# Classical modular forms downloaded from the LMFDB on 21 April 2026.
# Search link: https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/392/
# Query "{'level': 392}" returned 213 forms, sorted by analytic conductor.

# Each entry in the following data list has the form:
#    [Label, Dim, $A$, Field, CM, RM, Traces, Fricke sign, $q$-expansion]
# For more details, see the definitions at the bottom of the file.



"392.1.g.a"	1	0.19563348495213695	"1.1.1.1"	[-7, -8]	[56]	[1, 0, 0, 0]	NULL	"q+q^{2}+q^{4}+q^{8}-q^{9}-2q^{11}+q^{16}+\\cdots"
"392.1.g.b"	2	0.19563348495213695	"2.2.8.1"	[-8]	[]	[-2, 0, 0, 0]	NULL	"q-q^{2}-\\beta q^{3}+q^{4}+\\beta q^{6}-q^{8}+q^{9}+\\cdots"
"392.1.j.a"	2	0.19563348495213695	"2.0.3.1"	[-7, -56]	[8]	[1, 0, 0, 0]	NULL	"q+\\zeta_{6}q^{2}+\\zeta_{6}^{2}q^{4}-q^{8}+\\zeta_{6}q^{9}-\\zeta_{6}q^{16}+\\cdots"
"392.1.k.a"	2	0.19563348495213695	"2.0.3.1"	[-7, -8]	[56]	[-1, 0, 0, 0]	NULL	"q-\\zeta_{6}q^{2}+\\zeta_{6}^{2}q^{4}+q^{8}+\\zeta_{6}q^{9}-\\zeta_{6}^{2}q^{11}+\\cdots"
"392.1.k.b"	4	0.19563348495213695	"4.0.576.2"	[-8]	[]	[2, 0, 0, 0]	NULL	"q-\\beta _{2}q^{2}-\\beta _{1}q^{3}+(-1-\\beta _{2})q^{4}+\\beta _{3}q^{6}+\\cdots"
"392.2.a.a"	1	3.130135759234191	"1.1.1.1"	[]	[]	[0, -3, 1, 0]	1	"q-3q^{3}+q^{5}+6q^{9}-q^{11}-2q^{13}+\\cdots"
"392.2.a.b"	1	3.130135759234191	"1.1.1.1"	[]	[]	[0, -2, 4, 0]	-1	"q-2q^{3}+4q^{5}+q^{9}-8q^{15}+2q^{17}+\\cdots"
"392.2.a.c"	1	3.130135759234191	"1.1.1.1"	[]	[]	[0, -1, -1, 0]	1	"q-q^{3}-q^{5}-2q^{9}+3q^{11}-6q^{13}+\\cdots"
"392.2.a.d"	1	3.130135759234191	"1.1.1.1"	[]	[]	[0, 0, -2, 0]	1	"q-2q^{5}-3q^{9}-4q^{11}-2q^{13}+6q^{17}+\\cdots"
"392.2.a.e"	1	3.130135759234191	"1.1.1.1"	[]	[]	[0, 1, 1, 0]	-1	"q+q^{3}+q^{5}-2q^{9}+3q^{11}+6q^{13}+\\cdots"
"392.2.a.f"	1	3.130135759234191	"1.1.1.1"	[]	[]	[0, 3, -1, 0]	-1	"q+3q^{3}-q^{5}+6q^{9}-q^{11}+2q^{13}+\\cdots"
"392.2.a.g"	2	3.130135759234191	"2.2.8.1"	[]	[]	[0, 0, 0, 0]	-1	"q+\\beta q^{3}+2\\beta q^{5}-q^{9}+6q^{11}-4\\beta q^{13}+\\cdots"
"392.2.a.h"	2	3.130135759234191	"2.2.8.1"	[]	[]	[0, 0, 0, 0]	-1	"q+\\beta q^{3}+\\beta q^{5}+5q^{9}-4q^{11}-\\beta q^{13}+\\cdots"
"392.2.b.a"	2	3.130135759234191	"2.0.7.1"	[-7]	[]	[-1, 0, 0, 0]	NULL	"q-\\beta q^{2}+(-2+\\beta )q^{4}+(2+\\beta )q^{8}+3q^{9}+\\cdots"
"392.2.b.b"	2	3.130135759234191	"2.0.8.1"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta q^{2}-\\beta q^{3}-2q^{4}+\\beta q^{5}+2q^{6}+\\cdots"
"392.2.b.c"	4	3.130135759234191	"4.0.2312.1"	[]	[]	[-1, 0, 0, 0]	NULL	"q-\\beta _{1}q^{2}+(-\\beta _{1}+\\beta _{2})q^{3}+\\beta _{2}q^{4}+\\cdots"
"392.2.b.d"	4	3.130135759234191	"4.0.7168.1"	[-56]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{3}q^{2}+\\beta _{1}q^{3}+2q^{4}-\\beta _{2}q^{5}+(-\\beta _{1}+\\cdots)q^{6}+\\cdots"
"392.2.b.e"	6	3.130135759234191	"6.0.1142512.1"	[]	[]	[2, 0, 0, 0]	NULL	"q-\\beta _{4}q^{2}+\\beta _{3}q^{3}-\\beta _{2}q^{4}+(-\\beta _{1}+\\beta _{3}+\\cdots)q^{5}+\\cdots"
"392.2.b.f"	6	3.130135759234191	"6.0.1142512.1"	[]	[]	[2, 0, 0, 0]	NULL	"q-\\beta _{4}q^{2}-\\beta _{3}q^{3}-\\beta _{2}q^{4}+(\\beta _{1}-\\beta _{3}+\\cdots)q^{5}+\\cdots"
"392.2.b.g"	12	3.130135759234191	"12.0.11534581287092224.1"	[]	[]	[-2, 0, 0, 0]	NULL	"q-\\beta _{4}q^{2}-\\beta _{9}q^{3}-\\beta _{1}q^{4}+(\\beta _{7}-\\beta _{8}+\\cdots)q^{5}+\\cdots"
"392.2.e.a"	4	3.130135759234191	"4.0.2048.2"	[-8]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{2}q^{2}-\\beta _{3}q^{3}+2q^{4}-\\beta _{1}q^{6}-2\\beta _{2}q^{8}+\\cdots"
"392.2.e.b"	4	3.130135759234191	"4.0.2048.2"	[-8]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{2}q^{2}+\\beta _{1}q^{3}+2q^{4}+(-\\beta _{1}+\\beta _{3})q^{6}+\\cdots"
"392.2.e.c"	8	3.130135759234191	"8.0.339738624.1"	[]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{5}q^{2}+(\\beta _{4}+\\beta _{7})q^{3}+(-1+\\beta _{6}+\\cdots)q^{4}+\\cdots"
