LMFDB - Newform search results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twist	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 75 matches)

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Label	Dim.	$A$	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
1476.1.h.a	$1$	$0.737$	$\Q$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-41}) $	$\Q(\sqrt{41}) $	$-1$	$0$	$2$	$0$		$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{16}+\cdots$
1476.1.h.b	$2$	$0.737$	$\Q(\sqrt{2}) $	$\Q(\sqrt{-41}) $	None	$2$	$0$	$0$	$0$		$q+q^{2}+q^{4}-\beta q^{7}+q^{8}+\beta q^{11}-\beta q^{14}+\cdots$
1476.1.j.a	$2$	$0.737$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+iq^{2}-q^{4}-iq^{8}+(1+i)q^{13}+q^{16}+\cdots$
1476.1.j.b	$2$	$0.737$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-iq^{2}-q^{4}+iq^{8}+(1+i)q^{13}+q^{16}+\cdots$
1476.1.l.a	$4$	$0.737$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$0$	$0$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{3}q^{11}+\zeta_{8}q^{17}+\cdots$
1476.1.o.a	$2$	$0.737$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-41}) $	None	$-1$	$-2$	$1$	$-1$		$q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots$
1476.1.o.b	$2$	$0.737$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-41}) $	None	$-1$	$2$	$1$	$1$		$q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots$
1476.1.o.c	$4$	$0.737$	$\Q(\zeta_{12})$	$\Q(\sqrt{-41}) $	None	$-2$	$0$	$-2$	$0$		$q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
1476.1.o.d	$8$	$0.737$	$\Q(\zeta_{24})$	$\Q(\sqrt{-41}) $	None	$4$	$0$	$0$	$0$		$q+\zeta_{24}^{4}q^{2}+\zeta_{24}^{9}q^{3}+\zeta_{24}^{8}q^{4}+\cdots$
1476.1.w.a	$4$	$0.737$	$\Q(\zeta_{8})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-4$	$0$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{2})q^{5}+\cdots$
1476.1.w.b	$4$	$0.737$	$\Q(\zeta_{8})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$4$	$0$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{2})q^{5}+\cdots$
1476.1.z.a	$4$	$0.737$	$\Q(\zeta_{10})$	$\Q(\sqrt{-1}) $	None	$1$	$0$	$-2$	$0$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(-\zeta_{10}^{3}+\zeta_{10}^{4}+\cdots)q^{5}+\cdots$
1476.1.ba.a	$4$	$0.737$	$\Q(\zeta_{10})$	$\Q(\sqrt{-1}) $	None	$1$	$0$	$2$	$0$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+(-\zeta_{10}^{2}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots$
1476.1.bo.a	$8$	$0.737$	$\Q(\zeta_{20})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{4}+(-\zeta_{20}^{2}-\zeta_{20}^{4}+\cdots)q^{5}+\cdots$
1476.1.bo.b	$8$	$0.737$	$\Q(\zeta_{20})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{4}+(\zeta_{20}^{2}+\zeta_{20}^{4}+\cdots)q^{5}+\cdots$
1476.1.cc.a	$16$	$0.737$	$\Q(\zeta_{40})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-4$	$0$		$q+\zeta_{40}^{13}q^{2}-\zeta_{40}^{6}q^{4}+(\zeta_{40}^{8}+\zeta_{40}^{14}+\cdots)q^{5}+\cdots$
1476.1.cc.b	$16$	$0.737$	$\Q(\zeta_{40})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$4$	$0$		$q-\zeta_{40}^{13}q^{2}-\zeta_{40}^{6}q^{4}+(-\zeta_{40}^{8}+\cdots)q^{5}+\cdots$
