilpotent: False rank: 3 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/2*(2*s - 1)/((s - 1)^3*s) complex roots: 0.5000 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000 order@zero: -3 degree: -3 ess. value@zero: 1/3 zeta: 1/3/s^3 complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #219 ------------------------------------------------------------------------ names: 'M^2', 's(3)' id: 231 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/((s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 0.6667, 1.0000 order@zero: -2 degree: -4 ess. value@zero: 3/8 zeta: 3/4/((3*s - 2)*(s - 1)*s^2) complex roots: None ess. value@infinity: 1/4 ------------------------------------------------------------------------ ALGEBRA #220 ------------------------------------------------------------------------ names: 'M^3(0)' id: 232 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 2.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: (2*s - 1)/((2*s - 3)*(s - 1)^2*(s - 2)*s) complex roots: 0.5000 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 0.5000, 1.0000 order@zero: -2 degree: -4 ess. value@zero: 2/3 zeta: 2/3/((2*s - 1)*(s - 1)*s^2) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #221 ------------------------------------------------------------------------ names: 'M^4', 'Lie(2) (+) (ZZ^2,0)' id: 235 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 2.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: (2*s - 1)/((2*s - 3)*(s - 1)^2*(s - 2)*s) complex roots: 0.5000 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -2 degree: -4 ess. value@zero: 1/4 zeta: 1/2/((s - 1)*(s - 2)*s^2) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #222 ------------------------------------------------------------------------ names: 'M^6(0,0)' id: 236 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(12*s^2 - 23*s + 9)/((2*s - 3)^3*(s - 1)^2*s) complex roots: 0.5480, 1.3687 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 0.5000, 0.6667, 1.0000 order@zero: -2 degree: -4 ess. value@zero: 1/4 zeta: 1/4*(5*s - 2)/((3*s - 2)*(2*s - 1)*(s - 1)*s^2) complex roots: 0.4000 ess. value@infinity: 5/24 ------------------------------------------------------------------------ ALGEBRA #223 ------------------------------------------------------------------------ names: 'M^6(1,0)' id: 237 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(8*s^2 - 12*s + 3)/((2*s - 3)^2*(s - 1)^3*s) complex roots: 0.3170, 1.1830 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000 order@zero: -4 degree: -4 ess. value@zero: 1/4 zeta: 1/4/s^4 complex roots: None ess. value@infinity: 1/4 ------------------------------------------------------------------------ ALGEBRA #224 ------------------------------------------------------------------------ names: 'M^6(0,1)' id: 238 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(8*s^2 - 12*s + 3)/((2*s - 3)^2*(s - 1)^3*s) complex roots: 0.3170, 1.1830 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -3 degree: -4 ess. value@zero: -1/3 zeta: 1/3/((s - 1)*s^3) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #225 ------------------------------------------------------------------------ names: 'M^7(1,0)' id: 240 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(8*s^2 - 12*s + 3)/((2*s - 3)^2*(s - 1)^3*s) complex roots: 0.3170, 1.1830 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000 order@zero: -4 degree: -4 ess. value@zero: 1/4 zeta: 1/4/s^4 complex roots: None ess. value@infinity: 1/4 ------------------------------------------------------------------------ ALGEBRA #226 ------------------------------------------------------------------------ names: 'M^7(0,1)' id: 241 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(8*s^2 - 12*s + 3)/((2*s - 3)^2*(s - 1)^3*s) complex roots: 0.3170, 1.1830 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -3 degree: -4 ess. value@zero: -1/3 zeta: 1/3/((s - 1)*s^3) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #227 ------------------------------------------------------------------------ names: 'M^7(1,1)' id: 242 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(8*s^2 - 12*s + 3)/((2*s - 3)^2*(s - 1)^3*s) complex roots: 0.3170, 1.1830 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000 order@zero: -4 degree: -4 ess. value@zero: 1/4 zeta: 1/4/s^4 complex roots: None ess. value@infinity: 1/4 ------------------------------------------------------------------------ ALGEBRA #228 ------------------------------------------------------------------------ names: 'M^7(1,2)' id: 243 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(8*s^2 - 12*s + 3)/((2*s - 3)^2*(s - 1)^3*s) complex roots: 0.3170, 1.1830 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000 order@zero: -4 degree: -4 ess. value@zero: 1/4 zeta: 1/4/s^4 complex roots: None ess. value@infinity: 1/4 ------------------------------------------------------------------------ ALGEBRA #229 ------------------------------------------------------------------------ names: 'M^8', 'Lie(2)^2', 'Lie(2) (+) Lie(2)' id: 244 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.2000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(10*s^2 - 7*s + 2)/((5*s - 6)*(s - 1)^4*s) complex roots: 0.3500 - 0.2784*i, 0.3500 + 0.2784*i ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -3 degree: -4 ess. value@zero: -1/4 zeta: 1/4/((s - 1)*s^3) complex roots: None ess. value@infinity: 1/4 ------------------------------------------------------------------------ ALGEBRA #230 ------------------------------------------------------------------------ names: 'M^12' id: 245 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 3 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 2.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(3*s - 2)/((2*s - 3)*(s - 1)^2*(s - 2)*s) complex roots: 0.6667 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 0.5000 order@zero: -3 degree: -4 ess. value@zero: -1/6 zeta: 1/6/((2*s - 1)*s^3) complex roots: None ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #231 ------------------------------------------------------------------------ names: 'M^13(0)', 'Lie(2)[eps]', 'Lie(2) otimes ZZ[X]/X^2' id: 246 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.3333, 1.5000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(9*s - 4)/((3*s - 4)*(2*s - 3)*(s - 1)^2*s) complex roots: 0.4444 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 0.2500, 1.0000 order@zero: -2 degree: -4 ess. value@zero: 1/2 zeta: 1/2/((4*s - 1)*(s - 1)*s^2) complex roots: None ess. value@infinity: 1/8 ------------------------------------------------------------------------ ALGEBRA #232 ------------------------------------------------------------------------ names: 'M^13(1)' id: 247 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 3 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.2857, 1.3333 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 3/4*(63*s^3 - 172*s^2 + 142*s - 32)/((7*s - 9)*(3*s - 4)^2*(s - 1)^3*s) complex roots: 0.3655, 1.0916, 1.2730 ess. value@infinity: 3/4 ------------------------------------------------------------------------ ALGEBRA #233 ------------------------------------------------------------------------ names: 'M^14(1)' id: 248 Lie: True commutative: False nilpotent: False rank: 4 soluble: True derived length: 3 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.2857, 1.3333 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 3/4*(63*s^3 - 172*s^2 + 142*s - 32)/((7*s - 9)*(3*s - 4)^2*(s - 1)^3*s) complex roots: 0.3655, 1.0916, 1.2730 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 0.2500 order@zero: -3 degree: -4 ess. value@zero: -1/3 zeta: 1/3/((4*s - 1)*s^3) complex roots: None ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #234 ------------------------------------------------------------------------ names: 'Lie(2) (+) (ZZ^3,0)' id: 249 Lie: True commutative: False nilpotent: False rank: 5 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/2*(2*s - 1)/((s - 1)^2*(s - 2)^2*(s - 3)*s) complex roots: 0.5000 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000 order@zero: -2 degree: -5 ess. value@zero: -1/12 zeta: 1/2/((s - 1)*(s - 2)*(s - 3)*s^2) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #235 ------------------------------------------------------------------------ names: 'Lie(2) (+) h(ZZ)', 'Lie(2) (+) H(2)' id: 250 Lie: True commutative: False nilpotent: False rank: 5 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.3333, 1.5000, 1.6667, 1.7500, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/2*(108*s^4 - 505*s^3 + 848*s^2 - 594*s + 140)/((4*s - 7)*(3*s - 4)*(3*s - 5)*(2*s - 3)*(s - 1)^2*(s - 2)^2*s) complex roots: 0.4818, 1.2884 - 0.0604*i, 1.2884 + 0.0604*i, 1.6174 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -2 degree: -5 ess. value@zero: -1/12 zeta: 1/6/((s - 1)^2*(s - 2)*s^2) complex roots: None ess. value@infinity: 1/6 ------------------------------------------------------------------------ ALGEBRA #236 ------------------------------------------------------------------------ names: 'Lie(2) (+) h(ZZ) (+) (ZZ,0)', 'Lie(2) (+) H(2) (+) (ZZ,0)' id: 251 Lie: True commutative: False nilpotent: False rank: 6 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 2.5000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/24*(108*s^4 - 586*s^3 + 1143*s^2 - 921*s + 240)/((3*s - 5)*(2*s - 5)*(s - 1)^2*(s - 2)^4*(s - 3)*s) complex roots: 0.4925, 1.5977, 1.6679 - 0.2058*i, 1.6679 + 0.2058*i ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -2 degree: -6 ess. value@zero: 1/48 zeta: 1/2/((3*s - 4)*(s - 1)*(s - 2)*(s - 3)*s^2) complex roots: None ess. value@infinity: 1/6 ------------------------------------------------------------------------ ALGEBRA #237 ------------------------------------------------------------------------ names: 'Lie(2)^2 (+) (ZZ,0)', 'Lie(2) (+) Lie(2) (+) (ZZ,0)' id: 252 Lie: True commutative: False nilpotent: False rank: 5 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.3333, 1.4000, 1.5000, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/3*(360*s^6 - 2064*s^5 + 4732*s^4 - 5524*s^3 + 3481*s^2 - 1173*s + 189)/((5*s - 7)*(3*s - 4)*(2*s - 3)^3*(s - 1)^4*(s - 2)*s) complex roots: 0.3004 - 0.3244*i, 0.3004 + 0.3244*i, 1.1141, 1.3135, 1.3525 - 0.0797*i, 1.3525 + 0.0797*i ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -3 degree: -5 ess. value@zero: 1/8 zeta: 1/4/((s - 1)*(s - 2)*s^3) complex roots: None ess. value@infinity: 1/4 ------------------------------------------------------------------------ ALGEBRA #238 ------------------------------------------------------------------------ names: 'Lie(2)^3', 'Lie(2) (+) Lie(2) (+) Lie(2)' id: 253 Lie: True commutative: False nilpotent: False rank: 6 soluble: True derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -4 degree: -6 ess. value@zero: 1/16 zeta: 1/8/((s - 1)*(s - 2)*s^4) complex roots: None ess. value@infinity: 1/8 ------------------------------------------------------------------------ ALGEBRA #239 ------------------------------------------------------------------------ names: '(Lie(2) otimes ZZ[X]/X^2) (+) (ZZ,0)', 'Lie(2)[eps] (+) (ZZ,0)' id: 254 Lie: True commutative: False nilpotent: False rank: 5 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.3333, 1.5000, 1.6667, 1.7500, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: (108*s^4 - 481*s^3 + 766*s^2 - 501*s + 105)/((4*s - 7)*(3*s - 4)*(3*s - 5)*(2*s - 3)^2*(s - 1)^2*(s - 2)*s) complex roots: 0.3909, 1.3263 - 0.0685*i, 1.3263 + 0.0685*i, 1.4102 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 0.2500, 1.0000, 2.0000 order@zero: -2 degree: -5 ess. value@zero: -1/4 zeta: 1/2/((4*s - 1)*(s - 1)*(s - 2)*s^2) complex roots: None ess. value@infinity: 1/8 ------------------------------------------------------------------------ ALGEBRA #240 ------------------------------------------------------------------------ names: '(Lie(2) otimes ZZ[X]/X^2) (+) (ZZ^2,0)', '(Lie(2) (+) (ZZ,0)) otimes ZZ[X]/X^2', 'Lie(2)[eps] (+) (ZZ^2,0)' id: 255 Lie: True commutative: False nilpotent: False rank: 6 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 1.6667, 2.0000, 2.2500, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/12*(216*s^5 - 1558*s^4 + 4329*s^3 - 5680*s^2 + 3377*s - 648)/((4*s - 9)*(3*s - 5)*(2*s - 3)*(s - 1)^2*(s - 2)^4*(s - 3)*s) complex roots: 0.3480, 1.5634 - 0.1289*i, 1.5634 + 0.1289*i, 1.8691 - 0.0995*i, 1.8691 + 0.0995*i ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 0.2500, 1.0000, 2.0000, 3.0000 order@zero: -2 degree: -6 ess. value@zero: 1/12 zeta: 1/2/((4*s - 1)*(s - 1)*(s - 2)*(s - 3)*s^2) complex roots: None ess. value@infinity: 1/8 ------------------------------------------------------------------------ ALGEBRA #241 ------------------------------------------------------------------------ names: 'sl(2,ZZ)' id: 256 Lie: True commutative: False nilpotent: False rank: 3 soluble: False associative: False description: Lie ring sl(2,ZZ) with basis (e,f,h) Topological subalgebra zeta function: poles: 0.0000, 0.5000, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/2*(3*s - 1)/((2*s - 1)*(s - 1)^2*s) complex roots: 0.3333 ess. value@infinity: 3/4 Topological ideal zeta function: ess. value@zero: 0 zeta: 0 order@zero: +Infinity degree: -Infinity ess. value@infinity: 0 ------------------------------------------------------------------------ ALGEBRA #242 ------------------------------------------------------------------------ names: 'gl(2,ZZ)', 'sl(2,ZZ) (+) (ZZ,0)' id: 258 Lie: True commutative: False nilpotent: False rank: 4 soluble: False associative: False description: Lie ring gl(2,ZZ) with basis (e,h,f,1) Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.1667 order@zero: -1 degree: -4 ess. value@zero: -1/3 zeta: 1/6*(27*s - 14)/((6*s - 7)*(s - 1)^3*s) complex roots: 0.5185 ess. value@infinity: 3/4 Topological ideal zeta function: ess. value@zero: 0 zeta: 0 order@zero: +Infinity degree: -Infinity ess. value@infinity: 0 ------------------------------------------------------------------------ ALGEBRA #243 ------------------------------------------------------------------------ names: 'A(3,2)' id: 259 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 3 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.3333 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 2/((3*s - 4)*(s - 1)*s) complex roots: None ess. value@infinity: 2/3 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/2/((s - 1)^2*s) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #244 ------------------------------------------------------------------------ names: 'A(3,3;1)' id: 260 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 3 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/4*(3*s - 2)/((s - 1)^3*s) complex roots: 0.6667 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 0.6667, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/((3*s - 2)*(s - 1)*s) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #245 ------------------------------------------------------------------------ names: 'A(3,4;0)' id: 261 Lie: False commutative: False nilpotency class: 2 nilpotent: True rank: 3 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/4*(3*s - 2)/((s - 1)^3*s) complex roots: 0.6667 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 0.6667, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/((3*s - 2)*(s - 1)*s) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #246 ------------------------------------------------------------------------ names: 'A(3,6)', 'X*ZZ[X]/X^4' id: 262 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 3 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.8333, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/24*(72*s^2 - 131*s + 60)/((6*s - 5)*(s - 1)^3*s) complex roots: 0.9097 - 0.0758*i, 0.9097 + 0.0758*i ess. value@infinity: 1/2 Topological ideal zeta function: poles: 0.0000, 0.5000, 0.6667 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/((3*s - 2)*(2*s - 1)*s) complex roots: None ess. value@infinity: 1/6 ------------------------------------------------------------------------ ALGEBRA #247 ------------------------------------------------------------------------ names: 'X*ZZ[X]/X^5', 'A(4,8)' id: 263 Lie: False commutative: True nilpotency class: 4 nilpotent: True rank: 4 soluble: True derived length: 3 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.9000, 1.0833, 1.1667, 1.1818, 1.2000, 1.2500, 1.2667, 1.3333 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/10*(504662400*s^7 - 4095476640*s^6 + 14242040424*s^5 - 27510984828*s^4 + 31880599078*s^3 - 22163002945*s^2 + 8558212705*s - 1416051000)/((15*s - 19)*(12*s - 13)*(11*s - 13)*(10*s - 9)*(6*s - 7)^2*(5*s - 6)*(4*s - 5)^2*(3*s - 4)*s) complex roots: 1.0611 - 0.0068*i, 1.0611 + 0.0068*i, 1.1645 - 0.1156*i, 1.1645 + 0.1156*i, 1.1809, 1.2183, 1.2650 ess. value@infinity: 59/200 Topological ideal zeta function: poles: 0.0000, 0.5000, 0.6667, 0.7500 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/((4*s - 3)*(3*s - 2)*(2*s - 1)*s) complex roots: None ess. value@infinity: 1/24 ------------------------------------------------------------------------ ALGEBRA #248 ------------------------------------------------------------------------ names: 'C(3,2)' id: 264 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 3 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/4*(3*s - 2)/((s - 1)^3*s) complex roots: 0.6667 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 0.6667, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/((3*s - 2)*(s - 1)*s) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #249 ------------------------------------------------------------------------ names: 'C(4,2)', 'C(3,2) (+) (ZZ,0)' id: 265 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 4 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.5000, 2.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 3/((2*s - 3)^2*(s - 2)*s) complex roots: None ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/3/((s - 1)^2*(s - 2)*s) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #250 ------------------------------------------------------------------------ names: 'C(4,3)' id: 266 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 4 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.2500, 1.3333, 1.5000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/6*(78*s^2 - 143*s + 60)/((4*s - 5)*(3*s - 4)*(2*s - 3)*(s - 1)^2*s) complex roots: 0.6501, 1.1832 ess. value@infinity: 13/24 Topological ideal zeta function: poles: 0.0000, 0.5000, 0.6000, 0.6667, 1.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/2*(5*s - 2)/((5*s - 3)*(3*s - 2)*(2*s - 1)*(s - 1)*s) complex roots: 0.4000 ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #251 ------------------------------------------------------------------------ names: 'C(5,2)', 'C(3,2) (+) (ZZ^2,0)' id: 267 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 5 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/4*(3*s - 4)/((s - 1)*(s - 2)^3*(s - 3)*s) complex roots: 1.3333 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/((3*s - 4)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #252 ------------------------------------------------------------------------ names: 'C(5,3)', 'C(4,3) (+) (ZZ,0)' id: 268 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 5 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.3333, 1.5000, 1.7500, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/3*(39*s^3 - 156*s^2 + 202*s - 84)/((4*s - 7)*(3*s - 4)*(2*s - 3)*(s - 1)*(s - 2)^3*s) complex roots: 0.9083, 1.4104, 1.6813 ess. value@infinity: 13/24 Topological ideal zeta function: poles: 0.0000, 0.7500, 0.8000, 1.0000, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/3*(5*s - 3)/((5*s - 4)*(4*s - 3)*(s - 1)^2*(s - 2)*s) complex roots: 0.6000 ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #253 ------------------------------------------------------------------------ names: 'C(5,4)', 'C(3,2) curlyvee C(3,2)' id: 269 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 5 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.3333, 1.6667, 2.0000, 3.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: (17*s - 25)/((3*s - 4)*(3*s - 5)^2*(s - 2)*(s - 3)*s) complex roots: 1.4706 ess. value@infinity: 17/27 Topological ideal zeta function: poles: 0.0000, 0.8000, 1.0000, 2.0000, 3.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/((5*s - 4)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 1/5 ------------------------------------------------------------------------ ALGEBRA #254 ------------------------------------------------------------------------ names: 'C(5,5)' id: 270 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 5 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.3333, 1.4444, 1.5000, 1.7500, 1.8000, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/27*(220320*s^6 - 1842072*s^5 + 6367090*s^4 - 11632541*s^3 + 11830093*s^2 - 6337161*s + 1393119)/((9*s - 13)*(5*s - 9)*(4*s - 7)^2*(3*s - 4)*(2*s - 3)^3*(s - 1)*(s - 2)*s) complex roots: 0.8244, 1.3855 - 0.0553*i, 1.3855 + 0.0553*i, 1.4608, 1.6524 - 0.0245*i, 1.6524 + 0.0245*i ess. value@infinity: 17/36 Topological ideal zeta function: poles: 0.0000, 0.8000, 1.0000, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/3/((5*s - 4)*(s - 1)^2*(s - 2)*s) complex roots: None ess. value@infinity: 1/15 ------------------------------------------------------------------------ ALGEBRA #255 ------------------------------------------------------------------------ names: 'C(5,6)' id: 271 Lie: False commutative: True nilpotency class: 4 nilpotent: True rank: 5 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.9333, 1.0000, 1.0833, 1.1905, 1.2000, 1.2381, 1.2500, 1.2667, 1.2727, 1.2857, 1.2917, 1.3000, 1.3333, 1.3571, 1.3846, 1.3913, 1.4000, 1.4167, 1.4286, 1.4444, 1.4500, 1.4545, 1.4615, 1.4706, 1.5000, 1.5333, 1.5455, 1.5556, 1.5676, 1.5714, 1.5882, 1.6000, 1.6154, 1.6250 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/1080*(18774882624308439288940279132518088704000000000*s^44 - 1106997307621470729219346840157348811571200000000*s^43 + 31878683359134993453386093039762287221596160000000*s^42 - 597503399110376595952020014515215680222736384000000*s^41 + 8195409977007583430239184741454773931661870540800000*s^40 - 87691875443869633883226632480487791255575528942080000*s^39 + 762011194884112906783317269816707701672309875102976000*s^38 - 5527428238837005466380075580444486264180431848290752000*s^37 + 34142565708844849419113042395174338588616927292444439360*s^36 - 182305590873892729611961637657966416675137058233639681936*s^35 + 851317879986490615140555359914344254118933053187406114152*s^34 - 3508963324032647556898489991858214859423503381325704584592*s^33 + 12861351688642493015766824472664721898105147445983128326350*s^32 - 42173495068104608650323851061860505640908126650747186377257*s^31 + 124333385664606016925267192791367036995559781382803983488950*s^30 - 330900312369971462871638409653999119411022769945323038127283*s^29 + 797656942032503573312215380022630351744828125874331603384832*s^28 - 1746321596277300630583773174703198339879981618808795966750432*s^27 + 3479916108744307647857429322013640996883921305364812904113888*s^26 - 6322550181965188315379317318105718622405977945312769336141444*s^25 + 10487029836351430975814686126943023336202734959209328982414124*s^24 - 15894134200512385459637608959651804629290996355660246932380038*s^23 + 22022785454775521427279915184118924577179036734211845111568220*s^22 - 27901686532248322038711785505709291343594747554407399331714770*s^21 + 32316932734456156856272080922663297411431526472717257261126416*s^20 - 34200690680097683071502427411590021473217738105847805725675732*s^19 + 33040575944015526077194727747624858092896036249562969525807128*s^18 - 29100527158519735850173130491473119213630883752781304736002836*s^17 + 23326107252008475029585552264473007378938257406463509949709078*s^16 - 16979091144420470548965520303023293947943008840858382092045785*s^15 + 11192512262240176020009108071497515214661400103701415930316094*s^14 - 6659212758589232022369131510868555422128291374245325576322995*s^13 + 3561422737227761293607267356401158092461643580872481387695200*s^12 - 1703602935442040450637595691415995503465553273682018665760948*s^11 + 724471763577646067458830621605403555076937221151553416164944*s^10 - 271860078027587073094084225628819728122518925515724529670560*s^9 + 89190890166502561791358080941564008210374047198927974980160*s^8 - 25285789756103532318632442578915082477086600521758413319552*s^7 + 6102115031886688802395830301889426965000587545009633914624*s^6 - 1228757793771554810723855406686458358501666191831693515520*s^5 + 200850387243086610256307176579164869794879678540624788480*s^4 - 25599332671645653530508006311240761958319796607709496320*s^3 + 2386432673349745941610482375996990132562805016271872000*s^2 - 144714535590456003683083457070539861190024919449600000*s + 4283478253285228096192677719570198261789491200000000)/((37*s - 58)*(24*s - 31)*(23*s - 32)*(21*s - 25)*(21*s - 26)*(20*s - 29)*(17*s - 25)*(17*s - 27)*(15*s - 14)*(15*s - 19)*(15*s - 23)*(14*s - 19)*(13*s - 18)*(13*s - 19)^2*(13*s - 21)*(12*s - 13)*(12*s - 17)^3*(11*s - 14)^2*(11*s - 16)*(11*s - 17)^2*(10*s - 13)^2*(9*s - 13)^3*(9*s - 14)*(8*s - 13)*(7*s - 9)*(7*s - 10)*(7*s - 11)*(5*s - 6)*(5*s - 7)^2*(5*s - 8)*(4*s - 5)^2*(3*s - 4)*(2*s - 3)^2*(s - 1)^4*s) complex roots: 0.5926, 0.9335, 1.0627 - 0.1627*i, 1.0627 + 0.1627*i, 1.0832, 1.1199, 1.1381 - 0.1622*i, 1.1381 + 0.1622*i, 1.1905, 1.2397, 1.2619, 1.2709 - 0.0037*i, 1.2709 + 0.0037*i, 1.2838, 1.2899, 1.2949, 1.3144 - 0.0313*i, 1.3144 + 0.0313*i, 1.3204, 1.3570, 1.3803, 1.3847, 1.3946, 1.4078, 1.4084 - 0.0111*i, 1.4084 + 0.0111*i, 1.4254 - 0.0041*i, 1.4254 + 0.0041*i, 1.4402, 1.4491, 1.4500, 1.4591 - 0.0039*i, 1.4591 + 0.0039*i, 1.4659, 1.4885, 1.4999 - 0.0214*i, 1.4999 + 0.0214*i, 1.5437, 1.5482, 1.5560, 1.5662, 1.5834, 1.5890 - 0.0170*i, 1.5890 + 0.0170*i ess. value@infinity: 463/1350 Topological ideal zeta function: poles: 0.0000, 0.4000, 0.5714, 0.5833, 0.6000, 0.6250, 0.6667, 1.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/2*(5040*s^4 - 10157*s^3 + 7522*s^2 - 2412*s + 280)/((12*s - 7)*(8*s - 5)*(7*s - 4)*(5*s - 2)*(5*s - 3)*(3*s - 2)^2*(s - 1)*s) complex roots: 0.2996, 0.5120, 0.5939, 0.6098 ess. value@infinity: 1/60 ------------------------------------------------------------------------ ALGEBRA #256 ------------------------------------------------------------------------ names: 'C(5,7)' id: 272 Lie: False commutative: True nilpotency class: 4 nilpotent: True rank: 5 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.2857, 1.6000, 1.7500, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/72*(4140*s^5 - 23407*s^4 + 51802*s^3 - 56059*s^2 + 29580*s - 6048)/((7*s - 9)*(5*s - 8)*(4*s - 7)*(s - 1)^4*(s - 2)^2*s) complex roots: 0.6052, 1.0658 - 0.1622*i, 1.0658 + 0.1622*i, 1.2339, 1.6832 ess. value@infinity: 23/56 Topological ideal zeta function: poles: 0.0000, 0.4000, 0.5455, 0.5714, 0.5833, 0.6250, 0.6667, 1.