"392.2.e.d"	8	3.130135759234191	"8.0.1212153856.10"	[]	[]	[4, 0, 0, 0]	NULL	"q+(1-\\beta _{5})q^{2}-\\beta _{2}q^{3}+(\\beta _{3}-\\beta _{5}+\\beta _{6}+\\cdots)q^{4}+\\cdots"
"392.2.e.e"	12	3.130135759234191	"12.0.144054149089536.2"	[]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{5}q^{2}-\\beta _{10}q^{3}+\\beta _{1}q^{4}-\\beta _{9}q^{5}+\\cdots"
"392.2.i.a"	2	3.130135759234191	"2.0.3.1"	[]	[]	[0, -2, 4, 0]	NULL	"q+(-2+2\\zeta_{6})q^{3}+4\\zeta_{6}q^{5}-\\zeta_{6}q^{9}+\\cdots"
"392.2.i.b"	2	3.130135759234191	"2.0.3.1"	[]	[]	[0, -1, -1, 0]	NULL	"q+(-1+\\zeta_{6})q^{3}-\\zeta_{6}q^{5}+2\\zeta_{6}q^{9}+\\cdots"
"392.2.i.c"	2	3.130135759234191	"2.0.3.1"	[]	[]	[0, 0, -2, 0]	NULL	"q-2\\zeta_{6}q^{5}+3\\zeta_{6}q^{9}+(4-4\\zeta_{6})q^{11}+\\cdots"
"392.2.i.d"	2	3.130135759234191	"2.0.3.1"	[]	[]	[0, 0, 2, 0]	NULL	"q+2\\zeta_{6}q^{5}+3\\zeta_{6}q^{9}+(4-4\\zeta_{6})q^{11}+\\cdots"
"392.2.i.e"	2	3.130135759234191	"2.0.3.1"	[]	[]	[0, 2, -4, 0]	NULL	"q+(2-2\\zeta_{6})q^{3}-4\\zeta_{6}q^{5}-\\zeta_{6}q^{9}-8q^{15}+\\cdots"
"392.2.i.f"	2	3.130135759234191	"2.0.3.1"	[]	[]	[0, 3, -1, 0]	NULL	"q+(3-3\\zeta_{6})q^{3}-\\zeta_{6}q^{5}-6\\zeta_{6}q^{9}+(1+\\cdots)q^{11}+\\cdots"
"392.2.i.g"	4	3.130135759234191	"4.0.576.2"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{1}q^{3}+(-\\beta _{1}-\\beta _{3})q^{5}+5\\beta _{2}q^{9}+\\cdots"
"392.2.i.h"	4	3.130135759234191	"4.0.576.2"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{1}q^{3}+(-2\\beta _{1}-2\\beta _{3})q^{5}-\\beta _{2}q^{9}+\\cdots"
"392.2.m.a"	4	3.130135759234191	"4.0.441.1"	[-7]	[]	[-1, 0, 0, 0]	NULL	"q-\\beta _{3}q^{2}+(1+\\beta _{1}-\\beta _{2})q^{4}+(-3+\\beta _{1}+\\cdots)q^{8}+\\cdots"
"392.2.m.b"	8	3.130135759234191	"8.0.339738624.1"	[-8]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{6}q^{2}+\\beta _{3}q^{3}+(-2-2\\beta _{4})q^{4}+\\cdots"
"392.2.m.c"	8	3.130135759234191	"8.0.339738624.1"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{6}q^{2}+(-\\beta _{3}+\\beta _{5}-\\beta _{7})q^{3}+(-2+\\cdots)q^{4}+\\cdots"
"392.2.m.d"	8	3.130135759234191	"8.0.339738624.1"	[-8]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{5}q^{2}-\\beta _{1}q^{3}+(-2-2\\beta _{4})q^{4}+\\cdots"
"392.2.m.e"	8	3.130135759234191	"8.0.339738624.1"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{2}q^{2}+(-\\beta _{1}+\\beta _{3})q^{3}+2q^{4}+(2\\beta _{1}+\\cdots)q^{5}+\\cdots"
"392.2.m.f"	8	3.130135759234191	"8.0.5308416.1"	[]	[]	[4, 0, 0, 0]	NULL	"q+(-\\beta_{2}+\\beta_1+1)q^{2}+(\\beta_{7}-\\beta_{4})q^{3}+\\cdots"
"392.2.m.g"	12	3.130135759234191	"12.0.144054149089536.2"	[]	[]	[0, 6, 0, 0]	NULL	"q+(\\beta _{1}-\\beta _{8})q^{2}+(1+\\beta _{10})q^{3}+(\\beta _{2}-\\beta _{4}+\\cdots)q^{4}+\\cdots"
"392.2.m.h"	16	3.130135759234191	"16.0.9640188644209402576896.2"	[]	[]	[-4, 0, 0, 0]	NULL	"q+(\\beta _{5}+\\beta _{14})q^{2}-\\beta _{15}q^{3}+(1+\\beta _{5}+\\cdots)q^{4}+\\cdots"
"392.2.p.a"	4	3.130135759234191	"4.0.576.1"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{1}q^{2}+(-\\beta _{1}+\\beta _{3})q^{3}+2\\beta _{2}q^{4}+\\cdots"
"392.2.p.b"	4	3.130135759234191	"4.0.576.1"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{1}q^{2}+(\\beta _{1}-\\beta _{3})q^{3}+2\\beta _{2}q^{4}+\\beta _{1}q^{5}+\\cdots"
"392.2.p.c"	4	3.130135759234191	"4.0.441.1"	[-7]	[]	[1, 0, 0, 0]	NULL	"q+\\beta _{3}q^{2}+(1+\\beta _{1}-\\beta _{2})q^{4}+(3-\\beta _{1}+\\cdots)q^{8}+\\cdots"
"392.2.p.d"	8	3.130135759234191	"8.0.4161798144.10"	[-56]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{5}q^{2}-\\beta _{6}q^{3}+(-2+2\\beta _{2})q^{4}+\\cdots"
"392.2.p.e"	8	3.130135759234191	"8.0.432972864.2"	[]	[]	[1, 0, 0, 0]	NULL	"q+(-\\beta _{1}-\\beta _{6})q^{2}+(\\beta _{5}+\\beta _{6})q^{3}+\\beta _{5}q^{4}+\\cdots"