1476.2.a.a	$1$	$11.786$	$\Q$	None	None	$0$	$0$	$0$	$-2$	$+$	$q-2q^{7}+q^{11}-2q^{13}+q^{17}-4q^{19}+\cdots$
1476.2.a.b	$1$	$11.786$	$\Q$	None	None	$0$	$0$	$2$	$-4$	$-$	$q+2q^{5}-4q^{7}+5q^{11}+4q^{13}+5q^{17}+\cdots$
1476.2.a.c	$2$	$11.786$	$\Q(\sqrt{3}) $	None	None	$0$	$0$	$-2$	$2$	$+$	$q+(-1+\beta )q^{5}+(1-\beta )q^{7}+(-2-\beta )q^{11}+\cdots$
1476.2.a.d	$2$	$11.786$	$\Q(\sqrt{6}) $	None	None	$0$	$0$	$4$	$4$	$-$	$q+(2+\beta )q^{5}+(2-\beta )q^{7}+(1-\beta )q^{11}+\cdots$
1476.2.a.e	$3$	$11.786$	3.3.404.1	None	None	$0$	$0$	$-4$	$4$	$+$	$q+(-1-\beta _{2})q^{5}+(1+\beta _{1})q^{7}+(-2+\cdots)q^{11}+\cdots$
1476.2.a.f	$3$	$11.786$	3.3.404.1	None	None	$0$	$0$	$4$	$4$	$-$	$q+(1+\beta _{2})q^{5}+(1+\beta _{1})q^{7}+(2+2\beta _{1}+\cdots)q^{11}+\cdots$
1476.2.a.g	$4$	$11.786$	4.4.25808.1	None	None	$0$	$0$	$-4$	$0$	$-$	$q+(-2+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1476.2.c.a	$80$	$11.786$		None	None	$0$	$0$	$0$	$0$
1476.2.d.a	$4$	$11.786$	$\Q(\zeta_{8})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{8}^{2}q^{2}-2q^{4}-\zeta_{8}^{2}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots$
1476.2.d.b	$8$	$11.786$	8.0.$\cdots$.5	None	None	$-4$	$0$	$0$	$0$		$q+(-1+\beta _{4})q^{2}+(-1-\beta _{4})q^{4}-2\beta _{6}q^{5}+\cdots$
1476.2.d.c	$8$	$11.786$	8.0.$\cdots$.5	None	None	$4$	$0$	$0$	$0$		$q+\beta _{4}q^{2}+(-2+\beta _{4})q^{4}-2\beta _{6}q^{5}+\cdots$
1476.2.d.d	$64$	$11.786$		None	None	$0$	$0$	$0$	$0$
1476.2.f.a	$2$	$11.786$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$-8$	$0$		$q-4q^{5}-4iq^{7}-3iq^{11}-4iq^{13}+\cdots$
1476.2.f.b	$2$	$11.786$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$8$	$0$		$q+4q^{5}-4iq^{7}+3iq^{11}-4iq^{13}+\cdots$
1476.2.f.c	$4$	$11.786$	$\Q(i, \sqrt{41})$	$\Q(\sqrt{-123}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{11}+(\beta _{1}-2\beta _{2})q^{17}-5q^{25}+\cdots$
1476.2.f.d	$4$	$11.786$	4.0.25088.1	None	None	$0$	$0$	$4$	$0$		$q+(1-\beta _{2})q^{5}+\beta _{3}q^{7}+(2\beta _{1}+\beta _{3})q^{11}+\cdots$
1476.2.f.e	$6$	$11.786$	6.0.5089536.1	None	None	$0$	$0$	$-4$	$0$		$q+(-1-\beta _{1})q^{5}+(-\beta _{2}+\beta _{5})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots$
1476.2.i.a	$2$	$11.786$	$\Q(\sqrt{-3}) $	None	None	$0$	$0$	$-1$	$-5$		$q+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-5+5\zeta_{6})q^{7}+\cdots$
1476.2.i.b	$32$	$11.786$		None	None	$0$	$-1$	$1$	$-1$
1476.2.i.c	$46$	$11.786$		None	None	$0$	$-1$	$2$	$4$
1476.2.k.a	$6$	$11.786$	6.0.5089536.1	None	None	$0$	$0$	$0$	$0$		$q+(\beta _{4}-\beta _{5})q^{5}+(\beta _{1}+\beta _{2}-\beta _{5})q^{7}+\cdots$
1476.2.k.b	$12$	$11.786$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{6}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{10})q^{7}+\beta _{11}q^{11}+\cdots$
1476.2.k.c	$16$	$11.786$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{5}-\beta _{9}q^{7}+(\beta _{3}-\beta _{4}-\beta _{7}-\beta _{10}+\cdots)q^{11}+\cdots$
