# Classical modular forms downloaded from the LMFDB on 20 June 2026. # Search link: https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/882/ # Query "{'level': 882}" returned 317 forms, sorted by analytic conductor. # Each entry in the following data list has the form: # [Label, Dim, $A$, Field, CM, Traces, Fricke sign, $q$-expansion] # For more details, see the definitions at the bottom of the file. "882.2.a.a" 1 7.04280545827693 "1.1.1.1" [] [-1, 0, -3, 0] 1 "q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+3q^{11}+\\cdots" "882.2.a.b" 1 7.04280545827693 "1.1.1.1" [] [-1, 0, -2, 0] 1 "q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+4q^{11}+\\cdots" "882.2.a.c" 1 7.04280545827693 "1.1.1.1" [] [-1, 0, -1, 0] -1 "q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-5q^{11}+\\cdots" "882.2.a.d" 1 7.04280545827693 "1.1.1.1" [] [-1, 0, 1, 0] 1 "q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-5q^{11}+\\cdots" "882.2.a.e" 1 7.04280545827693 "1.1.1.1" [] [-1, 0, 3, 0] -1 "q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{11}+\\cdots" "882.2.a.f" 1 7.04280545827693 "1.1.1.1" [] [1, 0, -4, 0] -1 "q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+4q^{11}+\\cdots" "882.2.a.g" 1 7.04280545827693 "1.1.1.1" [] [1, 0, -3, 0] 1 "q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\\cdots" "882.2.a.h" 1 7.04280545827693 "1.1.1.1" [] [1, 0, -3, 0] 1 "q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\\cdots" "882.2.a.i" 1 7.04280545827693 "1.1.1.1" [] [1, 0, 0, 0] -1 "q+q^{2}+q^{4}+q^{8}+4q^{13}+q^{16}+6q^{17}+\\cdots" "882.2.a.j" 1 7.04280545827693 "1.1.1.1" [] [1, 0, 3, 0] -1 "q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\\cdots" "882.2.a.k" 1 7.04280545827693 "1.1.1.1" [] [1, 0, 3, 0] -1 "q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\\cdots" "882.2.a.l" 1 7.04280545827693 "1.1.1.1" [] [1, 0, 4, 0] -1 "q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+4q^{11}+\\cdots" "882.2.a.m" 2 7.04280545827693 "2.2.8.1" [] [-2, 0, 0, 0] 1 "q-q^{2}+q^{4}+\\beta q^{5}-q^{8}-\\beta q^{10}-4q^{11}+\\cdots" "882.2.a.n" 2 7.04280545827693 "2.2.8.1" [] [-2, 0, 0, 0] -1 "q-q^{2}+q^{4}+2\\beta q^{5}-q^{8}-2\\beta q^{10}+\\cdots" "882.2.a.o" 2 7.04280545827693 "2.2.8.1" [] [2, 0, 0, 0] -1 "q+q^{2}+q^{4}+\\beta q^{5}+q^{8}+\\beta q^{10}+4q^{11}+\\cdots" "882.2.d.a" 8 7.04280545827693 "8.0.5308416.1" [] [0, 0, 0, 0] NULL "q+\\beta_1 q^{2}-q^{4}+(-\\beta_{4}-\\beta_{3})q^{5}+\\cdots" "882.2.d.b" 8 7.04280545827693 "8.0.16777216.1" [] [0, 0, 0, 0] NULL "q-\\beta_1 q^{2}-q^{4}-\\beta_{5} q^{5}+\\beta_1 q^{8}+\\cdots" "882.2.e.a" 2 7.04280545827693 "2.0.3.1" [] [-2, -3, -2, 0] NULL "q-q^{2}+(-2+\\zeta_{6})q^{3}+q^{4}+(-2+2\\zeta_{6})q^{5}+\\cdots" "882.2.e.b" 2 7.04280545827693 "2.0.3.1" [] [-2, -3, 3, 0] NULL "q-q^{2}+(-1-\\zeta_{6})q^{3}+q^{4}+(3-3\\zeta_{6})q^{5}+\\cdots" "882.2.e.c" 2 7.04280545827693 "2.0.3.1" [] [-2, 0, 3, 0] NULL "q-q^{2}+(1-2\\zeta_{6})q^{3}+q^{4}+(3-3\\zeta_{6})q^{5}+\\cdots" "882.2.e.d" 2 7.04280545827693 "2.0.3.1" [] [-2, 3, -3, 0] NULL "q-q^{2}+(1+\\zeta_{6})q^{3}+q^{4}+(-3+3\\zeta_{6})q^{5}+\\cdots" "882.2.e.e" 2 7.04280545827693 "2.0.3.1" [] [-2, 3, 2, 0] NULL "q-q^{2}+(2-\\zeta_{6})q^{3}+q^{4}+(2-2\\zeta_{6})q^{5}+\\cdots" "882.2.e.f" 2 7.04280545827693 "2.0.3.1" [] [2, -3, -1, 0] NULL "q+q^{2}+(-1-\\zeta_{6})q^{3}+q^{4}+(-1+\\zeta_{6})q^{5}+\\cdots" "882.2.e.g" 2 7.04280545827693 "2.0.3.1" [] [2, -3, 0, 0] NULL "q+q^{2}+(-2+\\zeta_{6})q^{3}+q^{4}+(-2+\\zeta_{6})q^{6}+\\cdots" "882.2.e.h" 2 7.04280545827693 "2.0.3.1" [] [2, 0, -3, 0] NULL "q+q^{2}+(1-2\\zeta_{6})q^{3}+q^{4}+(-3+3\\zeta_{6})q^{5}+\\cdots" "882.2.e.i" 2 7.04280545827693 "2.0.3.1" [] [2, 3, 0, 0] NULL "q+q^{2}+(2-\\zeta_{6})q^{3}+q^{4}+(2-\\zeta_{6})q^{6}+\\cdots" "882.2.e.j" 2 7.04280545827693 "2.0.3.1" [] [2, 3, 1, 0] NULL "q+q^{2}+(1+\\zeta_{6})q^{3}+q^{4}+(1-\\zeta_{6})q^{5}+\\cdots" "882.2.e.k" 4 7.04280545827693 "4.0.1089.1" [] [-4, -2, 3, 0] NULL "q-q^{2}+(-\\beta _{1}+\\beta _{3})q^{3}+q^{4}+(-1+\\cdots)q^{5}+\\cdots" "882.2.e.l" 4 7.04280545827693 "4.0.1089.1" [] [-4, 2, -3, 0] NULL "q-q^{2}+(\\beta _{1}-\\beta _{3})q^{3}+q^{4}+(1-2\\beta _{1}+\\cdots)q^{5}+\\cdots" "882.2.e.m" 4 7.04280545827693 "4.0.576.1" [] [4, -2, -2, 0] NULL "q+q^{2}+(-\\beta _{1}-\\beta _{2}+\\beta _{3})q^{3}+q^{4}+\\cdots" "882.2.e.n" 4 7.04280545827693 "4.0.576.1" [] [4, 2, 2, 0] NULL "q+q^{2}+(\\beta _{1}+\\beta _{2}-\\beta _{3})q^{3}+q^{4}+(-\\beta _{1}+\\cdots)q^{5}+\\cdots" "882.2.e.o" 6 7.04280545827693 "6.0.309123.1" [] [-6, -2, -1, 0] NULL "q-q^{2}+(\\beta _{2}+\\beta _{4})q^{3}+q^{4}+(-1+\\beta _{1}+\\cdots)q^{5}+\\cdots" "882.2.e.p" 6 7.04280545827693 "6.0.309123.1" [] [6, 2, 5, 0] NULL "q+q^{2}+(-\\beta _{3}+\\beta _{4}+\\beta _{5})q^{3}+q^{4}+\\cdots" "882.2.e.q" 8 7.04280545827693 "8.0.5308416.1" [] [-8, 0, 0, 0] NULL "q-q^{2}+(\\beta_{7}+\\beta_{3})q^{3}+q^{4}-\\beta_{7} q^{5}+\\cdots" "882.2.e.r" 8 7.04280545827693 "8.0.31116960000.2" [] [-8, 0, 0, 0] NULL "q-q^{2}-\\beta _{3}q^{3}+q^{4}+(-\\beta _{5}-\\beta _{6})q^{5}+\\cdots" "882.2.e.s" 8 7.04280545827693 "8.0.5308416.1" [] [8, 0, 0, 0] NULL "q+q^{2}+(-\\beta_{7}+\\beta_{6}+\\cdots-\\beta_{3})q^{3}+\\cdots" "882.2.e.t" 8 7.04280545827693 "8.0.3317760000.3" [] [8, 0, 0, 0] NULL "q+q^{2}+(\\beta _{5}-\\beta _{6})q^{3}+q^{4}+(2\\beta _{1}-\\beta _{3}+\\cdots)q^{5}+\\cdots" "882.2.f.a" 2 7.04280545827693 "2.0.3.1" [] [-1, -3, -3, 0] NULL "q+(-1+\\zeta_{6})q^{2}+(-2+\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.f.b" 2 7.04280545827693 "2.0.3.1" [] [-1, 0, -1, 0] NULL "q+(-1+\\zeta_{6})q^{2}+(-1+2\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.f.c" 2 7.04280545827693 "2.0.3.1" [] [-1, 0, 1, 0] NULL "q+(-1+\\zeta_{6})q^{2}+(1-2\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.f.d" 2 7.04280545827693 "2.0.3.1" [] [-1, 3, 0, 0] NULL "q+(-1+\\zeta_{6})q^{2}+(1+\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.f.e" 2 7.04280545827693 "2.0.3.1" [] [-1, 3, 3, 0] NULL "q+(-1+\\zeta_{6})q^{2}+(2-\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.f.f" 