"392.2.p.f"	8	3.130135759234191	"8.0.432972864.2"	[]	[]	[1, 0, 0, 0]	NULL	"q+(-\\beta _{1}-\\beta _{6})q^{2}+(-\\beta _{5}-\\beta _{6})q^{3}+\\cdots"
"392.2.p.g"	12	3.130135759234191	"12.0.951588245534976.1"	[]	[]	[-2, 0, 0, 0]	NULL	"q+(-\\beta _{1}+\\beta _{5})q^{2}-\\beta _{6}q^{3}-\\beta _{3}q^{4}+\\cdots"
"392.2.p.h"	24	3.130135759234191	NULL	[]	[]	[2, 0, 0, 0]	NULL	NULL
"392.2.q.a"	42	3.130135759234191	NULL	[]	[]	[0, -7, -2, 1]	NULL	NULL
"392.2.q.b"	42	3.130135759234191	NULL	[]	[]	[0, 5, 4, -1]	NULL	NULL
"392.2.u.a"	324	3.130135759234191	NULL	[]	[]	[-5, -14, 0, 0]	NULL	NULL
"392.2.x.a"	324	3.130135759234191	NULL	[]	[]	[-5, 0, 0, -12]	NULL	NULL
"392.2.y.a"	84	3.130135759234191	NULL	[]	[]	[0, -8, -1, 4]	NULL	NULL
"392.2.y.b"	84	3.130135759234191	NULL	[]	[]	[0, 10, -1, -4]	NULL	NULL
"392.2.z.a"	648	3.130135759234191	NULL	[]	[]	[-13, 0, 0, -24]	NULL	NULL
"392.2.bc.a"	648	3.130135759234191	NULL	[]	[]	[-13, -22, 0, 0]	NULL	NULL
"392.3.c.a"	4	10.681226362923638	"4.0.2048.2"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{1}q^{3}+(\\beta _{1}-\\beta _{3})q^{5}+(7+\\beta _{2})q^{9}+\\cdots"
"392.3.c.b"	8	10.681226362923638	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+(-\\beta _{1}-\\beta _{4})q^{3}+(-\\beta _{4}-\\beta _{5}-\\beta _{6}+\\cdots)q^{5}+\\cdots"
"392.3.c.c"	8	10.681226362923638	"8.0.126303473664.2"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{6}q^{3}+\\beta _{7}q^{5}+(-5+\\beta _{1})q^{9}+(-1+\\cdots)q^{11}+\\cdots"
"392.3.g.a"	1	10.681226362923638	"1.1.1.1"	[-8]	[]	[-2, 2, 0, 0]	NULL	"q-2q^{2}+2q^{3}+4q^{4}-4q^{6}-8q^{8}+\\cdots"
"392.3.g.b"	2	10.681226362923638	"2.2.8.1"	[-8]	[]	[-4, 0, 0, 0]	NULL	"q-2q^{2}+\\beta q^{3}+4q^{4}-2\\beta q^{6}-8q^{8}+\\cdots"
"392.3.g.c"	2	10.681226362923638	"2.0.7.1"	[-7]	[]	[-3, 0, 0, 0]	NULL	"q+(-2+\\beta )q^{2}+(2-3\\beta )q^{4}+(2+5\\beta )q^{8}+\\cdots"
"392.3.g.d"	2	10.681226362923638	"2.0.3.1"	[]	[]	[2, -2, 0, 0]	NULL	"q+(\\beta+1)q^{2}-q^{3}+(2\\beta-2)q^{4}-3\\beta q^{5}+\\cdots"
"392.3.g.e"	2	10.681226362923638	"2.0.3.1"	[]	[]	[2, 2, 0, 0]	NULL	"q+(-\\beta+1)q^{2}+q^{3}+(-2\\beta-2)q^{4}+\\cdots"
"392.3.g.f"	2	10.681226362923638	"2.2.8.1"	[-8]	[]	[4, -8, 0, 0]	NULL	"q+2q^{2}+(-4+\\beta )q^{3}+4q^{4}+(-8+\\cdots)q^{6}+\\cdots"
"392.3.g.g"	2	10.681226362923638	"2.2.8.1"	[-8]	[]	[4, 8, 0, 0]	NULL	"q+2q^{2}+(4+\\beta )q^{3}+4q^{4}+(8+2\\beta )q^{6}+\\cdots"
"392.3.g.h"	4	10.681226362923638	"4.0.3136.3"	[]	[]	[0, -8, 0, 0]	NULL	"q-\\beta _{1}q^{2}+(-2-\\beta _{2})q^{3}+(-3+\\beta _{3})q^{4}+\\cdots"
"392.3.g.i"	6	10.681226362923638	"6.0.15582448.1"	[]	[]	[-2, -6, 0, 0]	NULL	"q+\\beta _{3}q^{2}+(\\beta _{1}+\\beta _{2}+\\beta _{3})q^{3}+(1+\\beta _{1}+\\cdots)q^{4}+\\cdots"
"392.3.g.j"	6	10.681226362923638	"6.0.15582448.1"	[]	[]	[-2, 6, 0, 0]	NULL	"q+\\beta _{2}q^{2}+(-\\beta _{1}-\\beta _{2}-\\beta _{3})q^{3}+(1+\\cdots)q^{4}+\\cdots"
"392.3.g.k"	6	10.681226362923638	"6.0.700560112.1"	[]	[]	[0, -6, 0, 0]	NULL	"q+\\beta _{1}q^{2}+(-1+\\beta _{1}-\\beta _{4})q^{3}+(1+\\beta _{3}+\\cdots)q^{4}+\\cdots"
"392.3.g.l"	6	10.681226362923638	"6.0.700560112.1"	[]	[]	[0, 6, 0, 0]	NULL	"q-\\beta _{4}q^{2}+(1-\\beta _{1}+\\beta _{4})q^{3}+(1+\\beta _{1}+\\cdots)q^{4}+\\cdots"
"392.3.g.m"	8	10.681226362923638	"8.0.292213762624.3"	[]	[]	[1, 8, 0, 0]	NULL	"q-\\beta _{3}q^{2}+(1-\\beta _{2}-\\beta _{3})q^{3}+(1+\\beta _{4}+\\cdots)q^{4}+\\cdots"
"392.3.g.n"	8	10.681226362923638	"8.0.160307347456.5"	[]	[]	[8, 0, 0, 0]	NULL	"q+(1-\\beta _{7})q^{2}+\\beta _{5}q^{3}+(-1-\\beta _{4}-\\beta _{6}+\\cdots)q^{4}+\\cdots"
"392.3.g.o"	20	10.681226362923638	NULL	[]	[]	[-6, 0, 0, 0]	NULL	"q-\\beta _{11}q^{2}-\\beta _{6}q^{3}+(-1+\\beta _{7})q^{4}+\\cdots"
"392.3.h.a"	28	10.681226362923638	NULL	[]	[]	[4, 0, 0, 0]	NULL	NULL
"392.3.h.b"	48	10.681226362923638	NULL	[]	[]	[-4, 0, 0, 0]	NULL	NULL