1476.2.n.a	$4$	$11.786$	$\Q(\zeta_{10})$	None	None	$0$	$0$	$-7$	$9$		$q+(-3+3\zeta_{10}+2\zeta_{10}^{3})q^{5}+(3+3\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
1476.2.n.b	$4$	$11.786$	$\Q(\zeta_{10})$	None	None	$0$	$0$	$-5$	$-3$		$q+(-1+\zeta_{10}-2\zeta_{10}^{3})q^{5}+(-1-\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
1476.2.n.c	$4$	$11.786$	$\Q(\zeta_{10})$	None	None	$0$	$0$	$-1$	$-3$		$q+(-1+\zeta_{10}+2\zeta_{10}^{3})q^{5}+(-1-\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
1476.2.n.d	$4$	$11.786$	$\Q(\zeta_{10})$	None	None	$0$	$0$	$7$	$4$		$q+(2-2\zeta_{10}+\zeta_{10}^{3})q^{5}+(2-2\zeta_{10}+\cdots)q^{7}+\cdots$
1476.2.n.e	$8$	$11.786$	8.0.2127515625.1	None	None	$0$	$0$	$2$	$-7$		$q-\beta _{4}q^{5}+(-2+\beta _{1}+2\beta _{2}-\beta _{3})q^{7}+\cdots$
1476.2.n.f	$16$	$11.786$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$0$	$0$	$4$	$0$		$q+(1+\beta _{3}+\beta _{4}-\beta _{6}-\beta _{9})q^{5}+(-1+\cdots)q^{7}+\cdots$
1476.2.n.g	$32$	$11.786$		None	None	$0$	$0$	$0$	$0$
1476.2.q.a	$8$	$11.786$	$\Q(\zeta_{24})$	None	None	$0$	$0$	$0$	$0$		$q+(\zeta_{24}-\zeta_{24}^{5}-2\zeta_{24}^{6}+\zeta_{24}^{7})q^{3}+\cdots$
1476.2.q.b	$76$	$11.786$		None	None	$0$	$0$	$4$	$0$
1476.2.x.a	$28$	$11.786$		None	None	$0$	$0$	$-4$	$0$

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$\zeta$ zeros

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Higher genus families
Abelian varieties over $\F_{q}$

Label	Dim.	\(A\)	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
1476.1.h.a	\(1\)	\(0.737\)	\(\Q\)	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \)	\(\Q(\sqrt{41}) \)	\(-1\)	\(0\)	\(2\)	\(0\)		\(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{16}+\cdots\)
1476.1.h.b	\(2\)	\(0.737\)	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-41}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q+q^{2}+q^{4}-\beta q^{7}+q^{8}+\beta q^{11}-\beta q^{14}+\cdots\)
1476.1.j.a	\(2\)	\(0.737\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{2}-q^{4}-iq^{8}+(1+i)q^{13}+q^{16}+\cdots\)
1476.1.j.b	\(2\)	\(0.737\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{2}-q^{4}+iq^{8}+(1+i)q^{13}+q^{16}+\cdots\)
1476.1.l.a	\(4\)	\(0.737\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{3}q^{11}+\zeta_{8}q^{17}+\cdots\)
1476.1.o.a	\(2\)	\(0.737\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-41}) \)	None	\(-1\)	\(-2\)	\(1\)	\(-1\)		\(q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
1476.1.o.b	\(2\)	\(0.737\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-41}) \)	None	\(-1\)	\(2\)	\(1\)	\(1\)		\(q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots\)
1476.1.o.c	\(4\)	\(0.737\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-41}) \)	None	\(-2\)	\(0\)	\(-2\)	\(0\)		\(q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
1476.1.o.d	\(8\)	\(0.737\)	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-41}) \)	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{24}^{4}q^{2}+\zeta_{24}^{9}q^{3}+\zeta_{24}^{8}q^{4}+\cdots\)
1476.1.w.a	\(4\)	\(0.737\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{2})q^{5}+\cdots\)