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 2*(1386*s^3 - 2023*s^2 + 948*s - 140)*(2*s - 1)/((12*s - 7)*(11*s - 6)*(8*s - 5)*(7*s - 4)*(5*s - 2)*(3*s - 2)^2*(s - 1)*s) complex roots: 0.3023, 0.5000, 0.5520, 0.6053 ess. value@infinity: 1/60 ------------------------------------------------------------------------ ALGEBRA #257 ------------------------------------------------------------------------ names: 'C(5,8)' id: 273 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 5 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.5000, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/6*(7*s - 12)/((2*s - 3)*(s - 2)^4*s) complex roots: 1.7143 ess. value@infinity: 7/12 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 1.3333, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 2/((5*s - 6)*(3*s - 4)*(s - 1)*(s - 2)*s) complex roots: None ess. value@infinity: 2/15 ------------------------------------------------------------------------ ALGEBRA #258 ------------------------------------------------------------------------ names: 'C(5,9)' id: 274 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 5 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.2000, 1.2500, 1.2857, 1.3333, 1.4000, 1.4286, 1.4444, 1.5000, 1.5455, 1.5714, 1.6000, 1.6154, 1.6364, 1.6667 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/6*(21152086956000*s^15 - 423151417319400*s^14 + 3943558602184740*s^13 - 22711174555480221*s^12 + 90389215618290355*s^11 - 263338127267231139*s^10 + 580160351714746447*s^9 - 984196868957355745*s^8 + 1296189686685135409*s^7 - 1325261049322273033*s^6 + 1043313593653271505*s^5 - 621060214800949438*s^4 + 270600244961186328*s^3 - 81468766171906992*s^2 + 15154535967671520*s - 1312986795120000)/((13*s - 21)*(11*s - 17)*(11*s - 18)*(9*s - 13)*(7*s - 9)*(7*s - 10)*(7*s - 11)*(5*s - 6)^2*(5*s - 7)^2*(5*s - 8)*(4*s - 5)^2*(3*s - 4)*(3*s - 5)*(2*s - 3)^2*(s - 1)*s) complex roots: 0.8823, 0.9998 - 0.1851*i, 0.9998 + 0.1851*i, 1.2165, 1.2718, 1.3261 - 0.0518*i, 1.3261 + 0.0518*i, 1.3637, 1.4117 - 0.0088*i, 1.4117 + 0.0088*i, 1.4833, 1.5174, 1.5719, 1.6116 - 0.0136*i, 1.6116 + 0.0136*i ess. value@infinity: 121/300 Topological ideal zeta function: poles: 0.0000, 0.6667, 0.7500, 0.8000, 0.8571, 1.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 2*(35*s^2 - 42*s + 12)/((7*s - 6)*(5*s - 4)^2*(4*s - 3)*(3*s - 2)*(s - 1)*s) complex roots: 0.4691, 0.7309 ess. value@infinity: 1/30 ------------------------------------------------------------------------ ALGEBRA #259 ------------------------------------------------------------------------ names: 'C(6,2)' id: 275 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 6 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 3.0000, 4.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: (3*s - 5)/((2*s - 5)^2*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: 1.6667 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/((3*s - 5)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #260 ------------------------------------------------------------------------ names: 'C(6,3)' id: 276 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 6 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 2.2500, 2.5000, 2.6667, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/2*(78*s^3 - 403*s^2 + 673*s - 360)/((4*s - 9)*(3*s - 5)*(3*s - 8)*(2*s - 5)*(s - 1)*(s - 2)^2*(s - 3)*s) complex roots: 1.1571, 1.8303, 2.1793 ess. value@infinity: 13/24 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/20*(5*s - 4)/((3*s - 4)*(s - 1)^3*(s - 2)*(s - 3)*s) complex roots: 0.8000 ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #261 ------------------------------------------------------------------------ names: 'C(6,4)' id: 277 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 6 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/9*(17*s^2 - 50*s + 36)/((3*s - 5)*(s - 1)*(s - 2)^3*(s - 3)*(s - 4)*s) complex roots: 1.2585, 1.6827 ess. value@infinity: 17/27 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 4.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/5/((s - 1)^2*(s - 2)*(s - 3)*(s - 4)*s) complex roots: None ess. value@infinity: 1/5 ------------------------------------------------------------------------ ALGEBRA #262 ------------------------------------------------------------------------ names: 'C(6,5)' id: 278 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 6 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 1.7778, 1.8333, 2.0000, 2.2500, 2.4000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: (220320*s^7 - 2732208*s^6 + 14434662*s^5 - 42088815*s^4 + 73094297*s^3 - 75532858*s^2 + 42949558*s - 10349856)/((9*s - 16)*(6*s - 11)^3*(5*s - 12)*(4*s - 9)^2*(3*s - 5)*(s - 1)*(s - 2)^2*(s - 3)*s) complex roots: 1.0492, 1.6866 - 0.0762*i, 1.6866 + 0.0762*i, 1.7917, 2.0115 - 0.0724*i, 2.0115 + 0.0724*i, 2.1641 ess. value@infinity: 17/36 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/5/((3*s - 4)*(s - 1)^2*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 1/15 ------------------------------------------------------------------------ ALGEBRA #263 ------------------------------------------------------------------------ names: 'C(6,6)' id: 279 Lie: False commutative: True nilpotency class: 4 nilpotent: True rank: 6 soluble: True derived length: 2 associative: False Topological ideal zeta function: poles: 0.0000, 0.6000, 0.7143, 0.7500, 0.8000, 0.8750, 0.8889, 1.0000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/6*(5040*s^4 - 13845*s^3 + 14044*s^2 - 6215*s + 1008)/((9*s - 8)*(8*s - 7)*(7*s - 5)*(5*s - 3)*(5*s - 4)*(4*s - 3)*(s - 1)^2*(s - 2)*s) complex roots: 0.4514, 0.6770, 0.7863, 0.8324 ess. value@infinity: 1/60 ------------------------------------------------------------------------ ALGEBRA #264 ------------------------------------------------------------------------ names: 'C(6,7)' id: 280 Lie: False commutative: True nilpotency class: 4 nilpotent: True rank: 6 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.2500, 1.3333, 1.5000, 1.7143, 2.0000, 2.2000, 2.2500, 2.5000, 2.6667 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: (8280*s^5 - 60918*s^4 + 176591*s^3 - 251555*s^2 + 175380*s - 47520)/((7*s - 12)*(5*s - 11)*(4*s - 5)*(4*s - 9)*(3*s - 4)*(3*s - 8)*(2*s - 3)*(2*s - 5)*(s - 1)*(s - 2)*s) complex roots: 0.8089, 1.4445 - 0.2182*i, 1.4445 + 0.2182*i, 1.6769, 1.9824 ess. value@infinity: 23/56 Topological ideal zeta function: poles: 0.0000, 0.6000, 0.7143, 0.7273, 0.7500, 0.8750, 0.8889, 1.0000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 4*(154*s^3 - 309*s^2 + 201*s - 42)*(3*s - 2)/((11*s - 8)*(9*s - 8)*(8*s - 7)*(7*s - 5)*(5*s - 3)*(4*s - 3)*(s - 1)^2*(s - 2)*s) complex roots: 0.4556, 0.6667, 0.7233, 0.8275 ess. value@infinity: 1/60 ------------------------------------------------------------------------ ALGEBRA #265 ------------------------------------------------------------------------ names: 'C(6,8)' id: 281 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 6 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 2.6667, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/2*(14*s^2 - 49*s + 40)/((3*s - 8)*(2*s - 5)^2*(s - 1)*(s - 2)^2*(s - 3)*s) complex roots: 1.2968, 2.2032 ess. value@infinity: 7/12 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.6000, 1.6667, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 2/((5*s - 8)*(3*s - 5)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: None ess. value@infinity: 2/15 ------------------------------------------------------------------------ ALGEBRA #266 ------------------------------------------------------------------------ names: 'C(6,9)' id: 282 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 6 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 1.7143, 1.7500, 1.8000, 1.8750, 1.8889, 1.9000, 1.9091, 2.0000, 2.0714, 2.0769, 2.1667, 2.1818, 2.2000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/1260*(20306003477760000*s^17 - 625524424953120000*s^16 + 9057626381698171200*s^15 - 81877365020768680320*s^14 + 517487274818918916200*s^13 - 2426704538598780656300*s^12 + 8742853890932162544230*s^11 - 24717312849476062943161*s^10 + 55512951190411737341021*s^9 - 99606391224611410365833*s^8 + 142776664513046115170549*s^7 - 162556242061128199466175*s^6 + 145192942152832459184559*s^5 - 99595476073203752094327*s^4 + 50663300187748548610161*s^3 - 18007418579791943122524*s^2 + 3992439769890017685120*s - 415668720845285107200)/((14*s - 29)*(13*s - 27)*(11*s - 21)*(11*s - 24)*(10*s - 19)^2*(9*s - 17)*(8*s - 15)*(7*s - 12)*(6*s - 13)*(5*s - 9)^2*(5*s - 11)*(4*s - 7)^2*(3*s - 5)*(s - 1)*(s - 2)^5*s) complex roots: 1.0136, 1.4774 - 0.3474*i, 1.4774 + 0.3474*i, 1.7291, 1.7792, 1.8036 - 0.0819*i, 1.8036 + 0.0819*i, 1.8234 - 0.0227*i, 1.8234 + 0.0227*i, 1.8923, 1.9095, 1.9165 - 0.0206*i, 1.9165 + 0.0206*i, 2.0706, 2.0782, 2.1453 - 0.0323*i, 2.1453 + 0.0323*i ess. value@infinity: 121/300 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.1429, 1.2000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/30*(35*s - 24)/((7*s - 8)*(5*s - 6)*(s - 1)^3*(s - 2)*s) complex roots: 0.6857 ess. value@infinity: 1/30 ------------------------------------------------------------------------ ALGEBRA #267 ------------------------------------------------------------------------ names: 'C(6,10)' id: 283 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 6 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 1.6667, 1.7143, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/3200*(11657100*s^11 - 213081750*s^10 + 1767158385*s^9 - 8776374414*s^8 + 28999047006*s^7 - 66931292792*s^6 + 110098560983*s^5 - 129060759924*s^4 + 105643535726*s^3 - 57502225520*s^2 + 18728536800*s - 2764800000)/((7*s - 12)^2*(3*s - 5)^4*(2*s - 3)*(s - 1)*(s - 2)^7*(s - 3)*s) complex roots: 1.1322, 1.3364, 1.5415, 1.5741 - 0.1286*i, 1.5741 + 0.1286*i, 1.6883, 1.8755 - 0.1820*i, 1.8755 + 0.1820*i, 1.8777, 1.9018 - 0.0674*i, 1.9018 + 0.0674*i ess. value@infinity: 793/1728 Topological ideal zeta function: poles: 0.0000, 0.6667, 0.7143, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/2*(7*s - 4)/((7*s - 5)*(3*s - 2)*(3*s - 4)*(s - 1)*(s - 2)*(s - 3)*s) complex roots: 0.5714 ess. value@infinity: 1/18 ------------------------------------------------------------------------ ALGEBRA #268 ------------------------------------------------------------------------ names: 'C(6,19;0)' id: 292 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 6 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 1.7500, 1.7778, 1.8000, 1.8333, 2.0000, 2.2000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/7056*(34720812000*s^13 - 776417367600*s^12 + 8000947962000*s^11 - 50306131945512*s^10 + 215308335028338*s^9 - 662372541794643*s^8 + 1506796330037939*s^7 - 2566173790116152*s^6 + 3271659686744033*s^5 - 3083716474422428*s^4 + 2088512876939882*s^3 - 962398505053265*s^2 + 270419622473616*s - 34988805992448)/((9*s - 16)*(6*s - 11)^3*(5*s - 9)^2*(5*s - 11)*(4*s - 7)^2*(3*s - 5)*(s - 1)*(s - 2)^7*s) complex roots: 1.1359, 1.4110, 1.5353 - 0.1360*i, 1.5353 + 0.1360*i, 1.7629 - 0.0098*i, 1.7629 + 0.0098*i, 1.8075 - 0.0213*i, 1.8075 + 0.0213*i, 1.8099, 1.9045 - 0.0162*i, 1.9045 + 0.0162*i, 1.9924 - 0.0266*i, 1.9924 + 0.0266*i ess. value@infinity: 27/64 Topological ideal zeta function: poles: 0.0000, 0.7500, 1.0000, 1.2000, 1.3333, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/210*(455*s^3 - 1144*s^2 + 942*s - 252)/((5*s - 6)*(4*s - 3)*(3*s - 4)*(s - 1)^4*(s - 2)*s) complex roots: 0.6061, 0.9541 - 0.0589*i, 0.9541 + 0.0589*i ess. value@infinity: 13/360 ------------------------------------------------------------------------ ALGEBRA #269 ------------------------------------------------------------------------ names: 'C(6,22;0)' id: 297 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 6 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 2.2500, 2.4000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/9*(1072*s^4 - 7461*s^3 + 19150*s^2 - 21404*s + 8748)/((5*s - 12)*(4*s - 9)^2*(3*s - 5)*(s - 1)*(s - 2)^3*(s - 3)*s) complex roots: 1.1235, 1.6759, 2.0803 - 0.0818*i, 2.0803 + 0.0818*i ess. value@infinity: 67/135 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.3333, 1.5000, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/15*(8*s - 9)/((3*s - 4)*(2*s - 3)*(s - 1)^2*(s - 2)*(s - 3)*s) complex roots: 1.1250 ess. value@infinity: 4/45 ------------------------------------------------------------------------ ALGEBRA #270 ------------------------------------------------------------------------ names: 'C(6,23)' id: 299 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 6 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 1.6667, 1.7778, 1.8333, 1.8571, 1.8750, 1.8889, 2.0000, 2.0667, 2.0833, 2.0909, 2.1111, 2.1250, 2.2000, 2.2222 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/105840*(7656569020412928000*s^18 - 256098362074002201600*s^17 + 4040314741843835120640*s^16 - 39945727303449544185696*s^15 + 277332067303198479861696*s^14 - 1435724448094079306191368*s^13 + 5743279326694476168106524*s^12 - 18150531561351403413007428*s^11 + 45935588752816214780459901*s^10 - 93784671910453883289567231*s^9 + 154816973138568357937419625*s^8 - 206121824684395161912177287*s^7 + 219659481768774041443778011*s^6 - 184797573132869294665988125*s^5 + 120011608724929847752011503*s^4 - 58040088734716993157207665*s^3 + 19679098351732355331011700*s^2 - 4173220890976256256456000*s + 416426942452814092800000)/((15*s - 31)*(12*s - 25)*(11*s - 23)*(9*s - 16)*(9*s - 17)*(9*s - 19)*(9*s - 20)*(8*s - 15)*(8*s - 17)*(7*s - 13)*(6*s - 11)^3*(5*s - 11)^2*(3*s - 5)*(2*s - 3)*(s - 1)*(s - 2)^5*s) complex roots: 0.9020, 1.6444, 1.7681 - 0.1381*i, 1.7681 + 0.1381*i, 1.7697 - 0.2333*i, 1.7697 + 0.2333*i, 1.7921, 1.8580, 1.8730 - 0.0325*i, 1.8730 + 0.0325*i, 1.8732, 1.8903, 2.0667, 2.0801, 2.0909, 2.1202 - 0.0143*i, 2.1202 + 0.0143*i, 2.1884 ess. value@infinity: 1243/3240 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.1429, 1.2000, 1.2222, 1.3333, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/30*(63*s^2 - 130*s + 66)*(15*s - 16)/((9*s - 11)*(7*s - 8)*(5*s - 6)*(3*s - 4)*(s - 1)^3*(s - 2)*s) complex roots: 0.9018, 1.0667, 1.1617 ess. value@infinity: 1/30 ------------------------------------------------------------------------ ALGEBRA #271 ------------------------------------------------------------------------ names: 'C(6,24;0)' id: 300 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 6 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 1.5714, 1.6000, 1.6667, 1.7000, 1.7500, 1.7778, 1.8000, 1.8333, 1.8571, 1.8750, 1.8824, 1.8889, 1.9000, 1.9091, 1.9167, 1.9231, 2.0000, 2.0526, 2.0667, 2.1111, 2.1250, 2.1538, 2.2000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/3528*(18318478497368818728960000000*s^30 - 993999468573661828981248000000*s^29 + 26055884746354403433883622400000*s^28 - 439406265493012663314729570240000*s^27 + 5356254303307055494633486019760000*s^26 - 50271114171005244349404277230979200*s^25 + 377849671629715635421127100181210080*s^24 - 2335589486045237356493837292527518368*s^23 + 12098887623935468556734724078767382792*s^22 - 53257097466246665641781192680282841784*s^21 + 201271852073779099370236260650871305586*s^20 - 658164012875528613035973368070783098988*s^19 + 1873011618544262988103905187983038552456*s^18 - 4658176998311757604020009697140474197769*s^17 + 10152832726796496097911658062262809459061*s^16 - 19425013195798828290260921219160486212711*s^15 + 32640990275678875393894850666993552576029*s^14 - 48144662963005083121522820631977846614278*s^13 + 62228383229217492729189391946519561157348*s^12 - 70280920236845748019541625425846464998570*s^11 + 69065337952308025237634721945704678248194*s^10 - 58711814368070086543090117353892835282261*s^9 + 42839002179510474981087968338741060728069*s^8 - 26551451806950980322331870149295377119155*s^7 + 13785944650200736464350968438631034488129*s^6 - 5883885245439268299446636112929410310548*s^5 + 2010067614067392600278138404655778537696*s^4 - 528404438621382698836208667898062701568*s^3 + 100339746135152196976440019485628354560*s^2 - 12249078355994879081419637708692684800*s + 721778584617539142006209265008640000)/((19*s - 39)*(17*s - 32)*(15*s - 31)*(13*s - 25)*(13*s - 28)*(12*s - 23)*(11*s - 21)*(10*s - 17)*(10*s - 19)^2*(9*s - 16)^2*(9*s - 17)*(9*s - 19)*(8*s - 15)*(8*s - 17)*(7*s - 11)*(7*s - 13)*(6*s - 11)^2*(5*s - 8)*(5*s - 9)^2*(5*s - 11)*(4*s - 7)^2*(3*s - 5)^2*(2*s - 3)*(s - 1)*(s - 2)^5*s) complex roots: 0.8873, 1.5347, 1.5963 - 0.0724*i, 1.5963 + 0.0724*i, 1.6210 - 0.2537*i, 1.6210 + 0.2537*i, 1.6349, 1.7277, 1.7619 - 0.0103*i, 1.7619 + 0.0103*i, 1.7930, 1.8118 - 0.0075*i, 1.8118 + 0.0075*i, 1.8468 - 0.0611*i, 1.8468 + 0.0611*i, 1.8539, 1.8686 - 0.0153*i, 1.8686 + 0.0153*i, 1.8729, 1.8946, 1.9077, 1.9105 - 0.0355*i, 1.9105 + 0.0355*i, 1.9223, 1.9306, 2.0526, 2.0669, 2.1129, 2.1179 - 0.0264*i, 2.1179 + 0.0264*i ess. value@infinity: 227/630 Topological ideal zeta function: poles: 0.0000, 0.8750, 1.0000, 1.0714, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/60*(168*s^2 - 268*s + 105)/((14*s - 15)*(8*s - 7)*(s - 1)^4*(s - 2)*s) complex roots: 0.6918, 0.9034 ess. value@infinity: 1/40 ------------------------------------------------------------------------ ALGEBRA #272 ------------------------------------------------------------------------ names: 'C(6,25)' id: 302 Lie: False commutative: True nilpotency class: 3 nilpotent: True rank: 6 soluble: True derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 1.6667, 2.0000, 2.2000, 2.2500, 2.5000, 2.6667 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/2*(636*s^4 - 4176*s^3 + 10079*s^2 - 10523*s + 3960)/((5*s - 11)*(4*s - 9)*(3*s - 5)*(3*s - 8)*(2*s - 3)*(2*s - 5)*(s - 1)*(s - 2)^2*s) complex roots: 0.9442, 1.7896 - 0.1601*i, 1.7896 + 0.1601*i, 2.0426 ess. value@infinity: 53/120 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2000, 1.2222, 1.3333, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/120*(585*s^2 - 1130*s + 528)/((9*s - 11)*(5*s - 6)*(3*s - 4)*(s - 1)^3*(s - 2)*s) complex roots: 0.7919, 1.1397 ess. value@infinity: 13/360 ------------------------------------------------------------------------ ALGEBRA #273 ------------------------------------------------------------------------ names: 'C(6,26)' id: 303 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 6 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.1667, 2.2000, 2.2857 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/540*(262500*s^5 - 2248675*s^4 + 7655715*s^3 - 12954648*s^2 + 10888888*s - 3624192)/((7*s - 16)*(6*s - 13)*(5*s - 11)^2*(s - 1)*(s - 2)^5*s) complex roots: 1.1106, 1.5823 - 0.4429*i, 1.5823 + 0.4429*i, 2.1455 - 0.0303*i, 2.1455 + 0.0303*i ess. value@infinity: 25/54 Topological ideal zeta function: poles: 0.0000, 1.0000, 1.2500, 1.3333, 1.5000, 1.6000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 2*(12*s^2 - 27*s + 16)/((5*s - 8)*(4*s - 5)*(3*s - 4)^2*(2*s - 3)*(s - 1)*(s - 2)*s) complex roots: 1.1250 - 0.2602*i, 1.1250 + 0.2602*i ess. value@infinity: 1/15 ------------------------------------------------------------------------ ALGEBRA #274 ------------------------------------------------------------------------ names: 'csl(2,ZZ)' id: 304 Lie: False commutative: True nilpotent: False rank: 3 soluble: False associative: False description: Commutative version of sl(2,ZZ) Topological subalgebra zeta function: poles: 0.0000, 0.4286, 0.5000 order@zero: -2 degree: -3 ess. value@zero: -1/3 zeta: 1/3*(294*s^3 - 274*s^2 + 84*s - 9)*(3*s - 1)/((7*s - 3)^2*(2*s - 1)^3*s^2) complex roots: 0.2445 - 0.0966*i, 0.2445 + 0.0966*i, 0.3333, 0.4430 ess. value@infinity: 3/4 Topological ideal zeta function: ess. value@zero: 0 zeta: 0 order@zero: +Infinity degree: -Infinity ess. value@infinity: 0 ------------------------------------------------------------------------ ALGEBRA #275 ------------------------------------------------------------------------ names: 'CLie(2)' id: 305 Lie: False commutative: True nilpotent: False rank: 2 soluble: True derived length: 2 associative: False description: Commutative version of Lie(2) Topological subalgebra zeta function: poles: 0.0000, 0.5000 order@zero: -1 degree: -2 ess. value@zero: -2 zeta: 2/((2*s - 1)*s) complex roots: None ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000 order@zero: -2 degree: -2 ess. value@zero: 1/2 zeta: 1/2/s^2 complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #276 ------------------------------------------------------------------------ names: 'Tr(2,ZZ)' id: 306 Lie: False commutative: False nilpotent: False rank: 3 soluble: False associative: True description: Associative ring of upper triangular 2x2 matrices over ZZ Topological subalgebra zeta function: poles: 0.0000, 0.6667, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 2 zeta: 4/((3*s - 2)*(s - 1)*s) complex roots: None ess. value@infinity: 4/3 Topological ideal zeta function: poles: 0.0000 order@zero: -3 degree: -3 ess. value@zero: 1/3 zeta: 1/3/s^3 complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #277 ------------------------------------------------------------------------ names: '(ZZ^2,*)' id: 307 Lie: False commutative: True nilpotent: False rank: 2 soluble: False associative: True description: ZZ^2 with componentwise multiplication Topological subalgebra zeta function: poles: 0.0000, 0.3333 order@zero: -1 degree: -2 ess. value@zero: -4 zeta: 4/((3*s - 1)*s) complex roots: None ess. value@infinity: 4/3 Topological ideal zeta function: poles: 0.0000 order@zero: -2 degree: -2 ess. value@zero: 1 zeta: s^(-2) complex roots: None ess. value@infinity: 1 ------------------------------------------------------------------------ ALGEBRA #278 ------------------------------------------------------------------------ names: 'ZZ[X]/X^2' id: 308 Lie: False commutative: True nilpotent: False rank: 2 soluble: False associative: True Topological subalgebra zeta function: poles: 0.0000, 0.5000 order@zero: -1 degree: -2 ess. value@zero: -2 zeta: 2/((2*s - 1)*s) complex roots: None ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 0.5000 order@zero: -1 degree: -2 ess. value@zero: -1 zeta: 1/((2*s - 1)*s) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #279 ------------------------------------------------------------------------ names: '(ZZ^3,*)' id: 309 Lie: False commutative: True nilpotent: False rank: 3 soluble: False associative: True description: ZZ^3 with componentwise multiplication Topological ideal zeta function: poles: 0.0000 order@zero: -3 degree: -3 ess. value@zero: 1 zeta: s^(-3) complex roots: None ess. value@infinity: 1 ------------------------------------------------------------------------ ALGEBRA #280 ------------------------------------------------------------------------ names: '(ZZ^2,*) (+) (ZZ,0)' id: 310 Lie: False commutative: True nilpotent: False rank: 3 soluble: False associative: True Topological subalgebra zeta function: poles: 0.0000, 0.5000, 0.6000, 0.6667 order@zero: -2 degree: -3 ess. value@zero: -1/3 zeta: 2*(20*s^2 - 11*s + 1)/((5*s - 3)*(3*s - 2)*(2*s - 1)*s^2) complex roots: 0.1149, 0.4351 ess. value@infinity: 4/3 Topological ideal zeta function: poles: 0.0000 order@zero: -3 degree: -3 ess. value@zero: 1 zeta: s^(-3) complex roots: None ess. value@infinity: 1 ------------------------------------------------------------------------ ALGEBRA #281 ------------------------------------------------------------------------ names: '(ZZ^2,*) (+) (ZZ^2,0)' id: 311 Lie: False commutative: True nilpotent: False rank: 4 soluble: False associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000 order@zero: -2 degree: -4 ess. value@zero: 1/5 zeta: 1/30*(40*s^3 - 76*s^2 + 43*s - 6)/((s - 1)^5*s^2) complex roots: 0.2070, 0.8465 - 0.0892*i, 0.8465 + 0.0892*i ess. value@infinity: 4/3 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -3 degree: -4 ess. value@zero: -1 zeta: 1/((s - 1)*s^3) complex roots: None ess. value@infinity: 1 ------------------------------------------------------------------------ ALGEBRA #282 ------------------------------------------------------------------------ names: 'ZZ[X]/X^2 (+) (ZZ,0)' id: 312 Lie: False commutative: True nilpotent: False rank: 3 soluble: False associative: True Topological subalgebra zeta function: poles: 0.0000, 0.7500, 1.0000 order@zero: -2 degree: -3 ess. value@zero: -1/3 zeta: (4*s - 1)/((4*s - 3)*(s - 1)*s^2) complex roots: 0.2500 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 0.5000 order@zero: -2 degree: -3 ess. value@zero: -1 zeta: 1/((2*s - 1)*s^2) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #283 ------------------------------------------------------------------------ names: 'ZZ[X]/X^2 (+) (ZZ,*)' id: 313 Lie: False commutative: True nilpotent: False rank: 3 soluble: False associative: True Topological subalgebra zeta function: poles: 0.0000, 0.5000, 0.6000, 0.6667 order@zero: -2 degree: -3 ess. value@zero: -1/3 zeta: 2*(20*s^2 - 11*s + 1)/((5*s - 3)*(3*s - 2)*(2*s - 1)*s^2) complex roots: 0.1149, 0.4351 ess. value@infinity: 4/3 Topological ideal zeta function: poles: 0.0000, 0.5000 order@zero: -2 degree: -3 ess. value@zero: -1 zeta: 1/((2*s - 1)*s^2) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #284 ------------------------------------------------------------------------ names: 'ZZ[X]/X^3' id: 314 Lie: False commutative: True nilpotent: False rank: 3 soluble: False associative: True Topological subalgebra zeta function: poles: 0.0000, 0.6667, 0.8000 order@zero: -1 degree: -3 ess. value@zero: 1 zeta: 2*(15*s - 8)/((5*s - 4)*(3*s - 2)^2*s) complex roots: 0.5333 ess. value@infinity: 2/3 Topological ideal zeta function: poles: 0.0000, 0.5000, 0.6667 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/((3*s - 2)*(2*s - 1)*s) complex roots: None ess. value@infinity: 1/6 ------------------------------------------------------------------------ ALGEBRA #285 ------------------------------------------------------------------------ names: 'ZZ[X]/X^2 (+) (ZZ^2,0)' id: 315 Lie: False commutative: True nilpotent: False rank: 4 soluble: False associative: True Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.2500, 1.3333, 1.5000 order@zero: -2 degree: -4 ess. value@zero: 1/5 zeta: 2*(12*s^2 - 19*s + 6)/((4*s - 5)*(3*s - 4)*(2*s - 3)*(s - 1)*s^2) complex roots: 0.4357, 1.1477 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 0.5000, 1.0000 order@zero: -2 degree: -4 ess. value@zero: 1 zeta: 1/((2*s - 1)*(s - 1)*s^2) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #286 ------------------------------------------------------------------------ names: 'ZZ[X]/X^3 (+) (ZZ,0)' id: 316 Lie: False commutative: True nilpotent: False rank: 4 soluble: False associative: True Topological subalgebra zeta function: poles: 0.0000, 0.6667, 0.8333, 1.0000, 1.0588, 1.1429, 1.1667, 1.2000 order@zero: -2 degree: -4 ess. value@zero: 1/5 zeta: 8/5*(26775*s^5 - 108930*s^4 + 173267*s^3 - 134415*s^2 + 50862*s - 7560)/((17*s - 18)*(7*s - 8)*(6*s - 5)*(6*s - 7)*(5*s - 6)*(3*s - 2)*(s - 1)*s^2) complex roots: 0.5046 - 0.1107*i, 0.5046 + 0.1107*i, 0.9845 - 0.0370*i, 0.9845 + 0.0370*i, 1.0902 ess. value@infinity: 2/3 Topological ideal zeta function: poles: 0.0000, 0.5000, 0.6667 order@zero: -2 degree: -4 ess. value@zero: 1/2 zeta: 1/((3*s - 2)*(2*s - 1)*s^2) complex roots: None ess. value@infinity: 1/6 ------------------------------------------------------------------------ ALGEBRA #287 ------------------------------------------------------------------------ names: 'ZZ[X]/X^3 (+) (ZZ,*)' id: 317 Lie: False commutative: True nilpotent: False rank: 4 soluble: False associative: True Topological ideal zeta function: poles: 0.0000, 0.5000, 0.6667 order@zero: -2 degree: -4 ess. value@zero: 1/2 zeta: 1/((3*s - 2)*(2*s - 1)*s^2) complex roots: None ess. value@infinity: 1/6 ------------------------------------------------------------------------ ALGEBRA #288 ------------------------------------------------------------------------ names: 'ZZ[X]/X^4' id: 318 Lie: False commutative: True nilpotent: False rank: 4 soluble: False associative: True Topological subalgebra zeta function: poles: 0.0000, 0.7500, 0.8333, 1.0000 