"392.3.j.a"	4	10.681226362923638	"4.0.576.2"	[-56]	[]	[-4, 0, 0, 0]	NULL	"q+2\\beta _{2}q^{2}+\\beta _{1}q^{3}+(-4-4\\beta _{2})q^{4}+\\cdots"
"392.3.j.b"	4	10.681226362923638	"4.0.441.1"	[-7]	[]	[-3, 0, 0, 0]	NULL	"q+(-\\beta _{2}-\\beta _{3})q^{2}+(-2+3\\beta _{1}+2\\beta _{2}+\\cdots)q^{4}+\\cdots"
"392.3.j.c"	4	10.681226362923638	"4.0.7056.3"	[-56]	[]	[4, 0, 0, 0]	NULL	"q-2\\beta _{2}q^{2}+\\beta _{1}q^{3}+(-4-4\\beta _{2})q^{4}+\\cdots"
"392.3.j.d"	16	10.681226362923638	NULL	[]	[]	[4, 0, 0, 0]	NULL	"q+(\\beta _{2}+\\beta _{5})q^{2}+(-\\beta _{3}+\\beta _{11})q^{3}+(2+\\cdots)q^{4}+\\cdots"
"392.3.j.e"	28	10.681226362923638	NULL	[]	[]	[-2, 0, 0, 0]	NULL	NULL
"392.3.j.f"	96	10.681226362923638	NULL	[]	[]	[4, 0, 0, 0]	NULL	NULL
"392.3.k.a"	2	10.681226362923638	"2.0.3.1"	[]	[]	[-4, 1, 9, 0]	NULL	"q-2q^{2}+\\zeta_{6}q^{3}+4q^{4}+(3+3\\zeta_{6})q^{5}+\\cdots"
"392.3.k.b"	2	10.681226362923638	"2.0.3.1"	[-8]	[]	[2, -2, 0, 0]	NULL	"q+(2-2\\zeta_{6})q^{2}-2\\zeta_{6}q^{3}-4\\zeta_{6}q^{4}+\\cdots"
"392.3.k.c"	2	10.681226362923638	"2.0.3.1"	[]	[]	[2, 1, -9, 0]	NULL	"q+2\\zeta_{6}q^{2}+\\zeta_{6}q^{3}+(-4+4\\zeta_{6})q^{4}+\\cdots"
"392.3.k.d"	2	10.681226362923638	"2.0.3.1"	[-8]	[]	[2, 2, 0, 0]	NULL	"q+(2-2\\zeta_{6})q^{2}+2\\zeta_{6}q^{3}-4\\zeta_{6}q^{4}+\\cdots"
"392.3.k.e"	4	10.681226362923638	"4.0.576.2"	[-8]	[]	[-4, -8, 0, 0]	NULL	"q+(-2-2\\beta _{2})q^{2}+(-\\beta _{1}+4\\beta _{2}-\\beta _{3})q^{3}+\\cdots"
"392.3.k.f"	4	10.681226362923638	"4.0.576.2"	[-8]	[]	[-4, 8, 0, 0]	NULL	"q+(-2-2\\beta _{2})q^{2}+(-\\beta _{1}-4\\beta _{2}-\\beta _{3})q^{3}+\\cdots"
"392.3.k.g"	4	10.681226362923638	"4.0.441.1"	[-7]	[]	[3, 0, 0, 0]	NULL	"q+(2-\\beta _{1}-2\\beta _{2})q^{2}+(\\beta _{2}-3\\beta _{3})q^{4}+\\cdots"
"392.3.k.h"	4	10.681226362923638	"4.0.576.2"	[-8]	[]	[4, 0, 0, 0]	NULL	"q-2\\beta _{2}q^{2}+\\beta _{1}q^{3}+(-4-4\\beta _{2})q^{4}+\\cdots"
"392.3.k.i"	8	10.681226362923638	"8.0.796594176.2"	[]	[]	[0, -8, 0, 0]	NULL	"q+(\\beta _{2}+\\beta _{3}+\\beta _{4}-\\beta _{6})q^{2}+(-2-2\\beta _{1}+\\cdots)q^{3}+\\cdots"
"392.3.k.j"	8	10.681226362923638	"8.0.796594176.2"	[]	[]	[0, 8, 0, 0]	NULL	"q+(-\\beta _{2}-\\beta _{3}-\\beta _{4})q^{2}+(2+2\\beta _{1}+\\beta _{3}+\\cdots)q^{3}+\\cdots"
"392.3.k.k"	12	10.681226362923638	NULL	[]	[]	[0, -6, 0, 0]	NULL	"q+\\beta _{1}q^{2}+(\\beta _{3}+\\beta _{4}+\\beta _{7}+\\beta _{8})q^{3}+\\cdots"
"392.3.k.l"	12	10.681226362923638	NULL	[]	[]	[2, 6, 0, 0]	NULL	"q+\\beta _{10}q^{2}+(-\\beta _{3}+\\beta _{5}+\\beta _{6}-\\beta _{9}+\\cdots)q^{3}+\\cdots"
"392.3.k.m"	16	10.681226362923638	NULL	[]	[]	[-8, 0, 0, 0]	NULL	"q+(-\\beta _{4}+\\beta _{8})q^{2}-\\beta _{7}q^{3}+(1-2\\beta _{3}+\\cdots)q^{4}+\\cdots"
"392.3.k.n"	16	10.681226362923638	NULL	[]	[]	[-1, -8, 0, 0]	NULL	"q+\\beta _{1}q^{2}+(-1+\\beta _{2}+\\beta _{6}+\\beta _{9})q^{3}+\\cdots"
"392.3.k.o"	16	10.681226362923638	NULL	[]	[]	[-1, 8, 0, 0]	NULL	"q-\\beta _{1}q^{2}+(-\\beta _{1}+\\beta _{2}-\\beta _{8}-\\beta _{10}+\\cdots)q^{3}+\\cdots"
"392.3.k.p"	40	10.681226362923638	NULL	[]	[]	[6, 0, 0, 0]	NULL	NULL
"392.3.o.a"	8	10.681226362923638	"8.0.339738624.1"	[]	[]	[0, 0, 0, 0]	NULL	"q+(-\\beta _{3}-\\beta _{7})q^{3}+(\\beta _{1}+\\beta _{3})q^{5}+(-7+\\cdots)q^{9}+\\cdots"
"392.3.o.b"	8	10.681226362923638	"8.0.339738624.1"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{5}q^{3}+(-\\beta _{1}+\\beta _{2})q^{5}+(\\beta _{3}+\\beta _{6}+\\cdots)q^{9}+\\cdots"
"392.3.o.c"	8	10.681226362923638	"8.0.126303473664.2"	[]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{2}q^{3}+\\beta _{7}q^{5}+(5-5\\beta _{1}-2\\beta _{4}+\\cdots)q^{9}+\\cdots"
"392.3.o.d"	16	10.681226362923638	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{2}q^{3}+(-\\beta _{5}-\\beta _{9}-\\beta _{10})q^{5}+(8+\\cdots)q^{9}+\\cdots"