1476.1.w.b	\(4\)	\(0.737\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{2})q^{5}+\cdots\)
1476.1.z.a	\(4\)	\(0.737\)	\(\Q(\zeta_{10})\)	\(\Q(\sqrt{-1}) \)	None	\(1\)	\(0\)	\(-2\)	\(0\)		\(q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(-\zeta_{10}^{3}+\zeta_{10}^{4}+\cdots)q^{5}+\cdots\)
1476.1.ba.a	\(4\)	\(0.737\)	\(\Q(\zeta_{10})\)	\(\Q(\sqrt{-1}) \)	None	\(1\)	\(0\)	\(2\)	\(0\)		\(q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+(-\zeta_{10}^{2}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots\)
1476.1.bo.a	\(8\)	\(0.737\)	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{4}+(-\zeta_{20}^{2}-\zeta_{20}^{4}+\cdots)q^{5}+\cdots\)
1476.1.bo.b	\(8\)	\(0.737\)	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{4}+(\zeta_{20}^{2}+\zeta_{20}^{4}+\cdots)q^{5}+\cdots\)
1476.1.cc.a	\(16\)	\(0.737\)	\(\Q(\zeta_{40})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+\zeta_{40}^{13}q^{2}-\zeta_{40}^{6}q^{4}+(\zeta_{40}^{8}+\zeta_{40}^{14}+\cdots)q^{5}+\cdots\)
1476.1.cc.b	\(16\)	\(0.737\)	\(\Q(\zeta_{40})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q-\zeta_{40}^{13}q^{2}-\zeta_{40}^{6}q^{4}+(-\zeta_{40}^{8}+\cdots)q^{5}+\cdots\)
1476.2.a.a	\(1\)	\(11.786\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(q-2q^{7}+q^{11}-2q^{13}+q^{17}-4q^{19}+\cdots\)
1476.2.a.b	\(1\)	\(11.786\)	\(\Q\)	None	None	\(0\)	\(0\)	\(2\)	\(-4\)	\(-\)	\(q+2q^{5}-4q^{7}+5q^{11}+4q^{13}+5q^{17}+\cdots\)
1476.2.a.c	\(2\)	\(11.786\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(2\)	\(+\)	\(q+(-1+\beta )q^{5}+(1-\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
1476.2.a.d	\(2\)	\(11.786\)	\(\Q(\sqrt{6}) \)	None	None	\(0\)	\(0\)	\(4\)	\(4\)	\(-\)	\(q+(2+\beta )q^{5}+(2-\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
1476.2.a.e	\(3\)	\(11.786\)	3.3.404.1	None	None	\(0\)	\(0\)	\(-4\)	\(4\)	\(+\)	\(q+(-1-\beta _{2})q^{5}+(1+\beta _{1})q^{7}+(-2+\cdots)q^{11}+\cdots\)
1476.2.a.f	\(3\)	\(11.786\)	3.3.404.1	None	None	\(0\)	\(0\)	\(4\)	\(4\)	\(-\)	\(q+(1+\beta _{2})q^{5}+(1+\beta _{1})q^{7}+(2+2\beta _{1}+\cdots)q^{11}+\cdots\)
1476.2.a.g	\(4\)	\(11.786\)	4.4.25808.1	None	None	\(0\)	\(0\)	\(-4\)	\(0\)	\(-\)	\(q+(-2+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1476.2.c.a	\(80\)	\(11.786\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
1476.2.d.a	\(4\)	\(11.786\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{8}^{2}q^{2}-2q^{4}-\zeta_{8}^{2}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots\)
1476.2.d.b	\(8\)	\(11.786\)	8.0.\(\cdots\).5	None	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q+(-1+\beta _{4})q^{2}+(-1-\beta _{4})q^{4}-2\beta _{6}q^{5}+\cdots\)
1476.2.d.c	\(8\)	\(11.786\)	8.0.\(\cdots\).5	None	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{4}q^{2}+(-2+\beta _{4})q^{4}-2\beta _{6}q^{5}+\cdots\)
1476.2.d.d	\(64\)	\(11.786\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
1476.2.f.a	\(2\)	\(11.786\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(-8\)	\(0\)		\(q-4q^{5}-4iq^{7}-3iq^{11}-4iq^{13}+\cdots\)