order@zero: -1 degree: -4 ess. value@zero: -1/3 zeta: 1/168480*(2021760*s^5 - 8509620*s^4 + 14322332*s^3 - 12036071*s^2 + 5044460*s - 842400)/((6*s - 5)*(4*s - 3)*(s - 1)^6*s) complex roots: 0.6399, 0.8589 - 0.0416*i, 0.8589 + 0.0416*i, 0.9257 - 0.1540*i, 0.9257 + 0.1540*i ess. value@infinity: 1/2 Topological ideal zeta function: poles: 0.0000, 0.5000, 0.6667, 0.7500 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/((4*s - 3)*(3*s - 2)*(2*s - 1)*s) complex roots: None ess. value@infinity: 1/24 ------------------------------------------------------------------------ ALGEBRA #289 ------------------------------------------------------------------------ names: 'ZZ[X]/X^2 (+) ZZ[X]/X^2' id: 319 Lie: False commutative: True nilpotent: False rank: 4 soluble: False associative: True Topological ideal zeta function: poles: 0.0000, 0.5000 order@zero: -2 degree: -4 ess. value@zero: 1 zeta: 1/((2*s - 1)^2*s^2) complex roots: None ess. value@infinity: 1/4 ------------------------------------------------------------------------ ALGEBRA #290 ------------------------------------------------------------------------ names: 'ZZ[X]/X^2 (+) (ZZ,*) (+) (ZZ,0)' id: 320 Lie: False commutative: True nilpotent: False rank: 4 soluble: False associative: True Topological subalgebra zeta function: poles: 0.0000, 0.5000, 0.7500, 0.9000, 0.9091, 1.0000 order@zero: -2 degree: -4 ess. value@zero: 11/15 zeta: 1/3*(14080*s^6 - 60144*s^5 + 106346*s^4 - 99849*s^3 + 52701*s^2 - 14913*s + 1782)/((11*s - 10)*(10*s - 9)*(4*s - 3)^2*(2*s - 1)*(s - 1)^3*s^2) complex roots: 0.4747 - 0.2127*i, 0.4747 + 0.2127*i, 0.6940, 0.8617, 0.8832 - 0.0452*i, 0.8832 + 0.0452*i ess. value@infinity: 4/3 Topological ideal zeta function: poles: 0.0000, 0.5000 order@zero: -3 degree: -4 ess. value@zero: -1 zeta: 1/((2*s - 1)*s^3) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #291 ------------------------------------------------------------------------ names: 'X*ZZ[X]/X^3' id: 321 Lie: False commutative: True nilpotency class: 2 nilpotent: True rank: 2 soluble: True derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.6667 order@zero: -1 degree: -2 ess. value@zero: -1 zeta: 2/((3*s - 2)*s) complex roots: None ess. value@infinity: 2/3 Topological ideal zeta function: poles: 0.0000, 0.5000 order@zero: -1 degree: -2 ess. value@zero: -1 zeta: 1/((2*s - 1)*s) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #292 ------------------------------------------------------------------------ names: 'uv' id: 323 Lie: False commutative: True nilpotent: False rank: 3 soluble: False associative: False Topological subalgebra zeta function: poles: 0.0000, 0.5000, 0.6000, 0.6667 order@zero: -1 degree: -3 ess. value@zero: 19/9 zeta: 2/3*(45*s - 19)/((5*s - 3)*(3*s - 2)*(2*s - 1)*s) complex roots: 0.4222 ess. value@infinity: 1 Topological ideal zeta function: poles: 0.0000, 0.5000 order@zero: -2 degree: -3 ess. value@zero: -1/3 zeta: 1/3/((2*s - 1)*s^2) complex roots: None ess. value@infinity: 1/6 ------------------------------------------------------------------------ ALGEBRA #293 ------------------------------------------------------------------------ names: 'Cycle(123)' id: 324 Lie: False commutative: True nilpotent: False rank: 3 soluble: False associative: False Topological subalgebra zeta function: poles: 0.0000, 0.4286, 0.5000 order@zero: -2 degree: -3 ess. value@zero: -7/9 zeta: 1/3*(15*s - 7)*(5*s - 1)/((7*s - 3)*(2*s - 1)^2*s^2) complex roots: 0.2000, 0.4667 ess. value@infinity: 25/28 Topological ideal zeta function: ess. value@zero: 0 zeta: 0 order@zero: +Infinity degree: -Infinity ess. value@infinity: 0 ------------------------------------------------------------------------ ALGEBRA #294 ------------------------------------------------------------------------ names: id: 325 Lie: False commutative: True nilpotent: False rank: 3 soluble: False associative: False Topological subalgebra zeta function: poles: 0.0000, 0.5000, 0.6000, 0.6667 order@zero: -2 degree: -3 ess. value@zero: -2/3 zeta: 4/3*(30*s^2 - 20*s + 3)/((5*s - 3)*(3*s - 2)*(2*s - 1)*s^2) complex roots: 0.2279, 0.4387 ess. value@infinity: 4/3 Topological ideal zeta function: poles: 0.0000 order@zero: -3 degree: -3 ess. value@zero: 1/2 zeta: 1/2/s^3 complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #295 ------------------------------------------------------------------------ names: id: 326 Lie: False commutative: True nilpotent: False rank: 4 soluble: False associative: False Topological subalgebra zeta function: poles: 0.0000, 1.0000 order@zero: -2 degree: -4 ess. value@zero: 2/5 zeta: 1/45*(60*s^3 - 128*s^2 + 87*s - 18)/((s - 1)^5*s^2) complex roots: 0.3886, 0.8724 - 0.1047*i, 0.8724 + 0.1047*i ess. value@infinity: 4/3 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -3 degree: -4 ess. value@zero: -1/2 zeta: 1/2/((s - 1)*s^3) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #296 ------------------------------------------------------------------------ names: id: 327 Lie: False commutative: True nilpotent: False rank: 3 soluble: False associative: False Topological subalgebra zeta function: poles: 0.0000, 0.4286, 0.5000 order@zero: -2 degree: -3 ess. value@zero: -2/9 zeta: 2/3*(125*s^3 - 111*s^2 + 27*s - 1)/((7*s - 3)*(2*s - 1)^3*s^2) complex roots: 0.0449, 0.4215 - 0.0209*i, 0.4215 + 0.0209*i ess. value@infinity: 125/84 Topological ideal zeta function: poles: 0.0000 order@zero: -3 degree: -3 ess. value@zero: 1/2 zeta: 1/2/s^3 complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #297 ------------------------------------------------------------------------ names: id: 328 Lie: False commutative: False nilpotent: False rank: 3 soluble: False associative: False Topological subalgebra zeta function: poles: 0.0000, 0.3750, 0.4000, 0.5000 order@zero: -1 degree: -3 ess. value@zero: 47/18 zeta: 1/6*(3840*s^4 - 6132*s^3 + 3651*s^2 - 960*s + 94)/((8*s - 3)*(5*s - 2)*(2*s - 1)^4*s) complex roots: 0.3186, 0.3812, 0.4485 - 0.0193*i, 0.4485 + 0.0193*i ess. value@infinity: 1 Topological ideal zeta function: ess. value@zero: 0 zeta: 0 order@zero: +Infinity degree: -Infinity ess. value@infinity: 0 ------------------------------------------------------------------------ ALGEBRA #298 ------------------------------------------------------------------------ names: id: 329 Lie: False commutative: False nilpotent: False rank: 4 soluble: False associative: False Topological subalgebra zeta function: poles: 0.0000, 0.5000, 0.5556, 0.6000, 0.6364, 0.6667, 0.6923, 0.7143, 0.7500, 0.8000 order@zero: -1 degree: -4 ess. value@zero: -439/480 zeta: 1/8*(10897286400*s^10 - 65761563420*s^9 + 177725729355*s^8 - 283096315026*s^7 + 294111735544*s^6 - 208041908802*s^5 + 101349701397*s^4 - 33523685528*s^3 + 7190380152*s^2 - 900424080*s + 49782600)/((13*s - 9)*(11*s - 7)*(9*s - 5)*(7*s - 5)^2*(5*s - 3)*(5*s - 4)*(4*s - 3)^2*(3*s - 2)^3*(2*s - 1)*s) complex roots: 0.2484, 0.5474, 0.5926, 0.6122 - 0.0660*i, 0.6122 + 0.0660*i, 0.6396, 0.6800 - 0.0088*i, 0.6800 + 0.0088*i, 0.6977, 0.7246 ess. value@infinity: 1 Topological ideal zeta function: ess. value@zero: 0 zeta: 0 order@zero: +Infinity degree: -Infinity ess. value@infinity: 0 ------------------------------------------------------------------------ ALGEBRA #299 ------------------------------------------------------------------------ names: 'Mod(U_2(ZZ))', 'Mod(U_2)', 'Mod(Triv(2))' id: 330 Lie: True associative: True commutative: True rank: 2 Topological subalgebra zeta function: poles: 0.0000, 0.5000 order@zero: -1 degree: -2 ess. value@zero: -1 zeta: 1/((2*s - 1)*s) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #300 ------------------------------------------------------------------------ names: 'Mod(U_2 x U_1)' id: 331 Lie: True associative: True commutative: True rank: 3 Topological subalgebra zeta function: poles: 0.0000, 1.0000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/2/((s - 1)^2*s) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #301 ------------------------------------------------------------------------ names: 'Mod(U_3(ZZ))', 'Mod(U_3)' id: 332 Lie: True associative: True commutative: True rank: 3 Topological subalgebra zeta function: poles: 0.0000, 0.3333, 0.5000 order@zero: -1 degree: -3 ess. value@zero: 1/2 zeta: 1/2*(4*s - 1)/((3*s - 1)*(2*s - 1)^2*s) complex roots: 0.2500 ess. value@infinity: 1/6 ------------------------------------------------------------------------ ALGEBRA #302 ------------------------------------------------------------------------ names: 'Mod(U_2 x U_1 x U_1)', 'Mod(U_2 x U_1^2)' id: 333 Lie: True associative: True commutative: True rank: 4 Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 2.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/((2*s - 3)*(s - 1)*(s - 2)*s) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #303 ------------------------------------------------------------------------ names: 'Mod(U_2 x U_2)', 'Mod(U_2^2)' id: 334 Lie: True associative: True commutative: True rank: 4 Topological subalgebra zeta function: poles: 0.0000, 1.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/12*(3*s - 2)/((s - 1)^4*s) complex roots: 0.6667 ess. value@infinity: 1/4 ------------------------------------------------------------------------ ALGEBRA #304 ------------------------------------------------------------------------ names: 'Mod(U_3 x U_1)' id: 335 Lie: True associative: True commutative: True rank: 4 Topological subalgebra zeta function: poles: 0.0000, 0.6667, 0.7500, 1.0000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: (2*s - 1)/((4*s - 3)*(3*s - 2)*(s - 1)^2*s) complex roots: 0.5000 ess. value@infinity: 1/6 ------------------------------------------------------------------------ ALGEBRA #305 ------------------------------------------------------------------------ names: 'Mod(U_4(ZZ))', 'Mod(U_4)' id: 336 Lie: True associative: True commutative: True rank: 4 Topological subalgebra zeta function: poles: 0.0000, 0.2500, 0.3333, 0.4000, 0.4286, 0.5000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/8*(3360*s^5 - 5192*s^4 + 3139*s^3 - 930*s^2 + 136*s - 8)/((7*s - 3)*(5*s - 2)*(4*s - 1)*(3*s - 1)^2*(2*s - 1)^3*s) complex roots: 0.1880 - 0.0728*i, 0.1880 + 0.0728*i, 0.3630 - 0.0196*i, 0.3630 + 0.0196*i, 0.4432 ess. value@infinity: 1/24 ------------------------------------------------------------------------ ALGEBRA #306 ------------------------------------------------------------------------ names: 'Mod(U_2 x U_1 x U_1 x U_1)', 'Mod(U_2 x U_1^3)' id: 337 Lie: True associative: True commutative: True rank: 5 Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/2/((s - 1)*(s - 2)^2*(s - 3)*s) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #307 ------------------------------------------------------------------------ names: 'Mod(U_2^2 x U_1)' id: 338 Lie: True associative: True commutative: True rank: 5 Topological subalgebra zeta function: poles: 0.0000, 1.3333, 1.5000, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 3/((3*s - 4)*(2*s - 3)^2*(s - 2)*s) complex roots: None ess. value@infinity: 1/4 ------------------------------------------------------------------------ ALGEBRA #308 ------------------------------------------------------------------------ names: 'Mod(U_3 x U_1 x U_1)', 'Mod(U_3 x U_1^2)' id: 339 Lie: True associative: True commutative: True rank: 5 Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.5000, 2.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/12*(4*s - 3)/((2*s - 3)*(s - 1)^3*(s - 2)*s) complex roots: 0.7500 ess. value@infinity: 1/6 ------------------------------------------------------------------------ ALGEBRA #309 ------------------------------------------------------------------------ names: 'Mod(U_3 x U_2)' id: 340 Lie: True associative: True commutative: True rank: 5 Topological subalgebra zeta function: poles: 0.0000, 0.6667, 0.7500, 0.8000, 1.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/36*(180*s^4 - 489*s^3 + 490*s^2 - 216*s + 36)/((5*s - 4)*(4*s - 3)*(3*s - 2)*(s - 1)^5*s) complex roots: 0.4886 - 0.1576*i, 0.4886 + 0.1576*i, 0.8697 - 0.0493*i, 0.8697 + 0.0493*i ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #310 ------------------------------------------------------------------------ names: 'Mod(U_4 x U_1)' id: 341 Lie: True associative: True commutative: True rank: 5 Topological subalgebra zeta function: poles: 0.0000, 0.5000, 0.5714, 0.6000, 0.6667, 0.7500, 1.0000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/12*(3360*s^5 - 8584*s^4 + 8671*s^3 - 4338*s^2 + 1080*s - 108)/((7*s - 4)*(5*s - 3)*(4*s - 3)^2*(3*s - 2)*(2*s - 1)^2*(s - 1)^2*s) complex roots: 0.3546 - 0.1158*i, 0.3546 + 0.1158*i, 0.5465, 0.6495 - 0.0285*i, 0.6495 + 0.0285*i ess. value@infinity: 1/24 ------------------------------------------------------------------------ ALGEBRA #311 ------------------------------------------------------------------------ names: 'Mod(U_5(ZZ))', 'Mod(U_5)' id: 342 Lie: True commutative: True rank: 5 associative: True description: Natural module of U_5(ZZ) acting on ZZ^5 Topological subalgebra zeta function: poles: 0.0000, 0.2000, 0.2500, 0.2857, 0.3000, 0.3333, 0.3636, 0.3750, 0.4000, 0.4286, 0.4444, 0.4615, 0.5000 order@zero: -1 degree: -5 ess. value@zero: 1/24 zeta: 1/36*(435891456000*s^14 - 1957609382400*s^13 + 4053337786080*s^12 - 5128457632240*s^11 + 4429884320966*s^10 - 2763848527457*s^9 + 1284781950540*s^8 - 452226036325*s^7 + 121188554644*s^6 - 24624421916*s^5 + 3737984412*s^4 - 411498360*s^3 + 31087152*s^2 - 1443744*s + 31104)/((13*s - 6)*(11*s - 4)*(10*s - 3)*(9*s - 4)*(8*s - 3)*(7*s - 2)*(7*s - 3)*(5*s - 1)*(5*s - 2)^2*(4*s - 1)^2*(3*s - 1)^2*(2*s - 1)^4*s) complex roots: 0.1423, 0.1524 - 0.1123*i, 0.1524 + 0.1123*i, 0.2666 - 0.0084*i, 0.2666 + 0.0084*i, 0.3077, 0.3490 - 0.0288*i, 0.3490 + 0.0288*i, 0.3789 - 0.0116*i, 0.3789 + 0.0116*i, 0.4141, 0.4315 - 0.0133*i, 0.4315 + 0.0133*i, 0.4703 ess. value@infinity: 1/120 ------------------------------------------------------------------------ ALGEBRA #312 ------------------------------------------------------------------------ names: 'Mod(U_2 x U_1^4)' id: 343 Lie: True associative: True commutative: True rank: 6 Topological subalgebra zeta function: poles: 0.0000, 1.0000, 2.0000, 2.5000, 3.0000, 4.