"392.3.r.a"	660	10.681226362923638	NULL	[]	[]	[-5, 0, 0, -12]	NULL	NULL
"392.3.s.a"	660	10.681226362923638	NULL	[]	[]	[-5, -10, 0, 0]	NULL	NULL
"392.3.w.a"	168	10.681226362923638	NULL	[]	[]	[0, 0, 0, -4]	NULL	NULL
"392.3.ba.a"	336	10.681226362923638	NULL	[]	[]	[0, 0, 0, 4]	NULL	NULL
"392.3.be.a"	1320	10.681226362923638	NULL	[]	[]	[-13, -26, 0, 0]	NULL	NULL
"392.3.bf.a"	1320	10.681226362923638	NULL	[]	[]	[-13, 0, 0, -24]	NULL	NULL
"392.4.a.a"	1	23.12874872225032	"1.1.1.1"	[]	[]	[0, -6, -8, 0]	-1	"q-6q^{3}-8q^{5}+9q^{9}+56q^{11}+28q^{13}+\\cdots"
"392.4.a.b"	1	23.12874872225032	"1.1.1.1"	[]	[]	[0, -4, 12, 0]	-1	"q-4q^{3}+12q^{5}-11q^{9}+12q^{11}+\\cdots"
"392.4.a.c"	1	23.12874872225032	"1.1.1.1"	[]	[]	[0, 2, 16, 0]	1	"q+2q^{3}+2^{4}q^{5}-23q^{9}+24q^{11}+\\cdots"
"392.4.a.d"	1	23.12874872225032	"1.1.1.1"	[]	[]	[0, 4, -12, 0]	-1	"q+4q^{3}-12q^{5}-11q^{9}+12q^{11}+\\cdots"
"392.4.a.e"	1	23.12874872225032	"1.1.1.1"	[]	[]	[0, 4, 2, 0]	-1	"q+4q^{3}+2q^{5}-11q^{9}-44q^{11}-22q^{13}+\\cdots"
"392.4.a.f"	2	23.12874872225032	"2.2.8.1"	[]	[]	[0, 0, 0, 0]	1	"q+\\beta q^{3}-10\\beta q^{5}-5^{2}q^{9}+54q^{11}+\\cdots"
"392.4.a.g"	2	23.12874872225032	"2.2.8.1"	[]	[]	[0, 0, 0, 0]	1	"q+\\beta q^{3}+\\beta q^{5}+5q^{9}-4q^{11}-\\beta q^{13}+\\cdots"
"392.4.a.h"	2	23.12874872225032	"2.2.57.1"	[]	[]	[0, 2, -22, 0]	1	"q+(1+\\beta )q^{3}+(-11-\\beta )q^{5}+(31+2\\beta )q^{9}+\\cdots"
"392.4.a.i"	3	23.12874872225032	"3.3.1929.1"	[]	[]	[0, -7, -3, 0]	-1	"q+(-2+\\beta _{1})q^{3}+(-1+\\beta _{1}-\\beta _{2})q^{5}+\\cdots"
"392.4.a.j"	3	23.12874872225032	"3.3.1929.1"	[]	[]	[0, -1, -13, 0]	-1	"q+\\beta _{2}q^{3}+(-4-\\beta _{1})q^{5}+(15+3\\beta _{1}+\\cdots)q^{9}+\\cdots"
"392.4.a.k"	3	23.12874872225032	"3.3.1929.1"	[]	[]	[0, 1, 13, 0]	1	"q-\\beta _{2}q^{3}+(4+\\beta _{1})q^{5}+(15+3\\beta _{1}-2\\beta _{2})q^{9}+\\cdots"
"392.4.a.l"	3	23.12874872225032	"3.3.1929.1"	[]	[]	[0, 7, 3, 0]	1	"q+(2-\\beta _{1})q^{3}+(1-\\beta _{1}+\\beta _{2})q^{5}+(4+\\cdots)q^{9}+\\cdots"
"392.4.a.m"	4	23.12874872225032	"4.4.270400.4"	[]	[]	[0, 0, 0, 0]	-1	"q+(2\\beta _{1}+\\beta _{3})q^{3}+(-3\\beta _{1}-\\beta _{3})q^{5}+\\cdots"
"392.4.a.n"	4	23.12874872225032	"4.4.817216.1"	[]	[]	[0, 0, 0, 0]	1	"q+(2\\beta _{1}+\\beta _{3})q^{3}+(-9\\beta _{1}+\\beta _{3})q^{5}+\\cdots"
"392.4.i.a"	2	23.12874872225032	"2.0.3.1"	[]	[]	[0, -6, -8, 0]	NULL	"q+(-6+6\\zeta_{6})q^{3}-8\\zeta_{6}q^{5}-9\\zeta_{6}q^{9}+\\cdots"
"392.4.i.b"	2	23.12874872225032	"2.0.3.1"	[]	[]	[0, -4, -2, 0]	NULL	"q+(-4+4\\zeta_{6})q^{3}-2\\zeta_{6}q^{5}+11\\zeta_{6}q^{9}+\\cdots"
"392.4.i.c"	2	23.12874872225032	"2.0.3.1"	[]	[]	[0, -4, 12, 0]	NULL	"q+(-4+4\\zeta_{6})q^{3}+12\\zeta_{6}q^{5}+11\\zeta_{6}q^{9}+\\cdots"
"392.4.i.d"	2	23.12874872225032	"2.0.3.1"	[]	[]	[0, -2, -16, 0]	NULL	"q+(-2+2\\zeta_{6})q^{3}-2^{4}\\zeta_{6}q^{5}+23\\zeta_{6}q^{9}+\\cdots"
"392.4.i.e"	2	23.12874872225032	"2.0.3.1"	[]	[]	[0, 2, 16, 0]	NULL	"q+(2-2\\zeta_{6})q^{3}+2^{4}\\zeta_{6}q^{5}+23\\zeta_{6}q^{9}+\\cdots"
"392.4.i.f"	2	23.12874872225032	"2.0.3.1"	[]	[]	[0, 4, -12, 0]	NULL	"q+(4-4\\zeta_{6})q^{3}-12\\zeta_{6}q^{5}+11\\zeta_{6}q^{9}+\\cdots"
"392.4.i.g"	2	23.12874872225032	"2.0.3.1"	[]	[]	[0, 4, 2, 0]	NULL	"q+(4-4\\zeta_{6})q^{3}+2\\zeta_{6}q^{5}+11\\zeta_{6}q^{9}+\\cdots"
"392.4.i.h"	2	23.12874872225032	"2.0.3.1"	[]	[]	[0, 6, 8, 0]	NULL	"q+(6-6\\zeta_{6})q^{3}+8\\zeta_{6}q^{5}-9\\zeta_{6}q^{9}+\\cdots"
"392.4.i.i"	4	23.12874872225032	"4.0.3249.1"	[]	[]	[0, -2, 22, 0]	NULL	"q+(-1-\\beta _{1}+\\beta _{3})q^{3}+(-11\\beta _{1}-\\beta _{2}+\\cdots)q^{5}+\\cdots"
"392.4.i.j"	4	23.12874872225032	"4.0.576.2"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{1}q^{3}+(-\\beta _{1}-\\beta _{3})q^{5}+5\\beta _{2}q^{9}+\\cdots"
"392.4.i.k"	4	23.12874872225032	"4.0.576.2"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{1}q^{3}+(10\\beta _{1}+10\\beta _{3})q^{5}-5^{2}\\beta _{2}q^{9}+\\cdots"