2 7.04280545827693 "2.0.3.1" [] [1, -3, 2, 0] NULL "q+(1-\\zeta_{6})q^{2}+(-1-\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.f.g" 2 7.04280545827693 "2.0.3.1" [] [1, -3, 3, 0] NULL "q+(1-\\zeta_{6})q^{2}+(-2+\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.f.h" 2 7.04280545827693 "2.0.3.1" [] [1, 0, -3, 0] NULL "q+(1-\\zeta_{6})q^{2}+(1-2\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.f.i" 2 7.04280545827693 "2.0.3.1" [] [1, 3, -3, 0] NULL "q+(1-\\zeta_{6})q^{2}+(2-\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.f.j" 4 7.04280545827693 "4.0.576.1" [] [-2, -4, 2, 0] NULL "q+(-1+\\beta _{2})q^{2}+(-1-\\beta _{3})q^{3}-\\beta _{2}q^{4}+\\cdots" "882.2.f.k" 4 7.04280545827693 "4.0.1089.1" [] [2, 1, 3, 0] NULL "q+(1-\\beta _{2})q^{2}+(\\beta _{2}+\\beta _{3})q^{3}-\\beta _{2}q^{4}+\\cdots" "882.2.f.l" 6 7.04280545827693 "6.0.309123.1" [] [-3, -2, -5, 0] NULL "q+(-1-\\beta _{4})q^{2}+(-1+\\beta _{1}+\\beta _{2})q^{3}+\\cdots" "882.2.f.m" 6 7.04280545827693 "6.0.309123.1" [] [-3, 2, 5, 0] NULL "q+(-1-\\beta _{4})q^{2}+(1-\\beta _{1}-\\beta _{2})q^{3}+\\cdots" "882.2.f.n" 6 7.04280545827693 "6.0.309123.1" [] [3, -4, 1, 0] NULL "q+(1+\\beta _{4})q^{2}+(-1+\\beta _{5})q^{3}+\\beta _{4}q^{4}+\\cdots" "882.2.f.o" 6 7.04280545827693 "6.0.309123.1" [] [3, 4, -1, 0] NULL "q+(1+\\beta _{4})q^{2}+(1-\\beta _{5})q^{3}+\\beta _{4}q^{4}+\\cdots" "882.2.f.p" 8 7.04280545827693 "8.0.3317760000.3" [] [-4, 0, 0, 0] NULL "q-\\beta _{4}q^{2}+(-\\beta _{1}+\\beta _{3}+\\beta _{5}-\\beta _{6})q^{3}+\\cdots" "882.2.f.q" 8 7.04280545827693 "8.0.5308416.1" [] [-4, 0, 0, 0] NULL "q-\\beta_1 q^{2}+(-\\beta_{7}+\\beta_{6})q^{3}+(\\beta_1-1)q^{4}+\\cdots" "882.2.f.r" 8 7.04280545827693 "8.0.31116960000.2" [] [4, 0, 0, 0] NULL "q+(1+\\beta _{4})q^{2}+(-\\beta _{1}-\\beta _{5})q^{3}+\\beta _{4}q^{4}+\\cdots" "882.2.f.s" 8 7.04280545827693 "8.0.5308416.1" [] [4, 0, 0, 0] NULL "q+\\beta_1 q^{2}+(-\\beta_{6}-\\beta_{5}+\\beta_{3})q^{3}+\\cdots" "882.2.g.a" 2 7.04280545827693 "2.0.3.1" [] [-1, 0, -4, 0] NULL "q-\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}-4\\zeta_{6}q^{5}+\\cdots" "882.2.g.b" 2 7.04280545827693 "2.0.3.1" [] [-1, 0, -3, 0] NULL "q-\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}-3\\zeta_{6}q^{5}+\\cdots" "882.2.g.c" 2 7.04280545827693 "2.0.3.1" [] [-1, 0, 0, 0] NULL "q-\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}+q^{8}-4q^{13}+\\cdots" "882.2.g.d" 2 7.04280545827693 "2.0.3.1" [] [-1, 0, 0, 0] NULL "q-\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}+q^{8}+4q^{13}+\\cdots" "882.2.g.e" 2 7.04280545827693 "2.0.3.1" [] [-1, 0, 3, 0] NULL "q-\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}+3\\zeta_{6}q^{5}+\\cdots" "882.2.g.f" 2 7.04280545827693 "2.0.3.1" [] [-1, 0, 4, 0] NULL "q-\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}+4\\zeta_{6}q^{5}+\\cdots" "882.2.g.g" 2 7.04280545827693 "2.0.3.1" [] [1, 0, -3, 0] NULL "q+\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}-3\\zeta_{6}q^{5}+\\cdots" "882.2.g.h" 2 7.04280545827693 "2.0.3.1" [] [1, 0, -2, 0] NULL "q+\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}-2\\zeta_{6}q^{5}+\\cdots" "882.2.g.i" 2 7.04280545827693 "2.0.3.1" [] [1, 0, -1, 0] NULL "q+\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}-\\zeta_{6}q^{5}-q^{8}+\\cdots" "882.2.g.j" 2 7.04280545827693 "2.0.3.1" [] [1, 0, 2, 0] NULL "q+\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}+2\\zeta_{6}q^{5}+\\cdots" "882.2.g.k" 4 7.04280545827693 "4.0.576.2" [] [-2, 0, 0, 0] NULL "q+(-1-\\beta _{2})q^{2}+\\beta _{2}q^{4}+\\beta _{1}q^{5}+q^{8}+\\cdots" "882.2.g.l" 4 7.04280545827693 "4.0.576.2" [] [2, 0, 0, 0] NULL "q+(1+\\beta _{2})q^{2}+\\beta _{2}q^{4}+2\\beta _{1}q^{5}-q^{8}+\\cdots" "882.2.g.m" 4 7.04280545827693 "4.0.576.2" [] [2, 0, 0, 0] NULL "q+(1+\\beta _{2})q^{2}+\\beta _{2}q^{4}+\\beta _{1}q^{5}-q^{8}+\\cdots" "882.2.h.a" 2 7.04280545827693 "2.0.3.1" [] [-1, -3, -2, 0] NULL "q+(-1+\\zeta_{6})q^{2}+(-1-\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.h.b" 2 7.04280545827693 "2.0.3.1" [] [-1, 0, 0, 0] NULL "q+(-1+\\zeta_{6})q^{2}+(-1+2\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.h.c" 2 7.04280545827693 "2.0.3.1" [] [-1, 0, 0, 0] NULL "q+(-1+\\zeta_{6})q^{2}+(1-2\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.h.d" 2 7.04280545827693 "2.0.3.1" [] [-1, 3, 2, 0] NULL "q+(-1+\\zeta_{6})q^{2}+(1+\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.h.e" 2 7.04280545827693 "2.0.3.1" [] [-1, 3, 6, 0] NULL "q+(-1+\\zeta_{6})q^{2}+(2-\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.h.f" 2 7.04280545827693 "2.0.3.1" [] [1, -3, 6, 0] NULL "q+(1-\\zeta_{6})q^{2}+(-1-\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.h.g" 2 7.04280545827693 "2.0.3.1" [] [1, 0, -4, 0] NULL "q+(1-\\zeta_{6})q^{2}+(1-2\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.h.h" 2 7.04280545827693 "2.0.3.1" [] [1, 0, 4, 0] NULL "q+(1-\\zeta_{6})q^{2}+(-1+2\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.h.i" 2 7.04280545827693 "2.0.3.1" [] [1, 3, -6, 0] NULL "q+(1-\\zeta_{6})q^{2}+(2-\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.h.j" 2 7.04280545827693 "2.0.3.1" [] [1, 3, -6, 0] NULL "q+(1-\\zeta_{6})q^{2}+(1+\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots" "882.2.h.k" 4 7.04280545827693 "4.0.576.1" [] [-2, -2, 4, 0] NULL "q+(-1+\\beta _{2})q^{2}+(-1+\\beta _{1}+\\beta _{2})q^{3}+\\cdots" "882.2.h.l" 4 7.04280545827693 "4.0.576.1" [] [-2, 2, -4, 0] NULL "q-\\beta _{2}q^{2}+(\\beta _{1}+\\beta _{2}-\\beta _{3})q^{3}+(-1+\\cdots)q^{4}+\\cdots" "882.2.h.m" 4 7.04280545827693 "4.0.1089.1" [] [2, -1, 6, 0] NULL "q+\\beta _{2}q^{2}-\\beta _{1}q^{3}+(-1+\\beta _{2})q^{4}+(2+\\cdots)q^{5}+\\cdots" "882.2.h.n" 4 7.04280545827693 "4.0.1089.1" [] [2, 1, -6, 0] NULL "q+(1-\\beta _{2})q^{2}+(\\beta _{2}+\\beta _{3})q^{3}-\\beta _{2}q^{4}+\\cdots" "882.2.h.o" 6 7.04280545827693 "6.0.309123.1" [] [-3, -4, -10, 0] NULL "q+(-1-\\beta _{4})q^{2}+(\\beta _{2}+\\beta _{3}-\\beta _{5})q^{3}+\\cdots" "882.2.h.p" 6 7.04280545827693 "6.0.309123.1" [] [3, -2, 2, 0] NULL "q-\\beta _{4}q^{2}+(-\\beta _{1}-\\beta _{2}+\\beta _{5})q^{3}+(-1+\\cdots)q^{4}+\\cdots" "882.2.h.q" 8 7.04280545827693 "8.0.5308416.1" [] [-4, 0, 0, 0] NULL "q+(\\beta_1-1)q^{2}+(\\beta_{6}+\\beta_{3})q^{3}-\\beta_1 q^{4}+\\cdots" "882.2.h.r" 8 7.04280545827693 "8.0.3317760000.3" [] [-4, 0, 0, 0] NULL "q-\\beta _{4}q^{2}+(\\beta _{1}-\\beta _{3}-\\beta _{5})q^{3}+(-1+\\cdots)q^{4}+\\cdots" "882.2.h.s" 8 7.04280545827693 "8.0.31116960000.2" [] [4, 0, 0, 0] NULL "q+(1+\\beta _{4})q^{2}+(\\beta _{3}-\\beta _{6})q^{3}+\\beta _{4}q^{4}+\\cdots" "882.2.h.t" 8 7.04280545827693 "8.0.5308416.1" [] [4, 0, 0, 0] NULL "q+(-\\beta_1+1)q^{2}+(\\beta_{7}-\\beta_{5})q^{3}+\\cdots" "882.2.k.a" 8 7.04280545827693 "8.0.5308416.1" [] [0, 0, 0, 0] NULL "q-\\beta_1 q^{2}+\\beta_{2} q^{4}+(-\\beta_{6}+\\beta_{5}+\\cdots+\\beta_1)q^{5}+\\cdots" "882.2.k.b" 16 7.04280545827693 "16.0.1846757322198614016.1" [] [0, 0, 0, 0] NULL "q+(\\beta_{5}-\\beta_1)q^{2}+(-\\beta_{3}+1)q^{4}+\\cdots" "882.2.l.a" 16 7.04280545827693 NULL [] [0, 0, 0, 0] NULL "q+\\beta _{4}q^{2}+\\beta _{6}q^{3}-q^{4}+(-\\beta _{1}+\\beta _{6}+\\cdots)q^{5}+\\cdots" "882.2.l.b" 16 7.04280545827693 NULL [] [0, 0, 0, 0] NULL "q+\\beta _{6}q^{2}-\\beta _{8}q^{3}-q^{4}+(\\beta _{5}+\\beta _{7}-\\beta _{9}+\\cdots)q^{5}+\\cdots" "882.2.l.c" 48 7.04280545827693 NULL [] [0, 0, 0, 0] NULL NULL "882.2.m.a" 16 7.04280545827693 NULL [] [0, 0, 0, 0] NULL "q+\\beta _{1}q^{2}+\\beta _{14}q^{3}-\\beta _{7}q^{4}+(\\beta _{5}+\\beta _{7}+\\cdots)q^{5}+\\cdots" "882.2.m.b" 16 7.04280545827693 NULL [] [0, 0, 0, 0] NULL "q+\\beta _{1}q^{2}-\\beta _{14}q^{3}-\\beta _{7}q^{4}+(-\\beta _{5}+\\cdots)q^{5}+\\cdots" "882.2.m.c" 48 7.04280545827693 NULL [] [0, 0, 0, 0] NULL NULL "882.2.t.a" 16 7.04280545827693 NULL [] [0, 0, 0, 0] NULL "q+(-\\beta _{1}+\\beta _{6})q^{2}+(\\beta _{11}+\\beta _{14})q^{3}+\\cdots" "882.2.t.b" 16 7.04280545827693 NULL [] [0, 0, 0, 0] NULL "q+(\\beta _{4}-\\beta _{8})q^{2}+(\\beta _{5}-\\beta _{7})q^{3}+(1-\\beta _{9}+\\cdots)q^{4}+\\cdots" "882.2.t.c" 48 7.04280545827693 NULL [] [0, 0, 0, 0] NULL NULL "882.2.u.a" 6 7.04280545827693 "6.0.16807.1" [] [-1, 0, 4, -7] NULL "q+(-1+\\zeta_{14}-\\zeta_{14}^{2}+\\zeta_{14}^{3}-\\zeta_{14}^{4}+\\cdots)q^{2}+\\cdots" "882.2.u.b" 6 7.04280545827693 "6.0.16807.1" [] [1, 0, -5, 7] NULL "q+(1-\\zeta_{14}+\\zeta_{14}^{2}-\\zeta_{14}^{3}+\\zeta_{14}^{4}+\\cdots)q^{2}+\\cdots" "882.2.u.c" 6 7.04280545827693 "6.0.16807.1" [] [1, 0, -4, -7] NULL "q+(1-\\zeta_{14}+\\zeta_{14}^{2}-\\zeta_{14}^{3}+\\zeta_{14}^{4}+\\cdots)q^{2}+\\cdots" "882.2.u.d" 12 7.04280545827693 "12.0.7877952219361.1" [] [-2, 0, -1, 0] NULL "q+\\beta _{1}q^{2}-\\beta _{4}q^{4}+(\\beta _{5}-\\beta _{6}+\\beta _{7}-\\beta _{9}+\\cdots)q^{5}+\\cdots" "882.2.u.e" 12 7.04280545827693 "12.0.7877952219361.1" [] [-2, 0, 1, 0] NULL "q-\\beta _{4}q^{2}+\\beta _{3}q^{4}+(-\\beta _{1}+\\beta _{2}-\\beta _{3}+\\cdots)q^{5}+\\cdots" "882.2.u.f" 18 7.04280545827693 NULL [] [-3, 0, -4, 7] NULL "q+\\beta _{9}q^{2}-\\beta _{7}q^{4}+(-\\beta _{3}+\\beta _{14})q^{5}+\\cdots" "882.2.u.g" 18 7.04280545827693 NULL [] [-3, 0, 0, -1] NULL "q+\\beta _{9}q^{2}+(-1-\\beta _{5}+\\beta _{6}-\\beta _{9}+\\beta _{10}+\\cdots)q^{4}+\\cdots" "882.2.u.h" 18 7.04280545827693 NULL [] [3, 0, -3, 1] NULL "q+\\beta _{4}q^{2}-\\beta _{7}q^{4}+(\\beta _{9}-\\beta _{11}+\\beta _{16}+\\cdots)q^{5}+\\cdots" "882.2.u.i" 18 7.04280545827693 NULL [] [3, 0, 4, 7] NULL "q-\\beta _{9}q^{2}-\\beta _{7}q^{4}+(\\beta _{3}-\\beta _{14})q^{5}+(-\\beta _{2}+\\cdots)q^{7}+\\cdots" "882.2.u.j" 18 7.04280545827693 NULL [] [3, 0, 6, -7] NULL "q+\\beta _{13}q^{2}+(-1+\\beta _{8}-\\beta _{9}+\\beta _{10}+\\cdots)q^{4}+\\cdots" "882.2.v.a" 96 7.04280545827693 NULL [] [0, 0, 0, 0] NULL NULL "882.2.y.a" 336 7.04280545827693 NULL [] [-28, -13, -4, -1] NULL NULL "882.2.y.b" 336 7.04280545827693 NULL [] [28, 13, -4, 3] NULL NULL "882.2.z.a" 24 7.04280545827693 NULL [] [-2, 0, -1, 0] NULL NULL "882.2.z.b" 24 7.04280545827693 NULL [] [-2, 0, 0, 0] NULL NULL "882.2.z.c" 24 7.04280545827693 NULL [] [2, 0, -1, 0] NULL NULL "882.2.z.d" 24 7.04280545827693 NULL [] [2, 0, 0, 0] NULL NULL "882.2.z.e" 36 7.04280545827693 NULL [] [-3, 0, 0, -1] NULL NULL "882.2.z.f" 36 7.04280545827693 NULL [] [3, 0, -2, -5] NULL NULL "882.2.z.g" 60 7.04280545827693 NULL [] [-5, 0, -3, 1] NULL NULL "882.2.z.h" 60 7.04280545827693 NULL [] [5, 0, 3, 1] NULL NULL "882.2.ba.a" 336 7.04280545827693 NULL [] [-28, 5, 2, 2] NULL NULL "882.2.ba.b" 336 7.04280545827693 NULL [] [28, -5, 2, 0] NULL NULL "882.2.bb.a" 336 7.04280545827693 NULL [] [-56, -5, 2, 0] NULL NULL "882.2.bb.b" 336 7.04280545827693 NULL [] [56, 5, 2, 2] NULL NULL "882.2.bc.a" 672 7.04280545827693 NULL [] [0, 0, 0, -2] NULL NULL "882.2.bj.a" 672 7.04280545827693 NULL [] [0, 0, 0, -2] NULL NULL "882.2.bk.a" 672 7.04280545827693 NULL [] [0, 0, 0, -2] NULL NULL "882.2.bl.a" 240 7.04280545827693 NULL [] [0, 0, 0, -4] NULL NULL "882.3.b.a" 2 24.032759316578186 "2.0.8.1" [] [0, 0, 0, 0] NULL "q+\\beta q^{2}-2q^{4}+3\\beta q^{5}-2\\beta q^{8}-6q^{10}+\\cdots" "882.3.b.b" 2 24.032759316578186 "2.0.8.1" [] [0, 0, 0, 0] NULL "q+\\beta q^{2}-2q^{4}+3\\beta q^{5}-2\\beta q^{8}-6q^{10}+\\cdots" "882.3.b.c" 2 24.032759316578186 "2.0.8.1" [] [0, 0, 0, 0] NULL "q+\\beta q^{2}-2q^{4}+\\beta q^{5}-2\\beta q^{8}-2q^{10}+\\cdots" "882.3.b.d" 2 24.032759316578186 "2.0.8.1" [] [0, 0, 0, 0] NULL "q-\\beta q^{2}-2q^{4}+\\beta q^{5}+2\\beta q^{8}+2q^{10}+\\cdots" "882.3.b.e" 2 24.032759316578186 "2.0.8.1" [] [0, 0, 0, 0] NULL "q-\\beta q^{2}-2q^{4}+3\\beta q^{5}+2\\beta q^{8}+6q^{10}+\\cdots" "882.3.b.f" 4 24.032759316578186 "4.0.12544.1" [] [0, 0, 0, 0] NULL "q+\\beta _{1}q^{2}-2q^{4}+(\\beta _{1}-\\beta _{2})q^{5}-2\\beta _{1}q^{8}+\\cdots" "882.3.b.g" 4 24.032759316578186 "4.0.87616.2" [] [0, 0, 0, 0] NULL "q-\\beta _{1}q^{2}-2q^{4}-\\beta _{2}q^{5}+2\\beta _{1}q^{8}+\\cdots" "882.3.b.h" 4 24.032759316578186 "4.0.256.1" [] [0, 0, 0, 0] NULL "q+\\beta_{2} q^{2}-2 q^{4}+2\\beta_1 