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/((2*s - 5)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s) complex roots: None ess. value@infinity: 1/2 ------------------------------------------------------------------------ ALGEBRA #313 ------------------------------------------------------------------------ names: 'Mod(U_2^2 x U_1^2)' id: 344 Lie: True associative: True commutative: True rank: 6 Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.6667, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/4*(3*s - 4)/((3*s - 5)*(s - 1)*(s - 2)^3*(s - 3)*s) complex roots: 1.3333 ess. value@infinity: 1/4 ------------------------------------------------------------------------ ALGEBRA #314 ------------------------------------------------------------------------ names: 'Mod(U_2^3)' id: 345 Lie: True associative: True commutative: True rank: 6 Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.2500, 1.3333, 1.5000, 1.6000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: (60*s^3 - 191*s^2 + 201*s - 72)/((5*s - 8)*(4*s - 5)*(3*s - 4)*(2*s - 3)^3*(s - 1)*(s - 2)*s) complex roots: 0.8837 - 0.2581*i, 0.8837 + 0.2581*i, 1.4160 ess. value@infinity: 1/8 ------------------------------------------------------------------------ ALGEBRA #315 ------------------------------------------------------------------------ names: 'Mod(U_3 x U_1^3)' id: 346 Lie: True associative: True commutative: True rank: 6 Topological subalgebra zeta function: poles: 0.0000, 1.2500, 1.3333, 2.0000, 3.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 2/((4*s - 5)*(3*s - 4)*(s - 2)^2*(s - 3)*s) complex roots: None ess. value@infinity: 1/6 ------------------------------------------------------------------------ ALGEBRA #316 ------------------------------------------------------------------------ names: 'Mod(U_3 x U_2 x U_1)' id: 347 Lie: True associative: True commutative: True rank: 6 Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.3333, 1.5000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/60*(180*s^4 - 690*s^3 + 979*s^2 - 612*s + 144)/((3*s - 4)^2*(2*s - 3)^2*(s - 1)^4*(s - 2)*s) complex roots: 0.7161 - 0.2000*i, 0.7161 + 0.2000*i, 1.2006 - 0.0764*i, 1.2006 + 0.0764*i ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #317 ------------------------------------------------------------------------ names: 'Mod(U_3 x U_3)', 'Mod(U_3^2)' id: 348 Lie: True associative: True commutative: True rank: 6 Topological subalgebra zeta function: poles: 0.0000, 0.6000, 0.6667, 0.7143, 0.7500, 0.8000, 0.8571, 1.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/648*(793800*s^9 - 4912110*s^8 + 13409001*s^7 - 21208645*s^6 + 21445130*s^5 - 14400213*s^4 + 6435207*s^3 - 1849878*s^2 + 311040*s - 23328)/((7*s - 5)*(7*s - 6)*(5*s - 3)*(5*s - 4)*(4*s - 3)*(3*s - 2)^2*(s - 1)^7*s) complex roots: 0.3963, 0.4178 - 0.2591*i, 0.4178 + 0.2591*i, 0.6786, 0.7184, 0.8268, 0.9053, 0.9136 - 0.0799*i, 0.9136 + 0.0799*i ess. value@infinity: 1/36 ------------------------------------------------------------------------ ALGEBRA #318 ------------------------------------------------------------------------ names: 'Mod(U_4 x U_1^2)' id: 349 Lie: True associative: True commutative: True rank: 6 Topological subalgebra zeta function: poles: 0.0000, 0.6667, 0.7143, 0.7500, 0.8000, 1.0000, 1.5000, 2.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/32*(1120*s^5 - 3992*s^4 + 5637*s^3 - 3948*s^2 + 1376*s - 192)/((7*s - 5)*(5*s - 4)*(4*s - 3)*(3*s - 2)*(2*s - 3)*(s - 1)^4*(s - 2)*s) complex roots: 0.5193 - 0.1443*i, 0.5193 + 0.1443*i, 0.7274, 0.8991 - 0.0532*i, 0.8991 + 0.0532*i ess. value@infinity: 1/24 ------------------------------------------------------------------------ ALGEBRA #319 ------------------------------------------------------------------------ names: 'Mod(U_4 x U_2)' id: 350 Lie: True associative: True commutative: True rank: 6 Topological subalgebra zeta function: poles: 0.0000, 0.5000, 0.5714, 0.6000, 0.6250, 0.6667, 0.7500, 0.8000, 0.8571, 0.8889, 0.9000, 1.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/12*(42336000*s^12 - 332018400*s^11 + 1186079760*s^10 - 2552470644*s^9 + 3686349053*s^8 - 3765420755*s^7 + 2790738712*s^6 - 1513116364*s^5 + 596113296*s^4 - 166561128*s^3 + 31358232*s^2 - 3574368*s + 186624)/((10*s - 9)*(9*s - 8)*(8*s - 5)*(7*s - 4)*(7*s - 6)*(5*s - 3)*(5*s - 4)*(4*s - 3)^2*(3*s - 2)*(2*s - 1)^2*(s - 1)^5*s) complex roots: 0.3490, 0.3793 - 0.2207*i, 0.3793 + 0.2207*i, 0.5391, 0.6181, 0.6632 - 0.0567*i, 0.6632 + 0.0567*i, 0.7712, 0.8381, 0.8590 - 0.0786*i, 0.8590 + 0.0786*i, 0.9241 ess. value@infinity: 1/48 ------------------------------------------------------------------------ ALGEBRA #320 ------------------------------------------------------------------------ names: 'Mod(U_5 x U_1)' id: 351 Lie: True associative: True commutative: True rank: 6 Topological subalgebra zeta function: poles: 0.0000, 0.3750, 0.4000, 0.4286, 0.4444, 0.4545, 0.5000, 0.5455, 0.5714, 0.6000, 0.6667, 0.6923, 0.7500, 1.0000 order@zero: -1 degree: -6 ess. value@zero: -1/120 zeta: 1/48*(479480601600*s^14 - 3353436979200*s^13 + 10835736034176*s^12 - 21441840172880*s^11 + 29031859826547*s^10 - 28457484231924*s^9 + 20830412128130*s^8 - 11570736088224*s^7 + 4903227228015*s^6 - 1578206609388*s^5 + 380029898988*s^4 - 66427903008*s^3 + 7972717248*s^2 - 588425472*s + 20155392)/((13*s - 9)*(11*s - 5)*(11*s - 6)*(9*s - 4)*(8*s - 3)*(7*s - 3)*(7*s - 4)*(5*s - 2)*(5*s - 3)^2*(4*s - 3)^2*(3*s - 2)^3*(2*s - 1)^2*(s - 1)^2*s) complex roots: 0.2584, 0.2765 - 0.1686*i, 0.2765 + 0.1686*i, 0.4376 - 0.0119*i, 0.4376 + 0.0119*i, 0.4795 - 0.0107*i, 0.4795 + 0.0107*i, 0.5585 - 0.0209*i, 0.5585 + 0.0209*i, 0.5878, 0.6363, 0.6503 - 0.0587*i, 0.6503 + 0.0587*i, 0.7067 ess. value@infinity: 1/120 ------------------------------------------------------------------------ ALGEBRA #321 ------------------------------------------------------------------------ names: 'Mod(U_3 x U_2 x U_2)', 'Mod(U_3 x U_2^2)' id: 352 Lie: True associative: True commutative: True rank: 7 Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.2500, 1.3333, 1.4286, 1.5000, 1.6000, 2.0000 order@zero: -1 degree: -7 ess. value@zero: 1/720 zeta: 1/240*(201600*s^9 - 1954560*s^8 + 8373080*s^7 - 20814824*s^6 + 33119589*s^5 - 35018799*s^4 + 24638064*s^3 - 11139024*s^2 + 2940480*s - 345600)/((7*s - 10)*(5*s - 8)*(4*s - 5)*(3*s - 4)^2*(2*s - 3)^4*(s - 1)^5*(s - 2)*s) complex roots: 0.6540, 0.7055 - 0.3653*i, 0.7055 + 0.3653*i, 1.1331 - 0.1497*i, 1.1331 + 0.1497*i, 1.1563, 1.3038, 1.4521 - 0.0275*i, 1.4521 + 0.0275*i ess. value@infinity: 1/24 ------------------------------------------------------------------------ ALGEBRA #322 ------------------------------------------------------------------------ names: 'Mod(U_2^4)' id: 353 Lie: True associative: True commutative: True rank: 8 Topological subalgebra zeta function: poles: 0.0000, 1.0000, 1.4000, 1.5000, 1.6667, 2.0000, 2.1429, 3.0000 order@zero: -1 degree: -8 ess. value@zero: -1/5040 zeta: 1/80*(1050*s^5 - 7045*s^4 + 18885*s^3 - 25452*s^2 + 17360*s - 4800)/((7*s - 15)*(5*s - 7)*(3*s - 5)*(2*s - 3)*(s - 1)*(s - 2)^6*(s - 3)*s) complex roots: 1.0115, 1.0828 - 0.5223*i, 1.0828 + 0.5223*i, 1.7663 - 0.0873*i, 1.7663 + 0.0873*i ess. value@infinity: 1/16 ------------------------------------------------------------------------ ALGEBRA #323 ------------------------------------------------------------------------ names: 'Mod(b_3(ZZ))' id: 354 Lie: True associative: True commutative: True rank: 3 Topological subalgebra zeta function: poles: 0.0000 order@zero: -3 degree: -3 ess. value@zero: 1/6 zeta: 1/6/s^3 complex roots: None ess. value@infinity: 1/6 ------------------------------------------------------------------------ ALGEBRA #324 ------------------------------------------------------------------------ names: 'Mod(b_4(ZZ))' id: 355 Lie: True associative: True commutative: True rank: 4 Topological subalgebra zeta function: poles: 0.0000 order@zero: -4 degree: -4 ess. value@zero: 1/24 zeta: 1/24/s^4 complex roots: None ess. value@infinity: 1/24 ------------------------------------------------------------------------ ALGEBRA #325 ------------------------------------------------------------------------ names: 'Mod(b_5(ZZ))' id: 356 Lie: True associative: True commutative: True rank: 5 Topological subalgebra zeta function: poles: 0.0000 order@zero: -5 degree: -5 ess. value@zero: 1/120 zeta: 1/120/s^5 complex roots: None ess. value@infinity: 1/120 ------------------------------------------------------------------------ ALGEBRA #326 ------------------------------------------------------------------------ names: 'Mod(nb(sp_4(ZZ))))' id: 357 Lie: True commutative: True rank: 4 associative: True description: Natural module for the nilradical of the Borel subalgebra of sp(4,ZZ) Topological subalgebra zeta function: poles: 0.0000, 0.5000 order@zero: -1 degree: -4 ess. value@zero: -1/6 zeta: 1/6*(4*s - 1)/((2*s - 1)^4*s) complex roots: 0.2500 ess. value@infinity: 1/24 ------------------------------------------------------------------------ ALGEBRA #327 ------------------------------------------------------------------------ names: 'm3_2', 'gr(L(3,2))' id: 358 Lie: True blocks: (1, 2) commutative: False nilpotency class: 2 nilpotent: True cocentral dim: 2 rank: 3 soluble: True derived dim: 1 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.5000, 1.0000 order@zero: -2 degree: -3 ess. value@zero: -1/2 zeta: 1/2*(3*s - 1)/((2*s - 1)*(s - 1)*s^2) complex roots: 0.3333 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -2 degree: -3 ess. value@zero: -1/3 zeta: 1/3/((s - 1)*s^2) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #328 ------------------------------------------------------------------------ names: 'm4_2', 'gr(L(4,2))' id: 359 Lie: True blocks: (1, 3) commutative: False nilpotency class: 2 nilpotent: True cocentral dim: 2 rank: 4 soluble: True derived dim: 1 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.5000, 1.0000, 2.0000 order@zero: -2 degree: -4 ess. value@zero: 1/4 zeta: 1/2*(3*s - 1)/((2*s - 1)*(s - 1)*(s - 2)*s^2) complex roots: 0.3333 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -2 degree: -4 ess. value@zero: 1/6 zeta: 1/3/((s - 1)*(s - 2)*s^2) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #329 ------------------------------------------------------------------------ names: 'm4_3' id: 360 Lie: True blocks: (1, 1, 2) commutative: False nilpotency class: 3 nilpotent: True cocentral dim: 3 rank: 4 soluble: True derived dim: 2 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.3333, 0.5000, 1.0000 order@zero: -3 degree: -4 ess. value@zero: -3/8 zeta: 1/8*(26*s^2 - 17*s + 3)/((3*s - 1)*(2*s - 1)*(s - 1)*s^3) complex roots: 0.3269 - 0.0922*i, 0.3269 + 0.0922*i ess. value@infinity: 13/24 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -3 degree: -4 ess. value@zero: -1/12 zeta: 1/12/((s - 1)*s^3) complex roots: None ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #330 ------------------------------------------------------------------------ names: 'm5_2_1' id: 361 Lie: True blocks: (2, 3) commutative: False nilpotency class: 2 nilpotent: True cocentral dim: 3 rank: 5 soluble: True derived dim: 2 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.5000, 1.0000, 2.0000 order@zero: -2 degree: -5 ess. value@zero: -1/3 zeta: 1/6*(7*s - 4)/((2*s - 1)*(s - 1)^2*(s - 2)*s^2) complex roots: 0.5714 ess. value@infinity: 7/12 Topological ideal zeta function: poles: 0.0000, 0.3333, 1.0000, 2.0000 order@zero: -2 degree: -5 ess. value@zero: -1/5 zeta: 2/5/((3*s - 1)*(s - 1)*(s - 2)*s^2) complex roots: None ess. value@infinity: 2/15 ------------------------------------------------------------------------ ALGEBRA #331 ------------------------------------------------------------------------ names: 'm5_2_2', 'gr(L(5,2))' id: 362 Lie: True blocks: (1, 4) commutative: False nilpotency class: 2 nilpotent: True cocentral dim: 2 rank: 5 soluble: True derived dim: 1 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.5000, 1.0000, 2.0000, 3.0000 order@zero: -2 degree: -5 ess. value@zero: -1/12 zeta: 1/2*(3*s - 1)/((2*s - 1)*(s - 1)*(s - 2)*(s - 3)*s^2) complex roots: 0.3333 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000 order@zero: -2 degree: -5 ess. value@zero: -1/18 zeta: 1/3/((s - 1)*(s - 2)*(s - 3)*s^2) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #332 ------------------------------------------------------------------------ names: 'm5_2_3', 'gr(L(5,4))' id: 363 Lie: True blocks: (1, 4) commutative: False nilpotency class: 2 nilpotent: True cocentral dim: 4 rank: 5 soluble: True derived dim: 1 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.6667, 1.0000, 2.0000, 3.0000 order@zero: -2 degree: -5 ess. value@zero: -1/18 zeta: 1/9*(17*s - 6)/((3*s - 2)*(s - 1)*(s - 2)*(s - 3)*s^2) complex roots: 0.3529 ess. value@infinity: 17/27 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000 order@zero: -2 degree: -5 ess. value@zero: -1/30 zeta: 1/5/((s - 1)*(s - 2)*(s - 3)*s^2) complex roots: None ess. value@infinity: 1/5 ------------------------------------------------------------------------ ALGEBRA #333 ------------------------------------------------------------------------ names: 'm5_3_1' id: 364 Lie: True blocks: (2, 1, 2) commutative: False nilpotency class: 3 nilpotent: True cocentral dim: 3 rank: 5 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.2000, 