"392.4.i.l"	4	23.12874872225032	"4.0.3249.1"	[]	[]	[0, 2, -22, 0]	NULL	"q+(1+\\beta _{1}+\\beta _{3})q^{3}+(11\\beta _{1}-\\beta _{2}+\\beta _{3})q^{5}+\\cdots"
"392.4.i.m"	6	23.12874872225032	"6.0.11163123.4"	[]	[]	[0, -7, -3, 0]	NULL	"q+(-2\\beta _{1}+\\beta _{5})q^{3}+(-1+\\beta _{1}+\\beta _{2}+\\cdots)q^{5}+\\cdots"
"392.4.i.n"	6	23.12874872225032	"6.0.11163123.4"	[]	[]	[0, 1, 13, 0]	NULL	"q-\\beta _{4}q^{3}+(4-4\\beta _{1}+\\beta _{5})q^{5}+(-15+\\cdots)q^{9}+\\cdots"
"392.4.i.o"	8	23.12874872225032	"8.0.54095201243136.19"	[]	[]	[0, 0, 0, 0]	NULL	"q+(\\beta _{2}-\\beta _{4}-\\beta _{5})q^{3}+(\\beta _{5}+10\\beta _{6})q^{5}+\\cdots"
"392.4.i.p"	8	23.12874872225032	"8.0.5922408960000.19"	[]	[]	[0, 0, 0, 0]	NULL	"q+(\\beta _{4}-\\beta _{6})q^{3}+(-2\\beta _{2}+\\beta _{3}+\\beta _{4}+\\cdots)q^{5}+\\cdots"
"392.5.c.a"	12	40.52102552886698	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{5}q^{3}+(-\\beta _{2}-2\\beta _{3}+\\beta _{4}+\\beta _{5}+\\cdots)q^{5}+\\cdots"
"392.5.c.b"	12	40.52102552886698	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{7}q^{3}-\\beta _{11}q^{5}+(-8+\\beta _{1}+\\beta _{2}+\\cdots)q^{9}+\\cdots"
"392.5.c.c"	16	40.52102552886698	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{2}q^{3}+\\beta _{3}q^{5}+(-5^{2}+\\beta _{11})q^{9}+\\cdots"
"392.5.o.a"	16	40.52102552886698	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+(\\beta _{2}-\\beta _{6})q^{3}+\\beta _{5}q^{5}+(-5^{2}\\beta _{1}+\\beta _{2}+\\cdots)q^{9}+\\cdots"
"392.5.o.b"	16	40.52102552886698	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{8}q^{3}-\\beta _{7}q^{5}+(31-31\\beta _{1}+2\\beta _{2}+\\cdots)q^{9}+\\cdots"
"392.5.o.c"	24	40.52102552886698	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"392.5.o.d"	24	40.52102552886698	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"392.6.a.a"	1	62.870457366688406	"1.1.1.1"	[]	[]	[0, -30, -32, 0]	-1	"q-30q^{3}-2^{5}q^{5}+657q^{9}-624q^{11}+\\cdots"
"392.6.a.b"	1	62.870457366688406	"1.1.1.1"	[]	[]	[0, -20, 74, 0]	1	"q-20q^{3}+74q^{5}+157q^{9}+124q^{11}+\\cdots"
"392.6.a.c"	1	62.870457366688406	"1.1.1.1"	[]	[]	[0, 6, -4, 0]	1	"q+6q^{3}-4q^{5}-207q^{9}-240q^{11}+\\cdots"
"392.6.a.d"	2	62.870457366688406	"2.2.345.1"	[]	[]	[0, 6, -82, 0]	1	"q+(3+\\beta )q^{3}+(-41+3\\beta )q^{5}+(111+\\cdots)q^{9}+\\cdots"
"392.6.a.e"	2	62.870457366688406	"2.2.193.1"	[]	[]	[0, 14, -42, 0]	-1	"q+(7-\\beta )q^{3}+(-21+5\\beta )q^{5}+(-1+\\cdots)q^{9}+\\cdots"
"392.6.a.f"	2	62.870457366688406	"2.2.177.1"	[]	[]	[0, 26, 62, 0]	-1	"q+(13-\\beta )q^{3}+(31-5\\beta )q^{5}+(103-26\\beta )q^{9}+\\cdots"
"392.6.a.g"	4	62.870457366688406	"4.4.531210304.2"	[]	[]	[0, 0, 0, 0]	-1	"q+\\beta _{1}q^{3}+\\beta _{2}q^{5}+(-23+\\beta _{3})q^{9}+\\cdots"
"392.6.a.h"	4	62.870457366688406	"4.4.2732674592.1"	[]	[]	[0, 0, 0, 0]	1	"q+\\beta _{2}q^{3}+(-\\beta _{1}-2\\beta _{2})q^{5}+(209-\\beta _{3})q^{9}+\\cdots"
"392.6.a.i"	5	62.870457366688406	NULL	[]	[]	[0, -13, -31, 0]	1	"q+(-3+\\beta _{1})q^{3}+(-6-\\beta _{3})q^{5}+(47+\\cdots)q^{9}+\\cdots"
"392.6.a.j"	5	62.870457366688406	NULL	[]	[]	[0, -5, 81, 0]	-1	"q+(-1-\\beta _{1})q^{3}+(2^{4}+\\beta _{1}+\\beta _{2})q^{5}+\\cdots"
"392.6.a.k"	5	62.870457366688406	NULL	[]	[]	[0, 5, -81, 0]	1	"q+(1+\\beta _{1})q^{3}+(-2^{4}-\\beta _{1}-\\beta _{2})q^{5}+\\cdots"
"392.6.a.l"	5	62.870457366688406	NULL	[]	[]	[0, 13, 31, 0]	-1	"q+(3-\\beta _{1})q^{3}+(6+\\beta _{3})q^{5}+(47-4\\beta _{1}+\\cdots)q^{9}+\\cdots"
"392.6.a.m"	6	62.870457366688406	NULL	[]	[]	[0, 0, 0, 0]	1	"q+\\beta _{2}q^{3}+(\\beta _{1}-\\beta _{3})q^{5}+(-20+\\beta _{4}+\\cdots)q^{9}+\\cdots"
"392.6.a.n"	8	62.870457366688406	NULL	[]	[]	[0, 0, 0, 0]	-1	"q+\\beta _{2}q^{3}+(-\\beta _{1}-\\beta _{4})q^{5}+(116+\\beta _{3}+\\cdots)q^{9}+\\cdots"