q^{5}-2\\beta_{2} q^{8}+\\cdots" "882.3.b.i" 4 24.032759316578186 "4.0.256.1" [] [0, 0, 0, 0] NULL "q-\\beta_{2} q^{2}-2 q^{4}+\\beta_1 q^{5}+2\\beta_{2} q^{8}+\\cdots" "882.3.c.a" 4 24.032759316578186 "4.0.2048.2" [] [0, 0, 0, 0] NULL "q+\\beta _{2}q^{2}+2q^{4}+(\\beta _{1}+4\\beta _{3})q^{5}+2\\beta _{2}q^{8}+\\cdots" "882.3.c.b" 4 24.032759316578186 "4.0.576.2" [] [0, 0, 0, 0] NULL "q-\\beta _{1}q^{2}+2q^{4}+(2\\beta _{2}-2\\beta _{3})q^{5}-2\\beta _{1}q^{8}+\\cdots" "882.3.c.c" 4 24.032759316578186 "4.0.576.2" [] [0, 0, 0, 0] NULL "q-\\beta _{1}q^{2}+2q^{4}+2\\beta _{3}q^{5}-2\\beta _{1}q^{8}+\\cdots" "882.3.c.d" 4 24.032759316578186 "4.0.2048.2" [] [0, 0, 0, 0] NULL "q+\\beta _{2}q^{2}+2q^{4}+(\\beta _{1}+2\\beta _{3})q^{5}+2\\beta _{2}q^{8}+\\cdots" "882.3.c.e" 4 24.032759316578186 "4.0.2048.2" [] [0, 0, 0, 0] NULL "q-\\beta _{2}q^{2}+2q^{4}+(\\beta _{1}+2\\beta _{3})q^{5}-2\\beta _{2}q^{8}+\\cdots" "882.3.c.f" 4 24.032759316578186 "4.0.576.2" [] [0, 0, 0, 0] NULL "q+\\beta _{1}q^{2}+2q^{4}+(\\beta _{2}+2\\beta _{3})q^{5}+2\\beta _{1}q^{8}+\\cdots" "882.3.c.g" 8 24.032759316578186 "8.0.339738624.1" [] [0, 0, 0, 0] NULL "q+\\beta _{1}q^{2}+2q^{4}+(-\\beta _{2}-\\beta _{4})q^{5}+2\\beta _{1}q^{8}+\\cdots" "882.3.n.a" 4 24.032759316578186 "4.0.576.2" [] [0, 0, -12, 0] NULL "q+\\beta _{1}q^{2}+2\\beta _{2}q^{4}+(-2-\\beta _{1}+2\\beta _{2}+\\cdots)q^{5}+\\cdots" "882.3.n.b" 4 24.032759316578186 "4.0.576.2" [] [0, 0, -6, 0] NULL "q+(\\beta _{1}+\\beta _{3})q^{2}+(-2-2\\beta _{2})q^{4}+(-2+\\cdots)q^{5}+\\cdots" "882.3.n.c" 4 24.032759316578186 "4.0.576.2" [] [0, 0, 0, 0] NULL "q+(-\\beta _{1}-\\beta _{3})q^{2}+(-2-2\\beta _{2})q^{4}+\\cdots" "882.3.n.d" 4 24.032759316578186 "4.0.576.2" [] [0, 0, 12, 0] NULL "q+\\beta _{1}q^{2}+2\\beta _{2}q^{4}+(2+\\beta _{1}-2\\beta _{2}+\\cdots)q^{5}+\\cdots" "882.3.n.e" 4 24.032759316578186 "4.0.576.2" [] [0, 0, 12, 0] NULL "q+(-\\beta _{1}-\\beta _{3})q^{2}+(-2-2\\beta _{2})q^{4}+\\cdots" "882.3.n.f" 8 24.032759316578186 "8.0.339738624.1" [] [0, 0, 0, 0] NULL "q+(-\\beta _{2}-\\beta _{5})q^{2}+2\\beta _{4}q^{4}+(\\beta _{1}+2\\beta _{2}+\\cdots)q^{5}+\\cdots" "882.3.n.g" 8 24.032759316578186 "8.0.339738624.1" [] [0, 0, 0, 0] NULL "q+(\\beta _{2}+\\beta _{6})q^{2}+2\\beta _{4}q^{4}+(\\beta _{1}+2\\beta _{3}+\\cdots)q^{5}+\\cdots" "882.3.n.h" 8 24.032759316578186 "8.0.339738624.1" [] [0, 0, 0, 0] NULL "q+(-\\beta _{2}-\\beta _{6})q^{2}+2\\beta _{4}q^{4}+(\\beta _{1}+2\\beta _{3}+\\cdots)q^{5}+\\cdots" "882.3.n.i" 8 24.032759316578186 "8.0.77720518656.7" [] [0, 0, 0, 0] NULL "q+\\beta _{3}q^{2}+(-2-2\\beta _{1})q^{4}+(-\\beta _{6}-\\beta _{7})q^{5}+\\cdots" "882.3.n.j" 8 24.032759316578186 "8.0.339738624.1" [] [0, 0, 0, 0] NULL "q+\\beta _{6}q^{2}+(-2-2\\beta _{4})q^{4}+(-4\\beta _{3}+\\cdots)q^{5}+\\cdots" "882.3.n.k" 8 24.032759316578186 "8.0.339738624.1" [] [0, 0, 0, 0] NULL "q-\\beta _{5}q^{2}+(-2-2\\beta _{4})q^{4}+(4\\beta _{2}+2\\beta _{5}+\\cdots)q^{5}+\\cdots" "882.3.s.a" 4 24.032759316578186 "4.0.576.1" [] [0, 0, 0, 0] NULL "q-\\beta _{1}q^{2}+2\\beta _{2}q^{4}+3\\beta _{1}q^{5}-2\\beta _{3}q^{8}+\\cdots" "882.3.s.b" 4 24.032759316578186 "4.0.576.1" [] [0, 0, 0, 0] NULL "q-\\beta _{1}q^{2}+2\\beta _{2}q^{4}+3\\beta _{1}q^{5}-2\\beta _{3}q^{8}+\\cdots" "882.3.s.c" 4 24.032759316578186 "4.0.576.1" [] [0, 0, 0, 0] NULL "q-\\beta _{1}q^{2}+2\\beta _{2}q^{4}+\\beta _{1}q^{5}-2\\beta _{3}q^{8}+\\cdots" "882.3.s.d" 4 24.032759316578186 "4.0.576.1" [] [0, 0, 0, 0] NULL "q+\\beta _{1}q^{2}+2\\beta _{2}q^{4}+3\\beta _{1}q^{5}+2\\beta _{3}q^{8}+\\cdots" "882.3.s.e" 8 24.032759316578186 "8.0.12745506816.5" [] [0, 0, 0, 0] NULL "q+(\\beta _{2}+\\beta _{6})q^{2}+2\\beta _{1}q^{4}+(-\\beta _{2}-\\beta _{6}+\\cdots)q^{5}+\\cdots" "882.3.s.f" 8 24.032759316578186 "8.0.5308416.1" [] [0, 0, 0, 0] NULL "q+\\beta_{6} q^{2}+2\\beta_{2} q^{4}-\\beta_1 q^{5}+(2\\beta_{6}-2\\beta_{5})q^{8}+\\cdots" "882.3.s.g" 8 24.032759316578186 "8.0.5308416.1" [] [0, 0, 0, 0] NULL "q+\\beta_{6} q^{2}+2\\beta_{2} q^{4}-2\\beta_1 q^{5}+(2\\beta_{6}-2\\beta_{5})q^{8}+\\cdots" "882.3.s.h" 8 24.032759316578186 "8.0.621801639936.1" [] [0, 0, 0, 0] NULL "q-\\beta _{4}q^{2}+2\\beta _{1}q^{4}-\\beta _{2}q^{5}+(-2\\beta _{4}+\\cdots)q^{8}+\\cdots" "882.3.s.i" 8 24.032759316578186 "8.0.12745506816.5" [] [0, 0, 0, 0] NULL "q+(-\\beta _{2}-\\beta _{6})q^{2}+2\\beta _{1}q^{4}+(-\\beta _{2}+\\cdots)q^{5}+\\cdots" "882.4.a.a" 1 52.039684625063224 "1.1.1.1" [] [-2, 0, -22, 0] -1 "q-2q^{2}+4q^{4}-22q^{5}-8q^{8}+44q^{10}+\\cdots" "882.4.a.b" 1 52.039684625063224 "1.1.1.1" [] [-2, 0, -12, 0] 1 "q-2q^{2}+4q^{4}-12q^{5}-8q^{8}+24q^{10}+\\cdots" "882.4.a.c" 1 52.039684625063224 "1.1.1.1" [] [-2, 0, -9, 0] 1 "q-2q^{2}+4q^{4}-9q^{5}-8q^{8}+18q^{10}+\\cdots" "882.4.a.d" 1 52.039684625063224 "1.1.1.1" [] [-2, 0, 2, 0] 1 "q-2q^{2}+4q^{4}+2q^{5}-8q^{8}-4q^{10}+\\cdots" "882.4.a.e" 1 52.039684625063224 "1.1.1.1" [] [-2, 0, 6, 0] -1 "q-2q^{2}+4q^{4}+6q^{5}-8q^{8}-12q^{10}+\\cdots" "882.4.a.f" 1 52.039684625063224 "1.1.1.1" [] [-2, 0, 9, 0] -1 "q-2q^{2}+4q^{4}+9q^{5}-8q^{8}-18q^{10}+\\cdots" "882.4.a.g" 1 52.039684625063224 "1.1.1.1" [] [-2, 0, 18, 0] 1 "q-2q^{2}+4q^{4}+18q^{5}-8q^{8}-6^{2}q^{10}+\\cdots" "882.4.a.h" 1 52.039684625063224 "1.1.1.1" [] [2, 0, -15, 0] -1 "q+2q^{2}+4q^{4}-15q^{5}+8q^{8}-30q^{10}+\\cdots" "882.4.a.i" 1 52.039684625063224 "1.1.1.1" [] [2, 0, -14, 0] -1 "q+2q^{2}+4q^{4}-14q^{5}+8q^{8}-28q^{10}+\\cdots" "882.4.a.j" 1 52.039684625063224 "1.1.1.1" [] [2, 0, -8, 0] -1 "q+2q^{2}+4q^{4}-8q^{5}+8q^{8}-2^{4}q^{10}+\\cdots" "882.4.a.k" 1 52.039684625063224 "1.1.1.1" [] [2, 0, -7, 0] 1 "q+2q^{2}+4q^{4}-7q^{5}+8q^{8}-14q^{10}+\\cdots" "882.4.a.l" 1 52.039684625063224 "1.1.1.1" [] [2, 0, -6, 0] -1 "q+2q^{2}+4q^{4}-6q^{5}+8q^{8}-12q^{10}+\\cdots" "882.4.a.m" 1 52.039684625063224 "1.1.1.1" [] [2, 0, -6, 0] 1 "q+2q^{2}+4q^{4}-6q^{5}+8q^{8}-12q^{10}+\\cdots" "882.4.a.n" 1 52.039684625063224 "1.1.1.1" [] [2, 0, 6, 0] -1 "q+2q^{2}+4q^{4}+6q^{5}+8q^{8}+12q^{10}+\\cdots" "882.4.a.o" 1 52.039684625063224 "1.1.1.1" [] [2, 0, 6, 0] 1 "q+2q^{2}+4q^{4}+6q^{5}+8q^{8}+12q^{10}+\\cdots" "882.4.a.p" 1 52.039684625063224 "1.1.1.1" [] [2, 0, 7, 0] -1 "q+2q^{2}+4q^{4}+7q^{5}+8q^{8}+14q^{10}+\\cdots" "882.4.a.q" 1 52.039684625063224 "1.1.1.1" [] [2, 0, 8, 0] -1 "q+2q^{2}+4q^{4}+8q^{5}+8q^{8}+2^{4}q^{10}+\\cdots" "882.4.a.r" 1 52.039684625063224 "1.1.1.1" [] [2, 0, 15, 0] 1 "q+2q^{2}+4q^{4}+15q^{5}+8q^{8}+30q^{10}+\\cdots" "882.4.a.s" 1 52.039684625063224 "1.1.1.1" [] [2, 0, 22, 0] 1 "q+2q^{2}+4q^{4}+22q^{5}+8q^{8}+44q^{10}+\\cdots" "882.4.a.t" 2 52.039684625063224 "2.2.8.1" [] [-4, 0, -12, 0] -1 "q-2q^{2}+4q^{4}+(-6+\\beta )q^{5}-8q^{8}+\\cdots" "882.4.a.u" 2 52.039684625063224 "2.2.193.1" [] [-4, 0, -7, 0] -1 "q-2q^{2}+4q^{4}+(-3-\\beta )q^{5}-8q^{8}+\\cdots" "882.4.a.v" 2 52.039684625063224 "2.2.1345.1" [] [-4, 0, -5, 0] -1 "q-2q^{2}+4q^{4}+(-2-\\beta )q^{5}-8q^{8}+\\cdots" "882.4.a.w" 2 52.039684625063224 "2.2.88.1" [] [-4, 0, 0, 0] 1 "q-2q^{2}+4q^{4}+\\beta q^{5}-8q^{8}-2\\beta q^{10}+\\cdots" "882.4.a.x" 2 52.039684625063224 "2.2.232.1" [] [-4, 0, 0, 0] -1 "q-2q^{2}+4q^{4}+\\beta q^{5}-8q^{8}-2\\beta q^{10}+\\cdots" "882.4.a.y" 2 52.039684625063224 "2.2.8.1" [] [-4, 0, 0, 0] 1 "q-2q^{2}+4q^{4}+5\\beta q^{5}-8q^{8}-10\\beta q^{10}+\\cdots" "882.4.a.z" 2 52.039684625063224 "2.2.1345.1" [] [-4, 0, 5, 0] 1 "q-2q^{2}+4q^{4}+(3-\\beta )q^{5}-8q^{8}+(-6+\\cdots)q^{10}+\\cdots" "882.4.a.ba" 2 52.039684625063224 "2.2.193.1" [] [-4, 0, 7, 0] 1 "q-2q^{2}+4q^{4}+(4-\\beta )q^{5}-8q^{8}+(-8+\\cdots)q^{10}+\\cdots" "882.4.a.bb" 2 52.039684625063224 "2.2.8.1" [] [-4, 0, 12, 0] -1 "q-2q^{2}+4q^{4}+(6+\\beta )q^{5}-8q^{8}+(-12+\\cdots)q^{10}+\\cdots" "882.4.a.bc" 2 52.039684625063224 "2.2.8.1" [] [4, 0, -12, 0] 1 "q+2q^{2}+4q^{4}+(-6+\\beta )q^{5}+8q^{8}+\\cdots" "882.4.a.bd" 2 52.039684625063224 "2.2.193.1" [] [4, 0, -7, 0] -1 "q+2q^{2}+4q^{4}+(-3-\\beta )q^{5}+8q^{8}+\\cdots" "882.4.a.be" 2 52.039684625063224 "2.2.8.1" [] [4, 0, 0, 0] -1 "q+2q^{2}+4q^{4}+5\\beta q^{5}+8q^{8}+10\\beta q^{10}+\\cdots" "882.4.a.bf" 2 52.039684625063224 "2.2.232.1" [] [4, 0, 0, 0] 1 "q+2q^{2}+4q^{4}+\\beta q^{5}+8q^{8}+2\\beta q^{10}+\\cdots" "882.4.a.bg" 2 52.039684625063224 "2.2.8.1" [] [4, 0, 0, 0] 1 "q+2q^{2}+4q^{4}+14\\beta q^{5}+8q^{8}+28\\beta q^{10}+\\cdots" "882.4.a.bh" 2 52.039684625063224 "2.2.193.1" [] [4, 0, 7, 0] 1 "q+2q^{2}+4q^{4}+(4-\\beta )q^{5}+8q^{8}+(8+\\cdots)q^{10}+\\cdots" "882.4.a.bi" 2 52.039684625063224 "2.2.8.1" [] [4, 0, 12, 0] 1 "q+2q^{2}+4q^{4}+(6+\\beta )q^{5}+8q^{8}+(12+\\cdots)q^{10}+\\cdots" "882.4.d.a" 8 52.039684625063224 "8.0.16777216.1" [] [0, 0, 0, 0] NULL "q+\\beta_1 q^{2}-4 q^{4}+(4\\beta_{7}-3\\beta_{5})q^{5}+\\cdots" "882.4.d.b" 16 52.039684625063224 NULL [] [0, 0, 0, 0] NULL "q-\\beta _{3}q^{2}-4q^{4}+(\\beta _{11}+\\beta _{14})q^{5}+4\\beta _{3}q^{8}+\\cdots" "882.4.d.c" 16 52.039684625063224 NULL [] [0, 0, 0, 0] NULL "q+\\beta _{4}q^{2}-4q^{4}+(\\beta _{2}-\\beta _{5}-\\beta _{11})q^{5}+\\cdots" "882.4.g.a" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, -22, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}-22\\zeta_{6}q^{5}+\\cdots" "882.4.g.b" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, -14, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}-14\\zeta_{6}q^{5}+\\cdots" "882.4.g.c" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, -8, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}-8\\zeta_{6}q^{5}+\\cdots" "882.4.g.d" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, -7, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}-7\\zeta_{6}q^{5}+\\cdots" "882.4.g.e" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, -6, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}-6\\zeta_{6}q^{5}+\\cdots" "882.4.g.f" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, -6, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}-6\\zeta_{6}q^{5}+\\cdots" "882.4.g.g" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, 6, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+6\\zeta_{6}q^{5}+\\cdots" "882.4.g.h" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, 6, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+6\\zeta_{6}q^{5}+\\cdots" "882.4.g.i" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, 6, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+6\\zeta_{6}q^{5}+\\cdots" "882.4.g.j" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, 8, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+8\\zeta_{6}q^{5}+\\cdots" "882.4.g.k" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, 14, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+14\\zeta_{6}q^{5}+\\cdots" "882.4.g.l" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, 15, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+15\\zeta_{6}q^{5}+\\cdots" "882.4.g.m" 2 52.039684625063224 "2.0.3.1" [] [-2, 0, 22, 0] NULL "q-2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+22\\zeta_{6}q^{5}+\\cdots" "882.4.g.n" 2 52.039684625063224 "2.0.3.1" [] [2, 0, -22, 0] NULL "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}-22\\zeta_{6}q^{5}+\\cdots" "882.4.g.o" 2 52.039684625063224 "2.0.3.1" [] [2, 0, -18, 0] NULL "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}-18\\zeta_{6}q^{5}+\\cdots" "882.4.g.p" 2 52.039684625063224 "2.0.3.1" [] [2, 0, -12, 0] NULL "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}-12\\zeta_{6}q^{5}+\\cdots" "882.4.g.q" 2 52.039684625063224 "2.0.3.1" [] [2, 0, -6, 0] NULL "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}-6\\zeta_{6}q^{5}+\\cdots" "882.4.g.r" 2 52.039684625063224 "2.0.3.1" [] [2, 0, -2, 0] NULL "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}-2\\zeta_{6}q^{5}+\\cdots" "882.4.g.s" 2 52.039684625063224 "2.0.3.1" [] [2, 0, 2, 0] NULL "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+2\\zeta_{6}q^{5}+\\cdots" "882.4.g.t" 2 52.039684625063224 "2.0.3.1" [] [2, 0, 6, 0] NULL "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+6\\zeta_{6}q^{5}+\\cdots" "882.4.g.u" 2 52.039684625063224 "2.0.3.1" [] [2, 0, 9, 0] NULL "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+9\\zeta_{6}q^{5}+\\cdots" "882.4.g.v" 2 