1476.2.f.b	\(2\)	\(11.786\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(8\)	\(0\)		\(q+4q^{5}-4iq^{7}+3iq^{11}-4iq^{13}+\cdots\)
1476.2.f.c	\(4\)	\(11.786\)	\(\Q(i, \sqrt{41})\)	\(\Q(\sqrt{-123}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{11}+(\beta _{1}-2\beta _{2})q^{17}-5q^{25}+\cdots\)
1476.2.f.d	\(4\)	\(11.786\)	4.0.25088.1	None	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q+(1-\beta _{2})q^{5}+\beta _{3}q^{7}+(2\beta _{1}+\beta _{3})q^{11}+\cdots\)
1476.2.f.e	\(6\)	\(11.786\)	6.0.5089536.1	None	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+(-1-\beta _{1})q^{5}+(-\beta _{2}+\beta _{5})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots\)
1476.2.i.a	\(2\)	\(11.786\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(0\)	\(-1\)	\(-5\)		\(q+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-5+5\zeta_{6})q^{7}+\cdots\)
1476.2.i.b	\(32\)	\(11.786\)		None	None	\(0\)	\(-1\)	\(1\)	\(-1\)
1476.2.i.c	\(46\)	\(11.786\)		None	None	\(0\)	\(-1\)	\(2\)	\(4\)
1476.2.k.a	\(6\)	\(11.786\)	6.0.5089536.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\beta _{4}-\beta _{5})q^{5}+(\beta _{1}+\beta _{2}-\beta _{5})q^{7}+\cdots\)
1476.2.k.b	\(12\)	\(11.786\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{6}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{10})q^{7}+\beta _{11}q^{11}+\cdots\)
1476.2.k.c	\(16\)	\(11.786\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{5}-\beta _{9}q^{7}+(\beta _{3}-\beta _{4}-\beta _{7}-\beta _{10}+\cdots)q^{11}+\cdots\)
1476.2.n.a	\(4\)	\(11.786\)	\(\Q(\zeta_{10})\)	None	None	\(0\)	\(0\)	\(-7\)	\(9\)		\(q+(-3+3\zeta_{10}+2\zeta_{10}^{3})q^{5}+(3+3\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1476.2.n.b	\(4\)	\(11.786\)	\(\Q(\zeta_{10})\)	None	None	\(0\)	\(0\)	\(-5\)	\(-3\)		\(q+(-1+\zeta_{10}-2\zeta_{10}^{3})q^{5}+(-1-\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1476.2.n.c	\(4\)	\(11.786\)	\(\Q(\zeta_{10})\)	None	None	\(0\)	\(0\)	\(-1\)	\(-3\)		\(q+(-1+\zeta_{10}+2\zeta_{10}^{3})q^{5}+(-1-\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1476.2.n.d	\(4\)	\(11.786\)	\(\Q(\zeta_{10})\)	None	None	\(0\)	\(0\)	\(7\)	\(4\)		\(q+(2-2\zeta_{10}+\zeta_{10}^{3})q^{5}+(2-2\zeta_{10}+\cdots)q^{7}+\cdots\)
1476.2.n.e	\(8\)	\(11.786\)	8.0.2127515625.1	None	None	\(0\)	\(0\)	\(2\)	\(-7\)		\(q-\beta _{4}q^{5}+(-2+\beta _{1}+2\beta _{2}-\beta _{3})q^{7}+\cdots\)
1476.2.n.f	\(16\)	\(11.786\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q+(1+\beta _{3}+\beta _{4}-\beta _{6}-\beta _{9})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1476.2.n.g	\(32\)	\(11.786\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
1476.2.q.a	\(8\)	\(11.786\)	\(\Q(\zeta_{24})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{24}-\zeta_{24}^{5}-2\zeta_{24}^{6}+\zeta_{24}^{7})q^{3}+\cdots\)
1476.2.q.b	\(76\)	\(11.786\)		None	None	\(0\)	\(0\)	\(4\)	\(0\)
1476.2.x.a	\(28\)	\(11.786\)		None	None	\(0\)	\(0\)	\(-4\)	\(0\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.