"392.6.i.a"	2	62.870457366688406	"2.0.3.1"	[]	[]	[0, -30, -32, 0]	NULL	"q+(-30+30\\zeta_{6})q^{3}-2^{5}\\zeta_{6}q^{5}-657\\zeta_{6}q^{9}+\\cdots"
"392.6.i.b"	2	62.870457366688406	"2.0.3.1"	[]	[]	[0, -20, 74, 0]	NULL	"q+(-20+20\\zeta_{6})q^{3}+74\\zeta_{6}q^{5}-157\\zeta_{6}q^{9}+\\cdots"
"392.6.i.c"	2	62.870457366688406	"2.0.3.1"	[]	[]	[0, -6, 4, 0]	NULL	"q+(-6+6\\zeta_{6})q^{3}+4\\zeta_{6}q^{5}+207\\zeta_{6}q^{9}+\\cdots"
"392.6.i.d"	2	62.870457366688406	"2.0.3.1"	[]	[]	[0, 6, -4, 0]	NULL	"q+(6-6\\zeta_{6})q^{3}-4\\zeta_{6}q^{5}+207\\zeta_{6}q^{9}+\\cdots"
"392.6.i.e"	2	62.870457366688406	"2.0.3.1"	[]	[]	[0, 20, -74, 0]	NULL	"q+(20-20\\zeta_{6})q^{3}-74\\zeta_{6}q^{5}-157\\zeta_{6}q^{9}+\\cdots"
"392.6.i.f"	2	62.870457366688406	"2.0.3.1"	[]	[]	[0, 30, 32, 0]	NULL	"q+(30-30\\zeta_{6})q^{3}+2^{5}\\zeta_{6}q^{5}-657\\zeta_{6}q^{9}+\\cdots"
"392.6.i.g"	4	62.870457366688406	"4.0.31329.1"	[]	[]	[0, -26, -62, 0]	NULL	"q+(-13-13\\beta _{1}+\\beta _{3})q^{3}+(31\\beta _{1}+5\\beta _{2}+\\cdots)q^{5}+\\cdots"
"392.6.i.h"	4	62.870457366688406	"4.0.335241.2"	[]	[]	[0, -14, 42, 0]	NULL	"q+(-7\\beta _{1}-\\beta _{2})q^{3}+(21-21\\beta _{1}-5\\beta _{2}+\\cdots)q^{5}+\\cdots"
"392.6.i.i"	4	62.870457366688406	"4.0.119025.3"	[]	[]	[0, -6, 82, 0]	NULL	"q+(3\\beta _{1}+\\beta _{2}-\\beta _{3})q^{3}+(41+41\\beta _{1}+\\cdots)q^{5}+\\cdots"
"392.6.i.j"	4	62.870457366688406	"4.0.119025.3"	[]	[]	[0, 6, -82, 0]	NULL	"q+(3+3\\beta _{1}-\\beta _{3})q^{3}+(41\\beta _{1}-3\\beta _{2}+\\cdots)q^{5}+\\cdots"
"392.6.i.k"	4	62.870457366688406	"4.0.335241.2"	[]	[]	[0, 14, -42, 0]	NULL	"q+(7\\beta _{1}-\\beta _{2})q^{3}+(-21+21\\beta _{1}-5\\beta _{2}+\\cdots)q^{5}+\\cdots"
"392.6.i.l"	4	62.870457366688406	"4.0.31329.1"	[]	[]	[0, 26, 62, 0]	NULL	"q+(-13\\beta _{1}-\\beta _{2}+\\beta _{3})q^{3}+(31+31\\beta _{1}+\\cdots)q^{5}+\\cdots"
"392.6.i.m"	8	62.870457366688406	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+(-\\beta _{2}+\\beta _{6})q^{3}+(-2\\beta _{2}+\\beta _{3})q^{5}+\\cdots"
"392.6.i.n"	8	62.870457366688406	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{2}q^{3}-\\beta _{5}q^{5}+(23-23\\beta _{3}-\\beta _{4}+\\cdots)q^{9}+\\cdots"
"392.6.i.o"	10	62.870457366688406	NULL	[]	[]	[0, 5, -81, 0]	NULL	"q+(1-\\beta _{1}+\\beta _{3})q^{3}+(-\\beta _{1}+\\beta _{2}+2^{4}\\beta _{3}+\\cdots)q^{5}+\\cdots"
"392.6.i.p"	10	62.870457366688406	NULL	[]	[]	[0, 13, 31, 0]	NULL	"q+(3+3\\beta _{1}-\\beta _{4})q^{3}+(-6\\beta _{1}-\\beta _{6}+\\cdots)q^{5}+\\cdots"
"392.6.i.q"	12	62.870457366688406	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{6}q^{3}+(\\beta _{4}-\\beta _{5})q^{5}+(20+20\\beta _{1}+\\cdots)q^{9}+\\cdots"
"392.6.i.r"	16	62.870457366688406	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{1}q^{3}+(\\beta _{5}+\\beta _{8})q^{5}+(-116-117\\beta _{2}+\\cdots)q^{9}+\\cdots"
"392.7.c.a"	16	90.18120077898159	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{5}q^{3}+(\\beta _{2}+3\\beta _{3}-\\beta _{5}-\\beta _{6})q^{5}+\\cdots"
"392.7.c.b"	20	90.18120077898159	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{3}q^{3}+(-\\beta _{5}+\\beta _{7})q^{5}+(-248+\\cdots)q^{9}+\\cdots"
"392.7.c.c"	24	90.18120077898159	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"392.8.a.a"	1	122.45492998977574	"1.1.1.1"	[]	[]	[0, -46, 160, 0]	1	"q-46q^{3}+160q^{5}-71q^{9}-6840q^{11}+\\cdots"
"392.8.a.b"	1	122.45492998977574	"1.1.1.1"	[]	[]	[0, -44, -430, 0]	-1	"q-44q^{3}-430q^{5}-251q^{9}-3164q^{11}+\\cdots"
"392.8.a.c"	1	122.45492998977574	"1.1.1.1"	[]	[]	[0, 18, -160, 0]	1	"q+18q^{3}-160q^{5}-1863q^{9}+5704q^{11}+\\cdots"
"392.8.a.d"	1	122.45492998977574	"1.1.1.1"	[]	[]	[0, 84, 82, 0]	1	"q+84q^{3}+82q^{5}+4869q^{9}-2524q^{11}+\\cdots"