52.039684625063224 "2.0.3.1" [] [2, 0, 12, 0] NULL "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+12\\zeta_{6}q^{5}+\\cdots" "882.4.g.w" 2 52.039684625063224 "2.0.3.1" [] [2, 0, 18, 0] NULL "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+18\\zeta_{6}q^{5}+\\cdots" "882.4.g.x" 2 52.039684625063224 "2.0.3.1" [] [2, 0, 22, 0] NULL "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+22\\zeta_{6}q^{5}+\\cdots" "882.4.g.y" 4 52.039684625063224 "4.0.576.2" [] [-4, 0, -12, 0] NULL "q+(-2-2\\beta _{2})q^{2}+4\\beta _{2}q^{4}+(-6-\\beta _{1}+\\cdots)q^{5}+\\cdots" "882.4.g.z" 4 52.039684625063224 "4.0.335241.2" [] [-4, 0, -7, 0] NULL "q-2\\beta _{2}q^{2}+(-4+4\\beta _{2})q^{4}+(-\\beta _{1}+\\cdots)q^{5}+\\cdots" "882.4.g.ba" 4 52.039684625063224 "4.0.576.2" [] [-4, 0, 0, 0] NULL "q+(-2-2\\beta _{2})q^{2}+4\\beta _{2}q^{4}+14\\beta _{1}q^{5}+\\cdots" "882.4.g.bb" 4 52.039684625063224 "4.0.484416.7" [] [-4, 0, 0, 0] NULL "q+(-2-2\\beta _{2})q^{2}+4\\beta _{2}q^{4}+\\beta _{1}q^{5}+\\cdots" "882.4.g.bc" 4 52.039684625063224 "4.0.576.2" [] [-4, 0, 0, 0] NULL "q+(-2-2\\beta _{2})q^{2}+4\\beta _{2}q^{4}+5\\beta _{1}q^{5}+\\cdots" "882.4.g.bd" 4 52.039684625063224 "4.0.576.2" [] [-4, 0, 12, 0] NULL "q+(-2-2\\beta _{2})q^{2}+4\\beta _{2}q^{4}+(6+\\beta _{1}+\\cdots)q^{5}+\\cdots" "882.4.g.be" 4 52.039684625063224 "4.0.576.2" [] [4, 0, -12, 0] NULL "q-2\\beta _{2}q^{2}+(-4-4\\beta _{2})q^{4}+(-\\beta _{1}+\\cdots)q^{5}+\\cdots" "882.4.g.bf" 4 52.039684625063224 "4.0.16281225.4" [] [4, 0, -5, 0] NULL "q+2\\beta _{2}q^{2}+(-4+4\\beta _{2})q^{4}+(-\\beta _{1}+\\cdots)q^{5}+\\cdots" "882.4.g.bg" 4 52.039684625063224 "4.0.576.2" [] [4, 0, 0, 0] NULL "q+(2+2\\beta _{2})q^{2}+4\\beta _{2}q^{4}+5\\beta _{1}q^{5}+\\cdots" "882.4.g.bh" 4 52.039684625063224 "4.0.484416.7" [] [4, 0, 0, 0] NULL "q+(2+2\\beta _{2})q^{2}+4\\beta _{2}q^{4}+\\beta _{1}q^{5}-8q^{8}+\\cdots" "882.4.g.bi" 4 52.039684625063224 "4.0.69696.6" [] [4, 0, 0, 0] NULL "q+(2+2\\beta _{2})q^{2}+4\\beta _{2}q^{4}+\\beta _{1}q^{5}-8q^{8}+\\cdots" "882.4.g.bj" 4 52.039684625063224 "4.0.335241.2" [] [4, 0, 7, 0] NULL "q+2\\beta _{2}q^{2}+(-4+4\\beta _{2})q^{4}+(-\\beta _{1}+\\cdots)q^{5}+\\cdots" "882.4.g.bk" 4 52.039684625063224 "4.0.576.2" [] [4, 0, 12, 0] NULL "q-2\\beta _{2}q^{2}+(-4-4\\beta _{2})q^{4}+(-\\beta _{1}+\\cdots)q^{5}+\\cdots" "882.4.k.a" 16 52.039684625063224 NULL [] [0, 0, 0, 0] NULL "q+\\beta _{8}q^{2}+(4-4\\beta _{1})q^{4}+(2\\beta _{4}+\\beta _{8}+\\cdots)q^{5}+\\cdots" "882.4.k.b" 16 52.039684625063224 "16.0.1846757322198614016.1" [] [0, 0, 0, 0] NULL "q+\\beta_1 q^{2}+4\\beta_{3} q^{4}+(-3\\beta_{15}+4\\beta_{8}+3\\beta_{4})q^{5}+\\cdots" "882.4.k.c" 16 52.039684625063224 "16.0.721389578983833600000000.8" [] [0, 0, 0, 0] NULL "q+\\beta _{1}q^{2}+4\\beta _{2}q^{4}+(-\\beta _{4}+\\beta _{6})q^{5}+\\cdots" "882.4.k.d" 32 52.039684625063224 NULL [] [0, 0, 0, 0] NULL NULL "882.5.b.a" 4 91.1723074399507 "4.0.12544.1" [] [0, 0, 0, 0] NULL "q+2\\beta _{1}q^{2}-8q^{4}+(5\\beta _{1}+\\beta _{2})q^{5}-2^{4}\\beta _{1}q^{8}+\\cdots" "882.5.b.b" 4 91.1723074399507 "4.0.215296.2" [] [0, 0, 0, 0] NULL "q+2\\beta _{1}q^{2}-8q^{4}+\\beta _{3}q^{5}-2^{4}\\beta _{1}q^{8}+\\cdots" "882.5.b.c" 4 91.1723074399507 "4.0.719104.2" [] [0, 0, 0, 0] NULL "q-2\\beta _{1}q^{2}-8q^{4}+\\beta _{3}q^{5}+2^{4}\\beta _{1}q^{8}+\\cdots" "882.5.b.d" 4 91.1723074399507 "4.0.12544.1" [] [0, 0, 0, 0] NULL "q+2\\beta _{1}q^{2}-8q^{4}+(-13\\beta _{1}+\\beta _{2})q^{5}+\\cdots" "882.5.b.e" 6 91.1723074399507 NULL [] [0, 0, 0, 0] NULL "q-2\\beta _{1}q^{2}-8q^{4}+(-4\\beta _{1}+\\beta _{2})q^{5}+\\cdots" "882.5.b.f" 6 91.1723074399507 NULL [] [0, 0, 0, 0] NULL "q+2\\beta _{1}q^{2}-8q^{4}+(2\\beta _{1}-\\beta _{2})q^{5}-2^{4}\\beta _{1}q^{8}+\\cdots" "882.5.b.g" 6 91.1723074399507 NULL [] [0, 0, 0, 0] NULL "q-2\\beta _{1}q^{2}-8q^{4}+(2\\beta _{1}-\\beta _{2})q^{5}+2^{4}\\beta _{1}q^{8}+\\cdots" "882.5.b.h" 6 91.1723074399507 NULL [] [0, 0, 0, 0] NULL "q+2\\beta _{1}q^{2}-8q^{4}+(-4\\beta _{1}+\\beta _{2})q^{5}+\\cdots" "882.5.b.i" 8 91.1723074399507 "8.0.4494128644096.9" [] [0, 0, 0, 0] NULL "q+2\\beta _{2}q^{2}-8q^{4}+(-\\beta _{1}-\\beta _{4})q^{5}+\\cdots" "882.5.b.j" 8 91.1723074399507 "8.0.224054542336.12" [] [0, 0, 0, 0] NULL "q-2\\beta _{2}q^{2}-8q^{4}-\\beta _{3}q^{5}+2^{4}\\beta _{2}q^{8}+\\cdots" "882.5.c.a" 4 91.1723074399507 "4.0.576.2" [] [0, 0, 0, 0] NULL "q-\\beta _{1}q^{2}+8q^{4}+(-11\\beta _{2}-\\beta _{3})q^{5}+\\cdots" "882.5.c.b" 4 91.1723074399507 "4.0.576.2" [] [0, 0, 0, 0] NULL "q+\\beta _{1}q^{2}+8q^{4}+(-9\\beta _{2}-2\\beta _{3})q^{5}+\\cdots" "882.5.c.c" 4 91.1723074399507 "4.0.2048.2" [] [0, 0, 0, 0] NULL "q+2\\beta _{2}q^{2}+8q^{4}+(-5\\beta _{1}-13\\beta _{3})q^{5}+\\cdots" "882.5.c.d" 4 91.1723074399507 "4.0.2048.2" [] [0, 0, 0, 0] NULL "q+2\\beta _{2}q^{2}+8q^{4}+(19\\beta _{1}+13\\beta _{3})q^{5}+\\cdots" "882.5.c.e" 8 91.1723074399507 NULL [] [0, 0, 0, 0] NULL "q+\\beta _{3}q^{2}+8q^{4}+(-3\\beta _{1}-2\\beta _{2}-\\beta _{4}+\\cdots)q^{5}+\\cdots" "882.5.c.f" 8 91.1723074399507 "8.0.339738624.1" [] [0, 0, 0, 0] NULL "q+2\\beta _{1}q^{2}+8q^{4}+(5\\beta _{2}-11\\beta _{3})q^{5}+\\cdots" "882.5.c.g" 8 91.1723074399507 "8.0.950328623104.21" [] [0, 0, 0, 0] NULL "q+2\\beta _{1}q^{2}+8q^{4}+(-\\beta _{3}-4\\beta _{4})q^{5}+\\cdots" "882.5.c.h" 8 91.1723074399507 "8.0.950328623104.21" [] [0, 0, 0, 0] NULL "q-2\\beta _{1}q^{2}+8q^{4}+(-\\beta _{3}-4\\beta _{4})q^{5}+\\cdots" "882.5.c.i" 8 91.1723074399507 "8.0.339738624.1" [] [0, 0, 0, 0] NULL "q+2\\beta _{1}q^{2}+8q^{4}+(-5\\beta _{2}+\\beta _{3}-\\beta _{4}+\\cdots)q^{5}+\\cdots" "882.5.c.j" 12 91.1723074399507 NULL [] [0, 0, 0, 0] NULL "q-\\beta _{1}q^{2}+8q^{4}-\\beta _{3}q^{5}-8\\beta _{1}q^{8}+\\cdots" "882.6.a.a" 1 141.45852907504892 "1.1.1.1" [] [-4, 0, -66, 0] 1 "q-4q^{2}+2^{4}q^{4}-66q^{5}-2^{6}q^{8}+264q^{10}+\\cdots" "882.6.a.b" 1 141.45852907504892 "1.1.1.1" [] [-4, 0, -54, 0] -1 "q-4q^{2}+2^{4}q^{4}-54q^{5}-2^{6}q^{8}+6^{3}q^{10}+\\cdots" "882.6.a.c" 1 141.45852907504892 "1.1.1.1" [] [-4, 0, -26, 0] -1 "q-4q^{2}+2^{4}q^{4}-26q^{5}-2^{6}q^{8}+104q^{10}+\\cdots" "882.6.a.d" 1 141.45852907504892 "1.1.1.1" [] [-4, 0, -12, 0] 1 "q-4q^{2}+2^{4}q^{4}-12q^{5}-2^{6}q^{8}+48q^{10}+\\cdots" "882.6.a.e" 1 141.45852907504892 "1.1.1.1" [] [-4, 0, -6, 0] 1 "q-4q^{2}+2^{4}q^{4}-6q^{5}-2^{6}q^{8}+24q^{10}+\\cdots" "882.6.a.f" 1 141.45852907504892 "1.1.1.1" [] [-4, 0, 6, 0] -1 "q-4q^{2}+2^{4}q^{4}+6q^{5}-2^{6}q^{8}-24q^{10}+\\cdots" "882.6.a.g" 1 141.45852907504892 "1.1.1.1" [] [-4, 0, 10, 0] 1 "q-4q^{2}+2^{4}q^{4}+10q^{5}-2^{6}q^{8}-40q^{10}+\\cdots" "882.6.a.h" 1 141.45852907504892 "1.1.1.1" [] [-4, 0, 12, 0] -1 "q-4q^{2}+2^{4}q^{4}+12q^{5}-2^{6}q^{8}-48q^{10}+\\cdots" "882.6.a.i" 1 141.45852907504892 "1.1.1.1" [] [-4, 0, 24, 0] 1 "q-4q^{2}+2^{4}q^{4}+24q^{5}-2^{6}q^{8}-96q^{10}+\\cdots" "882.6.a.j" 1 141.45852907504892 "1.1.1.1" [] [-4, 0, 76, 0] 1 "q-4q^{2}+2^{4}q^{4}+76q^{5}-2^{6}q^{8}-304q^{10}+\\cdots" "882.6.a.k" 1 141.45852907504892 "1.1.1.1" [] [-4, 0, 96, 0] -1 "q-4q^{2}+2^{4}q^{4}+96q^{5}-2^{6}q^{8}-384q^{10}+\\cdots" "882.6.a.l" 1 141.45852907504892 "1.1.1.1" [] [4, 0, -96, 0] 1 "q+4q^{2}+2^{4}q^{4}-96q^{5}+2^{6}q^{8}-384q^{10}+\\cdots" "882.6.a.m" 1 141.45852907504892 "1.1.1.1" [] [4, 0, -86, 0] 1 "q+4q^{2}+2^{4}q^{4}-86q^{5}+2^{6}q^{8}-344q^{10}+\\cdots" "882.6.a.n" 1 141.45852907504892 "1.1.1.1" [] [4, 0, -72, 0] -1 "q+4q^{2}+2^{4}q^{4}-72q^{5}+2^{6}q^{8}-288q^{10}+\\cdots" "882.6.a.o" 1 141.45852907504892 "1.1.1.1" [] [4, 0, -54, 0] -1 "q+4q^{2}+2^{4}q^{4}-54q^{5}+2^{6}q^{8}-6^{3}q^{10}+\\cdots" "882.6.a.p" 1 141.45852907504892 "1.1.1.1" [] [4, 0, -26, 0] -1 "q+4q^{2}+2^{4}q^{4}-26q^{5}+2^{6}q^{8}-104q^{10}+\\cdots" "882.6.a.q" 1 141.45852907504892 "1.1.1.1" [] [4, 0, -12, 0] 1 "q+4q^{2}+2^{4}q^{4}-12q^{5}+2^{6}q^{8}-48q^{10}+\\cdots" "882.6.a.r" 1 141.45852907504892 "1.1.1.1" [] [4, 0, 12, 0] -1 "q+4q^{2}+2^{4}q^{4}+12q^{5}+2^{6}q^{8}+48q^{10}+\\cdots" "882.6.a.s" 1 141.45852907504892 "1.1.1.1" [] [4, 0, 26, 0] -1 "q+4q^{2}+2^{4}q^{4}+26q^{5}+2^{6}q^{8}+104q^{10}+\\cdots" "882.6.a.t" 1 141.45852907504892 "1.1.1.1" [] [4, 0, 26, 0] -1 "q+4q^{2}+2^{4}q^{4}+26q^{5}+2^{6}q^{8}+104q^{10}+\\cdots" "882.6.a.u" 1 141.45852907504892 "1.1.1.1" [] [4, 0, 26, 0] 1 "q+4q^{2}+2^{4}q^{4}+26q^{5}+2^{6}q^{8}+104q^{10}+\\cdots" "882.6.a.v" 1 141.45852907504892 "1.1.1.1" [] [4, 0, 44, 0] -1 "q+4q^{2}+2^{4}q^{4}+44q^{5}+2^{6}q^{8}+176q^{10}+\\cdots" "882.6.a.w" 1 141.45852907504892 "1.1.1.1" [] [4, 0, 54, 0] 1 "q+4q^{2}+2^{4}q^{4}+54q^{5}+2^{6}q^{8}+6^{3}q^{10}+\\cdots" "882.6.a.x" 1 141.45852907504892 "1.1.1.1" [] [4, 0, 84, 0] -1 "q+4q^{2}+2^{4}q^{4}+84q^{5}+2^{6}q^{8}+336q^{10}+\\cdots" "882.6.a.y" 1 141.45852907504892 "1.1.1.1" [] [4, 0, 86, 0] -1 "q+4q^{2}+2^{4}q^{4}+86q^{5}+2^{6}q^{8}+344q^{10}+\\cdots" "882.6.a.z" 2 141.45852907504892 "2.2.8.1" [] [-8, 0, -108, 0] -1 "q-4q^{2}+2^{4}q^{4}+(-54+5\\beta )q^{5}-2^{6}q^{8}+\\cdots" "882.6.a.ba" 2 141.45852907504892 "2.2.316.1" [] [-8, 0, -70, 0] -1 "q-4q^{2}+2^{4}q^{4}+(-35+4\\beta )q^{5}-2^{6}q^{8}+\\cdots" "882.6.a.bb" 2 141.45852907504892 "2.2.9601.1" [] [-8, 0, -53, 0] 1 "q-4q^{2}+2^{4}q^{4}+(-26-\\beta )q^{5}-2^{6}q^{8}+\\cdots" "882.6.a.bc" 2 141.45852907504892 "2.2.4705.1" [] [-8, 0, -18, 0] 1 "q-4q^{2}+2^{4}q^{4}+(-9-\\beta )q^{5}-2^{6}q^{8}+\\cdots" "882.6.a.bd" 2 141.45852907504892 "2.2.697.1" [] [-8, 0, -7, 0] 1 "q-4q^{2}+2^{4}q^{4}+(-1-5\\beta )q^{5}-2^{6}q^{8}+\\cdots" "882.6.a.be" 2 141.45852907504892 "2.2.1096.1" [] [-8, 0, 0, 0] -1 "q-4q^{2}+2^{4}q^{4}+\\beta q^{5}-2^{6}q^{8}-4\\beta q^{10}+\\cdots" "882.6.a.bf" 2 141.45852907504892 "2.2.697.1" [] [-8, 0, 7, 0] -1 "q-4q^{2}+2^{4}q^{4}+(1+5\\beta )q^{5}-2^{6}q^{8}+\\cdots" "882.6.a.bg" 2 141.45852907504892 "2.2.4705.1" [] [-8, 0, 18, 0] 1 "q-4q^{2}+2^{4}q^{4}+(9-\\beta )q^{5}-2^{6}q^{8}+\\cdots" "882.6.a.bh" 2 141.45852907504892 "2.2.9601.1" [] [-8, 0, 53, 0] -1 "q-4q^{2}+2^{4}q^{4}+(3^{3}-\\beta )q^{5}-2^{6}q^{8}+\\cdots" "882.6.a.bi" 2 141.45852907504892 "2.2.316.1" [] [-8, 0, 70, 0] 1 "q-4q^{2}+2^{4}q^{4}+(35+4\\beta )q^{5}-2^{6}q^{8}+\\cdots" "882.6.a.bj" 2 141.45852907504892 "2.2.8.1" [] [-8, 0, 108, 0] -1 "q-4q^{2}+2^{4}q^{4}+(54+5\\beta )q^{5}-2^{6}q^{8}+\\cdots" "882.6.a.bk" 2 141.45852907504892 "2.2.8.1" [] [8, 0, -108, 0] 1 "q+4q^{2}+2^{4}q^{4}+(-54+5\\beta )q^{5}+2^{6}q^{8}+\\cdots" "882.6.a.bl" 2 141.45852907504892 "2.2.520.1" [] [8, 0, -42, 0] -1 "q+4q^{2}+2^{4}q^{4}-21q^{5}+2^{6}q^{8}-84q^{10}+\\cdots" "882.6.a.bm" 2 141.45852907504892 "2.2.505.1" [] [8, 0, -17, 0] 1 "q+4q^{2}+2^{4}q^{4}+(-9-\\beta )q^{5}+2^{6}q^{8}+\\cdots" "882.6.a.bn" 2 141.45852907504892 "2.2.697.1" [] [8, 0, -7, 0] 1 "q+4q^{2}+2^{4}q^{4}+(-1-5\\beta )q^{5}+2^{6}q^{8}+\\cdots" "882.6.a.bo" 2 141.45852907504892 "2.2.184.1" [] [8, 0, 0, 0] -1 "q+4q^{2}+2^{4}q^{4}+7\\beta q^{5}+2^{6}q^{8}+28\\beta q^{10}+\\cdots" "882.6.a.bp" 2 141.45852907504892 "2.2.8.1" [] [8, 0, 0, 0] 1 "q+4q^{2}+2^{4}q^{4}+7\\beta q^{5}+2^{6}q^{8}+28\\beta q^{10}+\\cdots" "882.6.a.bq" 2 141.45852907504892 "2.2.1096.1" [] [8, 0, 0, 0] 1 "q+4q^{2}+2^{4}q^{4}+\\beta q^{5}+2^{6}q^{8}+4\\beta q^{10}+\\cdots" "882.6.a.br" 2 141.45852907504892 "2.2.697.1" [] [8, 0, 7, 0] -1 "q+4q^{2}+2^{4}q^{4}+(1+5\\beta )q^{5}+2^{6}q^{8}+\\cdots" "882.6.a.bs" 2 141.45852907504892 "2.2.505.1" [] [8, 0, 17, 0] -1 "q+4q^{2}+2^{4}q^{4}+(9+\\beta )q^{5}+2^{6}q^{8}+\\cdots" "882.6.a.bt" 2 141.45852907504892 "2.2.520.1" [] [8, 0, 42, 0] 1 "q+4q^{2}+2^{4}q^{4}+21q^{5}+2^{6}q^{8}+84q^{10}+\\cdots" "882.6.a.bu" 2 141.45852907504892 "2.2.8.1" [] [8, 0, 108, 0] 1 "q+4q^{2}+2^{4}q^{4}+(54+5\\beta )q^{5}+2^{6}q^{8}+\\cdots" "882.6.a.bv" 4 141.45852907504892 "4.4.40246336.5" [] [-16, 0, 0, 0] -1 "q-4q^{2}+2^{4}q^{4}+(3\\beta _{1}+\\beta _{3})q^{5}-2^{6}q^{8}+\\cdots" "882.6.a.bw" 6 141.45852907504892 NULL [] [-24, 0, 0, 0] 1 "q-4q^{2}+2^{4}q^{4}+(\\beta _{1}+2\\beta _{2})q^{5}-2^{6}q^{8}+\\cdots" "882.6.a.bx" 6 141.45852907504892 NULL [] [24, 0, 0, 0] -1 "q+4q^{2}+2^{4}q^{4}+(\\beta _{1}+2\\beta _{2})q^{5}+2^{6}q^{8}+\\cdots" "882.6.d.a" 16 141.45852907504892 NULL [] [0, 0, 0, 0] NULL "q+2\\beta _{3}q^{2}-2^{4}q^{4}+(-3\\beta _{10}-\\beta _{14}+\\cdots)q^{5}+\\cdots" "882.6.d.b" 24 141.45852907504892 NULL [] [0, 0, 0, 0] NULL NULL "882.6.d.c" 24 141.45852907504892 NULL [] [0, 0, 0, 0] NULL NULL # Label -- # The **label** of a newform $f\in S_k^{\rm new}(N,\chi)$ has the format \( N.k.a.x \), where # - \( N\) is the level; # - \(k\) is the weight; # - \(N.a\) is the label of the Galois orbit of the Dirichlet character $\chi$; # - \(x\) is the label of the Galois orbit of the newform $f$. # For each embedding of the coefficient field of $f$ into the complex numbers, the corresponding modular form over $\C$ has a label of the form \(N.k.a.x.n.i\), where # - \(n\) determines the Conrey label \(N.n\) of the Dirichlet character \(\chi\); # - \(i\) is an integer ranging from 1 to the relative dimension of the newform that distinguishes embeddings with the same character $\chi$. # Dim -- # The **dimension** of a space of modular forms is its dimension as a complex vector space; for spaces of newforms $S_k^{\rm new}(N,\chi)$ this is the same as the dimension of the $\Q$-vector space spanned by its eigenforms. # The **dimension** of a newform refers to the dimension of its newform subspace, equivalently, the cardinality of its newform orbit. This is equal to the degree of its coefficient field (as an extension of $\Q$). # The **relative dimension** of $S_k^{\rm new}(N,\chi)$ is its dimension as a $\Q(\chi)$-vector space, where $\Q(\chi)$ is the field generated by the values of $\chi$, and similarly for newform subspaces. #$A$ (analytic_conductor) -- # The **analytic conductor** of a newform $f \in S_k^{\mathrm{new}}(N,\chi)$ is the positive real number # \[ # N\left(\frac{\exp(\psi(k/2))}{2\pi}\right)^2, # \] # where $\psi(x):=\Gamma'(x)/\Gamma(x)$ is the logarithmic derivative of the Gamma function. #Field (nf_label) -- # The **coefficient field** of a modular form is the subfield of $\C$ generated by the coefficients $a_n$ of its $q$-expansion $\sum a_nq^n$. The space of cusp forms $S_k^\mathrm{new}(N,\chi)$ has a basis of modular forms that are simultaneous eigenforms for all Hecke operators and with algebraic Fourier coefficients. For such eigenforms the coefficient field will be a number field, and Galois conjugate eigenforms will share the same coefficient field. Moreover, if $m$ is the smallest positive integer such that the values of the character $\chi$ are contained in the cyclotomic field $\Q(\zeta_m)$, the coefficient field will contain $\Q(\zeta_m)$ # For eigenforms, the coefficient field is also known as the **Hecke field**. #CM (cm_discs) -- # A newform $f$ admits a **self-twist** by a primitive # Dirichlet character $\chi$ if the equality # \[ # a_p(f) = \chi(p)a_p(f) # \] # holds for all but finitely many primes $p$. # For non-trivial $\chi$ this can hold only when $\chi$ has order $2$ and $a_p=0$ for all primes $p$ not dividing the level of $f$ for which $\chi(p)=-1$. # The character $\chi$ is then the Kronecker character of a quadratic field $K$ and may be identified by the discriminant $D$ of $K$. # If $D$ is negative, the modular form $f$ is said to have complex multiplication (CM) by $K$, and if $D$ is positive, $f$ is said to have real multiplication (RM) by $K$. The latter can occur only when $f$ is a modular form of weight $1$ whose projective image is dihedral. # It is possible for a modular form to have multiple non-trivial self twists; this occurs precisely when $f$ is a modular form of weight one whose projective image is isomorphic to $D_2:=C_2\times C_2$; in this case $f$ admits three non-trivial self twists, two of which are CM and one of which is RM. #Traces (trace_display) -- # For a newform $f \in S_k^{\rm new}(\Gamma_1(N))$, its **trace form** $\mathrm{Tr}(f)$ is the sum of its distinct conjugates under $\mathrm{Aut}(\C)$ (equivalently, the sum under all embeddings of the coefficient field into $\C$). The trace form is a modular form $\mathrm{Tr}(f) \in S_k^{\rm new}(\Gamma_1(N))$ whose $q$-expansion has integral coefficients $a_n(\mathrm{Tr}(f)) \in \Z$. # The coefficient $a_1$ is equal to the dimension of the newform. # For $p$ prime, the coefficient $a_p$ is the trace of Frobenius in the direct sum of the $\ell$-adic Galois representations attached to the conjugates of $f$ (for any prime $\ell$). When $f$ has weight $k=2$, the coefficient $a_p(f)$ is the trace of Frobenius acting on the modular abelian variety associated to $f$. # For a newspace $S_k^{\rm new}(N,\chi)$, its trace form is the sum of the trace forms $\mathrm{Tr}(f)$ over all newforms $f\in S_k^{\rm new}(N,k)$; it is also a modular form in $S_k^{\rm new}(\Gamma_1(N))$. # The graphical plot displayed in the properties box on the home page of each newform or newspace is computed using the trace form. #Fricke sign (fricke_eigenval) -- # The **Fricke involution** is the Atkin-Lehner involution $w_N$ on the space $S_k(\Gamma_0(N))$ (induced by the corresponding involution on the modular curve $X_0(N)$). # For a newform $f \in S_k^{\textup{new}}(\Gamma_0(N))$, the sign of the functional equation satisfied by the L-function attached to $f$ is $i^{-k}$ times the eigenvalue of $\omega_N$ on $f$. So, for example when $k=2$, the signs swap, and the analytic rank of $f$ is even when $w_N f = -f$ and odd when $w_N f = +f$. #$q$-expansion (qexp_display) -- # The **$q$-expansion** of a modular form $f(z)$ is its Fourier expansion at the cusp $z=i\infty$, expressed as a power series $\sum_{n=0}^{\infty} a_n q^n$ in the variable $q=e^{2\pi iz}$. # For cusp forms, the constant coefficient $a_0$ of the $q$-expansion is zero. # For newforms, we have $a_1=1$ and the coefficients $a_n$ are algebraic integers in a number field $K \subseteq \C$. # Accordingly, we define the **$q$-expansion** of a newform orbit $[f]$ to be the $q$-expansion of any newform $f$ in the orbit, but with coefficients $a_n \in K$ (without an embedding into $\C$). Each embedding $K \hookrightarrow \C$ then gives rise to an embedded newform whose $q$-expansion has $a_n \in \C$, as above.