0.5000, 0.6667, 1.0000 order@zero: -3 degree: -5 ess. value@zero: 2/5 zeta: 1/5*(121*s^3 - 127*s^2 + 40*s - 4)/((5*s - 1)*(3*s - 2)*(2*s - 1)^2*(s - 1)*s^3) complex roots: 0.2378 - 0.0324*i, 0.2378 + 0.0324*i, 0.5740 ess. value@infinity: 121/300 Topological ideal zeta function: poles: 0.0000, 0.2500, 1.0000 order@zero: -3 degree: -5 ess. value@zero: 2/15 zeta: 2/15/((4*s - 1)*(s - 1)*s^3) complex roots: None ess. value@infinity: 1/30 ------------------------------------------------------------------------ ALGEBRA #334 ------------------------------------------------------------------------ names: 'm5_3_2' id: 365 Lie: True blocks: (1, 1, 3) commutative: False nilpotency class: 3 nilpotent: True cocentral dim: 3 rank: 5 soluble: True derived dim: 2 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.3333, 0.5000, 1.0000, 2.0000 order@zero: -3 degree: -5 ess. value@zero: 3/16 zeta: 1/8*(26*s^2 - 17*s + 3)/((3*s - 1)*(2*s - 1)*(s - 1)*(s - 2)*s^3) complex roots: 0.3269 - 0.0922*i, 0.3269 + 0.0922*i ess. value@infinity: 13/24 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -3 degree: -5 ess. value@zero: 1/24 zeta: 1/12/((s - 1)*(s - 2)*s^3) complex roots: None ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #335 ------------------------------------------------------------------------ names: 'm5_4_1' id: 366 Lie: True blocks: (1, 1, 1, 2) commutative: False nilpotency class: 4 nilpotent: True cocentral dim: 4 rank: 5 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.2500, 0.3333, 0.5000, 1.0000 order@zero: -4 degree: -5 ess. value@zero: -13/42 zeta: 1/84*(828*s^3 - 776*s^2 + 247*s - 26)/((4*s - 1)*(3*s - 1)*(2*s - 1)*(s - 1)*s^4) complex roots: 0.2384, 0.3494 - 0.0982*i, 0.3494 + 0.0982*i ess. value@infinity: 23/56 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -4 degree: -5 ess. value@zero: -1/60 zeta: 1/60/((s - 1)*s^4) complex roots: None ess. value@infinity: 1/60 ------------------------------------------------------------------------ ALGEBRA #336 ------------------------------------------------------------------------ names: 'm6_2_1' id: 367 Lie: True blocks: (3, 3) commutative: False nilpotency class: 2 nilpotent: True cocentral dim: 3 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.3333, 0.6667, 1.0000, 1.5000, 2.0000 order@zero: -2 degree: -6 ess. value@zero: 1/6 zeta: 1/3*(25*s^2 - 28*s + 6)/((3*s - 1)*(3*s - 2)*(2*s - 3)*(s - 1)^2*(s - 2)*s^2) complex roots: 0.2887, 0.8313 ess. value@infinity: 25/54 Topological ideal zeta function: poles: 0.0000, 0.4000, 0.6667, 1.0000, 2.0000 order@zero: -2 degree: -6 ess. value@zero: 1/8 zeta: 1/((5*s - 2)*(3*s - 2)*(s - 1)*(s - 2)*s^2) complex roots: None ess. value@infinity: 1/15 ------------------------------------------------------------------------ ALGEBRA #337 ------------------------------------------------------------------------ names: 'm6_2_2' id: 368 Lie: True blocks: (2, 4) commutative: False nilpotency class: 2 nilpotent: True cocentral dim: 3 rank: 6 soluble: True derived dim: 2 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.5000, 1.0000, 2.0000, 3.0000 order@zero: -2 degree: -6 ess. value@zero: 1/9 zeta: 1/6*(7*s - 4)/((2*s - 1)*(s - 1)^2*(s - 2)*(s - 3)*s^2) complex roots: 0.5714 ess. value@infinity: 7/12 Topological ideal zeta function: poles: 0.0000, 0.3333, 1.0000, 2.0000, 3.0000 order@zero: -2 degree: -6 ess. value@zero: 1/15 zeta: 2/5/((3*s - 1)*(s - 1)*(s - 2)*(s - 3)*s^2) complex roots: None ess. value@infinity: 2/15 ------------------------------------------------------------------------ ALGEBRA #338 ------------------------------------------------------------------------ names: 'm6_2_3' id: 369 Lie: True blocks: (2, 4) commutative: False nilpotency class: 2 nilpotent: True cocentral dim: 4 rank: 6 soluble: True derived dim: 2 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.3333, 0.5000, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -2 degree: -6 ess. value@zero: 7/48 zeta: 1/12*(243*s^4 - 685*s^3 + 671*s^2 - 279*s + 42)/((3*s - 1)*(3*s - 4)*(2*s - 1)^2*(s - 1)^2*(s - 2)*(s - 3)*s^2) complex roots: 0.4192, 0.5598 - 0.0931*i, 0.5598 + 0.0931*i, 1.2800 ess. value@infinity: 9/16 Topological ideal zeta function: poles: 0.0000, 0.2000, 1.0000, 2.0000, 3.0000 order@zero: -2 degree: -6 ess. value@zero: 5/54 zeta: 5/9/((5*s - 1)*(s - 1)*(s - 2)*(s - 3)*s^2) complex roots: None ess. value@infinity: 1/9 ------------------------------------------------------------------------ ALGEBRA #339 ------------------------------------------------------------------------ names: 'm6_2_4' id: 370 Lie: True blocks: (2, 4) commutative: False nilpotency class: 2 nilpotent: True cocentral dim: 4 rank: 6 soluble: True derived dim: 2 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.2500, 0.3333, 0.5000, 0.7500, 1.0000, 1.3333, 2.0000, 3.0000 order@zero: -2 degree: -6 ess. value@zero: 1/10 zeta: 1/15*(2144*s^5 - 6886*s^4 + 8164*s^3 - 4499*s^2 + 1155*s - 108)/((4*s - 1)*(4*s - 3)*(3*s - 1)*(3*s - 4)*(2*s - 1)*(s - 1)^2*(s - 2)*(s - 3)*s^2) complex roots: 0.2173, 0.4682 - 0.1146*i, 0.4682 + 0.1146*i, 0.7816, 1.2765 ess. value@infinity: 67/135 Topological ideal zeta function: poles: 0.0000, 0.1667, 0.2000, 1.0000, 2.0000, 3.0000 order@zero: -2 degree: -6 ess. value@zero: 1/18 zeta: 1/3*(8*s - 1)/((6*s - 1)*(5*s - 1)*(s - 1)*(s - 2)*(s - 3)*s^2) complex roots: 0.1250 ess. value@infinity: 4/45 ------------------------------------------------------------------------ ALGEBRA #340 ------------------------------------------------------------------------ names: 'm6_2_5' id: 371 Lie: True blocks: (1, 5) commutative: False nilpotency class: 2 nilpotent: True cocentral dim: 2 rank: 6 soluble: True derived dim: 1 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.5000, 1.0000, 2.0000, 3.0000, 4.0000 order@zero: -2 degree: -6 ess. value@zero: 1/48 zeta: 1/2*(3*s - 1)/((2*s - 1)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s^2) complex roots: 0.3333 ess. value@infinity: 3/4 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 4.0000 order@zero: -2 degree: -6 ess. value@zero: 1/72 zeta: 1/3/((s - 1)*(s - 2)*(s - 3)*(s - 4)*s^2) complex roots: None ess. value@infinity: 1/3 ------------------------------------------------------------------------ ALGEBRA #341 ------------------------------------------------------------------------ names: 'm6_2_6' id: 372 Lie: True blocks: (1, 5) commutative: False nilpotency class: 2 nilpotent: True cocentral dim: 4 rank: 6 soluble: True derived dim: 1 derived length: 2 associative: True Topological subalgebra zeta function: poles: 0.0000, 0.6667, 1.0000, 2.0000, 3.0000, 4.0000 order@zero: -2 degree: -6 ess. value@zero: 1/72 zeta: 1/9*(17*s - 6)/((3*s - 2)*(s - 1)*(s - 2)*(s - 3)*(s - 4)*s^2) complex roots: 0.3529 ess. value@infinity: 17/27 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000, 4.0000 order@zero: -2 degree: -6 ess. value@zero: 1/120 zeta: 1/5/((s - 1)*(s - 2)*(s - 3)*(s - 4)*s^2) complex roots: None ess. value@infinity: 1/5 ------------------------------------------------------------------------ ALGEBRA #342 ------------------------------------------------------------------------ names: 'm6_3_1' id: 373 Lie: True blocks: (2, 1, 3) commutative: False nilpotency class: 3 nilpotent: True cocentral dim: 3 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.2000, 0.5000, 0.6667, 1.0000, 2.0000 order@zero: -3 degree: -6 ess. value@zero: -1/5 zeta: 1/5*(121*s^3 - 127*s^2 + 40*s - 4)/((5*s - 1)*(3*s - 2)*(2*s - 1)^2*(s - 1)*(s - 2)*s^3) complex roots: 0.2378 - 0.0324*i, 0.2378 + 0.0324*i, 0.5740 ess. value@infinity: 121/300 Topological ideal zeta function: poles: 0.0000, 0.2500, 1.0000, 2.0000 order@zero: -3 degree: -6 ess. value@zero: -1/15 zeta: 2/15/((4*s - 1)*(s - 1)*(s - 2)*s^3) complex roots: None ess. value@infinity: 1/30 ------------------------------------------------------------------------ ALGEBRA #343 ------------------------------------------------------------------------ names: 'm6_3_2' id: 374 Lie: True blocks: (1, 2, 3) commutative: False nilpotency class: 3 nilpotent: True cocentral dim: 4 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.3333, 0.5000, 1.0000, 2.0000 order@zero: -3 degree: -6 ess. value@zero: -59/240 zeta: 1/120*(318*s^2 - 287*s + 59)/((3*s - 1)*(2*s - 1)*(s - 1)^2*(s - 2)*s^3) complex roots: 0.3167, 0.5858 ess. value@infinity: 53/120 Topological ideal zeta function: poles: 0.0000, 0.3333, 1.0000, 2.0000 order@zero: -3 degree: -6 ess. value@zero: -13/240 zeta: 13/120/((3*s - 1)*(s - 1)*(s - 2)*s^3) complex roots: None ess. value@infinity: 13/360 ------------------------------------------------------------------------ ALGEBRA #344 ------------------------------------------------------------------------ names: 'm6_3_3' id: 375 Lie: True blocks: (1, 2, 3) commutative: False nilpotency class: 3 nilpotent: True cocentral dim: 4 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.3333, 0.5000, 1.0000, 2.0000 order@zero: -3 degree: -6 ess. value@zero: -23/96 zeta: 1/96*(243*s^2 - 217*s + 46)/((3*s - 1)*(2*s - 1)*(s - 1)^2*(s - 2)*s^3) complex roots: 0.3462, 0.5468 ess. value@infinity: 27/64 Topological ideal zeta function: poles: 0.0000, 0.3333, 1.0000, 2.0000 order@zero: -3 degree: -6 ess. value@zero: -13/240 zeta: 13/120/((3*s - 1)*(s - 1)*(s - 2)*s^3) complex roots: None ess. value@infinity: 13/360 ------------------------------------------------------------------------ ALGEBRA #345 ------------------------------------------------------------------------ names: 'm6_3_4' id: 376 Lie: True blocks: (1, 2, 3) commutative: False nilpotency class: 3 nilpotent: True cocentral dim: 5 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.1667, 0.2000, 0.3750, 0.5000, 1.0000, 2.0000 order@zero: -3 degree: -6 ess. value@zero: -53/288 zeta: 1/288*(299760*s^5 - 433196*s^4 + 233416*s^3 - 58627*s^2 + 6965*s - 318)/((8*s - 3)*(6*s - 1)^2*(5*s - 1)*(2*s - 1)*(s - 1)^2*(s - 2)*s^3) complex roots: 0.1545 - 0.0275*i, 0.1545 + 0.0275*i, 0.1990, 0.4132, 0.5239 ess. value@infinity: 1249/3456 Topological ideal zeta function: poles: 0.0000, 0.3333, 1.0000, 2.0000 order@zero: -3 degree: -6 ess. value@zero: -1/30 zeta: 1/15/((3*s - 1)*(s - 1)*(s - 2)*s^3) complex roots: None ess. value@infinity: 1/45 ------------------------------------------------------------------------ ALGEBRA #346 ------------------------------------------------------------------------ names: 'm6_3_5' id: 377 Lie: True blocks: (1, 2, 3) commutative: False nilpotency class: 3 nilpotent: True cocentral dim: 5 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.1667, 0.3750, 0.5000, 1.0000, 2.0000 order@zero: -3 degree: -6 ess. value@zero: -41/216 zeta: 1/36*(1280*s^3 - 1396*s^2 + 457*s - 41)/((8*s - 3)*(6*s - 1)*(2*s - 1)*(s - 1)^2*(s - 2)*s^3) complex roots: 0.1464, 0.4081, 0.5361 ess. value@infinity: 10/27 Topological ideal zeta function: poles: 0.0000, 0.3333, 1.0000, 2.0000 order@zero: -3 degree: -6 ess. value@zero: -1/30 zeta: 1/15/((3*s - 1)*(s - 1)*(s - 2)*s^3) complex roots: None ess. value@infinity: 1/45 ------------------------------------------------------------------------ ALGEBRA #347 ------------------------------------------------------------------------ names: 'm6_3_6' id: 378 Lie: True blocks: (1, 1, 4) commutative: False nilpotency class: 3 nilpotent: True cocentral dim: 3 rank: 6 soluble: True derived dim: 2 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.3333, 0.5000, 1.0000, 2.0000, 3.0000 order@zero: -3 degree: -6 ess. value@zero: -1/16 zeta: 1/8*(26*s^2 - 17*s + 3)/((3*s - 1)*(2*s - 1)*(s - 1)*(s - 2)*(s - 3)*s^3) complex roots: 0.3269 - 0.0922*i, 0.3269 + 0.0922*i ess. value@infinity: 13/24 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000, 3.0000 order@zero: -3 degree: -6 ess. value@zero: -1/72 zeta: 1/12/((s - 1)*(s - 2)*(s - 3)*s^3) complex roots: None ess. value@infinity: 1/12 ------------------------------------------------------------------------ ALGEBRA #348 ------------------------------------------------------------------------ names: 'm6_4_1' id: 379 Lie: True blocks: (1, 2, 1, 2) commutative: False nilpotency class: 4 nilpotent: True cocentral dim: 4 rank: 6 soluble: True derived dim: 4 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.1667, 0.2000, 0.2500, 0.5000, 0.6667, 1.0000 order@zero: -4 degree: -6 ess. value@zero: 1109/3360 zeta: 1/3360*(1481688*s^5 - 2219166*s^4 + 1252147*s^3 - 338066*s^2 + 44015*s - 2218)/((6*s - 1)*(5*s - 1)*(4*s - 1)*(3*s - 2)*(2*s - 1)^2*(s - 1)*s^4) complex roots: 0.1606, 0.2337, 0.2621 - 0.0136*i, 0.2621 + 0.0136*i, 0.5794 ess. value@infinity: 20579/67200 Topological ideal zeta function: poles: 0.0000, 0.2500, 1.0000 order@zero: -4 degree: -6 ess. value@zero: 1/30 zeta: 1/30/((4*s - 1)*(s - 1)*s^4) complex roots: None ess. value@infinity: 1/120 ------------------------------------------------------------------------ ALGEBRA #349 ------------------------------------------------------------------------ names: 'm6_4_2' id: 380 Lie: True blocks: (1, 2, 1, 2) commutative: False nilpotency class: 4 nilpotent: True cocentral dim: 5 rank: 6 soluble: True derived dim: 4 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.1667, 0.2000, 0.2500, 0.5000, 0.6667, 1.0000 order@zero: -4 degree: -6 ess. value@zero: 16/63 zeta: 1/2205*(874464*s^5 - 1278271*s^4 + 696618*s^3 - 180619*s^2 + 22698*s - 1120)/((6*s - 1)*(5*s - 1)*(4*s - 1)*(3*s - 2)*(2*s - 1)^2*(s - 1)*s^4) complex roots: 0.1825, 0.1837 - 0.0539*i, 0.1837 + 0.0539*i, 0.3278, 0.5840 ess. value@infinity: 9109/33075 Topological ideal zeta function: poles: 0.0000, 0.2500, 1.0000 order@zero: -4 degree: -6 ess. value@zero: 1/45 zeta: 1/45/((4*s - 1)*(s - 1)*s^4) complex roots: None ess. value@infinity: 1/180 ------------------------------------------------------------------------ ALGEBRA #350 ------------------------------------------------------------------------ names: 'm6_4_3' id: 381 Lie: True blocks: (1, 1, 1, 3) commutative: False nilpotency class: 4 nilpotent: True cocentral dim: 4 rank: 6 soluble: True derived dim: 3 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.2500, 0.3333, 0.5000, 1.0000, 2.0000 order@zero: -4 degree: -6 ess. value@zero: 13/84 zeta: 1/84*(828*s^3 - 776*s^2 + 247*s - 26)/((4*s - 1)*(3*s - 1)*(2*s - 1)*(s - 1)*(s - 2)*s^4) complex roots: 0.2384, 0.3494 - 0.0982*i, 0.3494 + 0.0982*i ess. value@infinity: 23/56 Topological ideal zeta function: poles: 0.0000, 1.0000, 2.0000 order@zero: -4 degree: -6 ess. value@zero: 1/120 zeta: 1/60/((s - 1)*(s - 2)*s^4) complex roots: None ess. value@infinity: 1/60 ------------------------------------------------------------------------ ALGEBRA #351 ------------------------------------------------------------------------ names: 'm6_5_1' id: 382 Lie: True blocks: (1, 1, 1, 1, 2) commutative: False nilpotency class: 5 nilpotent: True cocentral dim: 5 rank: 6 soluble: True derived dim: 4 derived length: 2 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.2000, 0.2500, 0.3333, 0.5000, 1.0000 order@zero: -5 degree: -6 ess. value@zero: -491/1848 zeta: 1/9240*(366480*s^4 - 429078*s^3 + 186575*s^2 - 35352*s + 2455)/((5*s - 1)*(4*s - 1)*(3*s - 1)*(2*s - 1)*(s - 1)*s^5) complex roots: 0.2031, 0.2348, 0.3664 - 0.0786*i, 0.3664 + 0.0786*i ess. value@infinity: 509/1540 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -5 degree: -6 ess. value@zero: -1/360 zeta: 1/360/((s - 1)*s^5) complex roots: None ess. value@infinity: 1/360 ------------------------------------------------------------------------ ALGEBRA #352 ------------------------------------------------------------------------ names: 'm6_5_2' id: 383 Lie: True blocks: (1, 1, 1, 1, 2) commutative: False nilpotency class: 5 nilpotent: True cocentral dim: 5 rank: 6 soluble: True derived dim: 4 derived length: 3 associative: False Topological subalgebra zeta function: poles: 0.0000, 0.2000, 0.2500, 0.3333, 0.5000, 1.0000 order@zero: -5 degree: -6 ess. value@zero: -14251/75600 zeta: 1/151200*(4512840*s^4 - 5153558*s^3 + 2205667*s^2 - 413503*s + 28502)/((5*s - 1)*(4*s - 1)*(3*s - 1)*(2*s - 1)*(s - 1)*s^5) complex roots: 0.2046, 0.2295, 0.3540 - 0.0961*i, 0.3540 + 0.0961*i ess. value@infinity: 37607/151200 Topological ideal zeta function: poles: 0.0000, 1.0000 order@zero: -5 degree: -6 ess. value@zero: -1/360 zeta: 1/360/((s - 1)*s^5) complex roots: None ess. value@infinity: 1/360 ------------------------------------------------------------------------ ALGEBRA #353 ------------------------------------------------------------------------ names: 'L(4,3)[eps]' id: 384 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 8 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -2/27 complex roots: 0.0000, 0.1910, 1.3090 (zeta-1)@infinity: 3 zeta: 2*(4*s^2 - 6*s + 1)*s/(2*s - 3)^3 fixed points: 0.0000, 0.8256, 1.3020, 3.3724 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #354 ------------------------------------------------------------------------ names: 'L(5,4)[eps]' id: 385 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (4, 0) cocentral dim: 8 rank: 10 soluble: True derived dim: 2 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -4/3 complex roots: 0.0000 (zeta-1)@infinity: 3/4 zeta: 4*s/(4*s - 3) fixed points: 0.0000, 1.7500 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.7500 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #355 ------------------------------------------------------------------------ names: 'L(5,5)[eps]' id: 386 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (4, 2) cocentral dim: 8 rank: 10 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -16/45 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 9/4 zeta: 16*(s - 1)^2*s/((4*s - 5)*(2*s - 3)^2) fixed points: 0.0000, 1.1162 - 0.1322*i, 1.1162 + 0.1322*i, 3.0175 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.2500, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #356 ------------------------------------------------------------------------ names: 'L(5,7)[eps]' id: 388 Lie: True commutative: False nilpotency class: 4 nilpotent: True (u,v): (2, 2) cocentral dim: 8 rank: 10 soluble: True derived dim: 6 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/20 complex roots: 0.0000, 0.2929, 1.7071 (zeta-1)@infinity: 9/2 zeta: (2*s^2 - 4*s + 1)*s/((2*s - 5)*(s - 2)^2) fixed points: 0.0000, 1.5000, 1.5858, 4.4142 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 2.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #357 ------------------------------------------------------------------------ names: 'L(5,8)[eps]' id: 389 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 6 rank: 10 soluble: True derived dim: 4 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -3/10 complex roots: 0.0000, 1.5000 (zeta-1)@infinity: 3 zeta: (2*s - 3)*s/((2*s - 5)*(s - 2)) fixed points: 0.0000, 1.7192, 3.7808 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 2.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #358 ------------------------------------------------------------------------ names: 'L(5,9)[eps]' id: 390 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 6 rank: 10 soluble: True derived dim: 6 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -1/20 complex roots: 0.0000, 0.2929, 1.7071 (zeta-1)@infinity: 9/2 zeta: (2*s^2 - 4*s + 1)*s/((2*s - 5)*(s - 2)^2) fixed points: 0.0000, 1.5000, 1.5858, 4.4142 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 2.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #359 ------------------------------------------------------------------------ names: 'L(6,10)[eps]' id: 391 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (4, 2) cocentral dim: 10 rank: 12 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -2/27 complex roots: 0.0000, 0.0918, 0.9082 (zeta-1)@infinity: 9/4 zeta: 2/3*(12*s^2 - 12*s + 1)*s/((4*s - 3)*(2*s - 3)*(s - 1)) fixed points: 0.0000, 0.4580, 0.9180, 2.8740 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.7500, 1.0000, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #360 ------------------------------------------------------------------------ names: 'L(6,22;0)[eps]' id: 405 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (4, 0) cocentral dim: 8 rank: 12 soluble: True derived dim: 4 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -3/7 complex roots: 0.0000, 1.5000 (zeta-1)@infinity: 9/4 zeta: 2*(2*s - 3)*s/((4*s - 7)*(s - 2)) fixed points: 0.0000, 1.5746, 3.1754 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.7500, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #361 ------------------------------------------------------------------------ names: 'L(6,23)[eps]' id: 407 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (4, 2) cocentral dim: 8 rank: 12 soluble: True derived dim: 6 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -53/225 complex roots: 0.0000, 1.6141 - 0.5576*i, 1.6141 + 0.5576*i, 2.2718 (zeta-1)@infinity: 15/4 zeta: 2*(8*s^3 - 44*s^2 + 82*s - 53)*s/((4*s - 9)*(2*s - 5)^2*(s - 2)) fixed points: 0.0000, 1.8394 - 0.4171*i, 1.8394 + 0.4171*i, 2.2723, 4.2988 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 2.2500, 2.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #362 ------------------------------------------------------------------------ names: 'L(6,24;0)[eps]' id: 410 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (4, 2) cocentral dim: 8 rank: 12 soluble: True derived dim: 6 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -3769/30870 complex roots: 0.0000, 0.6117, 1.3196, 1.5997, 1.7669 - 0.1652*i, 1.7669 + 0.1652*i, 1.8101 (zeta-1)@infinity: 15/4 zeta: 2*(512*s^6 - 4544*s^5 + 16544*s^4 - 31500*s^3 + 32885*s^2 - 17685*s + 3769)*s/((8*s - 15)*(4*s - 7)^3*(2*s - 3)*(s - 2)^2) fixed points: 0.0000, 1.3491 - 0.2095*i, 1.3491 + 0.2095*i, 1.5948, 1.7682 - 0.1682*i, 1.7682 + 0.1682*i, 1.8101, 3.9855 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.5000, 1.7500, 1.8750, 2.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #363 ------------------------------------------------------------------------ names: 'L(6,25)[eps]' id: 411 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (2, 2) cocentral dim: 8 rank: 12 soluble: True derived dim: 6 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -19/125 complex roots: 0.0000, 1.3261 - 0.5144*i, 1.3261 + 0.5144*i, 2.3478 (zeta-1)@infinity: 9/2 zeta: 2*(4*s^3 - 20*s^2 + 33*s - 19)*s/((2*s - 5)^3*(s - 2)) fixed points: 0.0000, 1.7590 - 0.4641*i, 1.7590 + 0.4641*i, 2.3469, 4.6352 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.0000, 2.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #364 ------------------------------------------------------------------------ names: 'L(6,26)[eps]' id: 412 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 6 rank: 12 soluble: True derived dim: 6 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -4/21 complex roots: 0.0000, 2.0000 (zeta-1)@infinity: 9/2 zeta: 2*(s - 2)*s/((2*s - 7)*(s - 3)) fixed points: 0.0000, 2.5000, 5.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 3.0000, 3.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #365 ------------------------------------------------------------------------ names: 'g(37A)[eps]' id: 413 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (2, 0) cocentral dim: 8 rank: 14 soluble: True derived dim: 6 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -4/21 complex roots: 0.0000, 2.0000 (zeta-1)@infinity: 9/2 zeta: 2*(s - 2)*s/((2*s - 7)*(s - 3)) fixed points: 0.0000, 2.5000, 5.0000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 3.0000, 3.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #366 ------------------------------------------------------------------------ names: 'g(37C)[eps]' id: 414 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (4, 0) cocentral dim: 8 rank: 14 soluble: True derived dim: 6 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -8/33 complex roots: 0.0000, 2.0000 (zeta-1)@infinity: 15/4 zeta: 4*(s - 2)*s/((4*s - 11)*(s - 3)) fixed points: 0.0000, 2.3070, 4.4430 ess. value@infinity: 1 degree(zeta-1): -1 poles: 2.7500, 3.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #367 ------------------------------------------------------------------------ names: 'g(27A)[eps]' id: 415 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (4, 0) cocentral dim: 10 rank: 14 soluble: True derived dim: 4 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -3/10 complex roots: 0.0000, 0.6162, 1.2171 (zeta-1)@infinity: 9/4 zeta: 2*(12*s^2 - 22*s + 9)*s/((4*s - 5)*(3*s - 4)*(2*s - 3)) fixed points: 0.0000, 0.9015, 1.2152, 2.9666 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.2500, 1.3333, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #368 ------------------------------------------------------------------------ names: 'g(27B)[eps]' id: 416 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (4, 0) cocentral dim: 10 rank: 14 soluble: True derived dim: 4 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -19/30 complex roots: 0.0000, 0.9500 (zeta-1)@infinity: 3/2 zeta: (20*s - 19)*s/((5*s - 6)*(4*s - 5)) fixed points: 0.0000, 1.0000, 2.4500 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.2000, 1.2500 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #369 ------------------------------------------------------------------------ names: 'g(17)[eps]' id: 417 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (6, 0) cocentral dim: 12 rank: 14 soluble: True derived dim: 2 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -2 complex roots: 0.0000 (zeta-1)@infinity: 1/2 zeta: 2*s/(2*s - 1) fixed points: 0.0000, 1.5000 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #370 ------------------------------------------------------------------------ names: 'g(157)[eps]' id: 418 Lie: True commutative: False nilpotency class: 3 nilpotent: True (u,v): (6, 2) cocentral dim: 12 rank: 14 soluble: True derived dim: 4 derived length: 2 associative: False Topological representation zeta function: degree: 0 ess. value@zero: -16/45 complex roots: 0.0000, 0.6667, 0.6667 (zeta-1)@infinity: 2 zeta: 4/3*(3*s - 2)^2*s/((6*s - 5)*(2*s - 3)*(s - 1)) fixed points: 0.0000, 0.7728 - 0.1027*i, 0.7728 + 0.1027*i, 2.7876 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.8333, 1.0000, 1.5000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #371 ------------------------------------------------------------------------ names: 'N_3^(8,2)[eps]' id: 419 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (6, 0) cocentral dim: 12 rank: 16 soluble: True derived dim: 4 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -3/7 complex roots: 0.0000, 0.3600, 0.8825 - 0.0497*i, 0.8825 + 0.0497*i (zeta-1)@infinity: 3/2 zeta: 1/3*(96*s^3 - 204*s^2 + 136*s - 27)*s/((8*s - 7)*(4*s - 3)*(s - 1)^2) fixed points: 0.0000, 0.5094, 0.8841 - 0.0483*i, 0.8841 + 0.0483*i, 2.3473 ess. value@infinity: 1 degree(zeta-1): -1 poles: 0.7500, 0.8750, 1.0000 order@zero: 1 ------------------------------------------------------------------------ ALGEBRA #372 ------------------------------------------------------------------------ names: 'N_4^(8,2)[eps]' id: 420 Lie: True commutative: False nilpotency class: 2 nilpotent: True (u,v): (6, 0) cocentral dim: 12 rank: 16 soluble: True derived dim: 4 derived length: 2 associative: True Topological representation zeta function: degree: 0 ess. value@zero: -3/7 complex roots: 0.0000, 1.0000 (zeta-1)@infinity: 2 zeta: 36*(s - 1)^2*s/((6*s - 7)*(3*s - 4)*(2*s - 3)) fixed points: 0.0000, 1.0788 - 0.0941*i, 1.0788 + 0.0941*i, 2.8423 ess. value@infinity: 1 degree(zeta-1): -1 poles: 1.1667, 1.3333, 1.5000 order@zero: 1