"392.8.a.e"	2	122.45492998977574	"2.2.249.1"	[]	[]	[0, 42, -14, 0]	-1	"q+(21-3\\beta )q^{3}+(-7+11\\beta )q^{5}+(495+\\cdots)q^{9}+\\cdots"
"392.8.a.f"	3	122.45492998977574	"3.3.3109313.1"	[]	[]	[0, -28, -138, 0]	1	"q+(-9+\\beta _{1})q^{3}+(-46+\\beta _{1}+\\beta _{2})q^{5}+\\cdots"
"392.8.a.g"	3	122.45492998977574	"3.3.294792.1"	[]	[]	[0, -12, 598, 0]	-1	"q+(-4-\\beta _{1})q^{3}+(199+\\beta _{1}+\\beta _{2})q^{5}+\\cdots"
"392.8.a.h"	4	122.45492998977574	NULL	[]	[]	[0, 0, 0, 0]	-1	"q+\\beta _{1}q^{3}+(-\\beta _{1}-\\beta _{2})q^{5}+(437+\\beta _{3})q^{9}+\\cdots"
"392.8.a.i"	6	122.45492998977574	NULL	[]	[]	[0, 0, 0, 0]	1	"q-\\beta _{1}q^{3}+(-2\\beta _{1}+\\beta _{2})q^{5}+(1240+\\cdots)q^{9}+\\cdots"
"392.8.a.j"	7	122.45492998977574	NULL	[]	[]	[0, -29, 237, 0]	1	"q+(-4+\\beta _{1})q^{3}+(34+\\beta _{1}-\\beta _{3})q^{5}+\\cdots"
"392.8.a.k"	7	122.45492998977574	NULL	[]	[]	[0, -25, 13, 0]	-1	"q+(-4-\\beta _{1})q^{3}+(2+\\beta _{1}-\\beta _{2})q^{5}+\\cdots"
"392.8.a.l"	7	122.45492998977574	NULL	[]	[]	[0, 25, -13, 0]	1	"q+(4+\\beta _{1})q^{3}+(-2-\\beta _{1}+\\beta _{2})q^{5}+\\cdots"
"392.8.a.m"	7	122.45492998977574	NULL	[]	[]	[0, 29, -237, 0]	-1	"q+(4-\\beta _{1})q^{3}+(-34-\\beta _{1}+\\beta _{3})q^{5}+\\cdots"
"392.8.a.n"	10	122.45492998977574	NULL	[]	[]	[0, 0, 0, 0]	-1	"q-\\beta _{6}q^{3}+(-4\\beta _{5}-\\beta _{6}+\\beta _{7})q^{5}+(413+\\cdots)q^{9}+\\cdots"
"392.8.a.o"	12	122.45492998977574	NULL	[]	[]	[0, 0, 0, 0]	1	"q+\\beta _{8}q^{3}-\\beta _{7}q^{5}+(1236-\\beta _{1})q^{9}+\\cdots"
"392.9.c.a"	24	159.69241514396185	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"392.9.c.b"	24	159.69241514396185	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"392.9.c.c"	32	159.69241514396185	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"392.10.a.a"	1	201.89404777623827	"1.1.1.1"	[]	[]	[0, -68, -1510, 0]	1	"q-68q^{3}-1510q^{5}-15059q^{9}+3916q^{11}+\\cdots"
"392.10.a.b"	1	201.89404777623827	"1.1.1.1"	[]	[]	[0, 60, 2074, 0]	-1	"q+60q^{3}+2074q^{5}-16083q^{9}+93644q^{11}+\\cdots"
"392.10.a.c"	3	201.89404777623827	NULL	[]	[]	[0, -84, 2958, 0]	1	"q+(-28+\\beta _{1})q^{3}+(986-5\\beta _{1}+\\beta _{2})q^{5}+\\cdots"
"392.10.a.d"	3	201.89404777623827	NULL	[]	[]	[0, 92, -274, 0]	-1	"q+(31+\\beta _{1})q^{3}+(-92-\\beta _{1}+\\beta _{2})q^{5}+\\cdots"
"392.10.a.e"	4	201.89404777623827	NULL	[]	[]	[0, -84, -1540, 0]	1	"q+(-21+\\beta _{1})q^{3}+(-385+2\\beta _{1}-\\beta _{2}+\\cdots)q^{5}+\\cdots"
"392.10.a.f"	4	201.89404777623827	NULL	[]	[]	[0, -70, -1022, 0]	-1	"q+(-17+\\beta _{1})q^{3}+(-255+\\beta _{1}+\\beta _{2}+\\cdots)q^{5}+\\cdots"
"392.10.a.g"	6	201.89404777623827	NULL	[]	[]	[0, 0, 0, 0]	1	"q-\\beta _{1}q^{3}+(\\beta _{1}+\\beta _{2})q^{5}+(1898-\\beta _{3}+\\cdots)q^{9}+\\cdots"
"392.10.a.h"	8	201.89404777623827	NULL	[]	[]	[0, 0, 0, 0]	-1	"q+\\beta _{1}q^{3}-\\beta _{2}q^{5}+(6497+\\beta _{3})q^{9}+\\cdots"
"392.10.a.i"	9	201.89404777623827	NULL	[]	[]	[0, -91, 801, 0]	1	"q+(-10+\\beta _{1})q^{3}+(89+\\beta _{1}-\\beta _{2})q^{5}+\\cdots"
"392.10.a.j"	9	201.89404777623827	NULL	[]	[]	[0, -71, 449, 0]	-1	"q+(-8-\\beta _{1})q^{3}+(50+\\beta _{2})q^{5}+(8792+\\cdots)q^{9}+\\cdots"
"392.10.a.k"	9	201.89404777623827	NULL	[]	[]	[0, 71, -449, 0]	1	"q+(8+\\beta _{1})q^{3}+(-50-\\beta _{2})q^{5}+(8792+\\cdots)q^{9}+\\cdots"
"392.10.a.l"	9	201.89404777623827	NULL	[]	[]	[0, 91, -801, 0]	-1	"q+(10-\\beta _{1})q^{3}+(-89-\\beta _{1}+\\beta _{2})q^{5}+\\cdots"
"392.10.a.m"	12	201.89404777623827	NULL	[]	[]	[0, 0, 0, 0]	1	"q+\\beta _{1}q^{3}+(-\\beta _{1}-\\beta _{2}+\\beta _{5})q^{5}+(3654+\\cdots)q^{9}+\\cdots"
"392.10.a.n"	14	201.89404777623827	NULL	[]	[]	[0, 0, 0, 0]	-1	"q-\\beta _{3}q^{3}+(-4\\beta _{1}-\\beta _{4})q^{5}+(7178+\\cdots)q^{9}+\\cdots"


# 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.



#RM (rm_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.