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 208 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
1764.1.d.a	$2$	$0.880$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{13}+(\zeta_{6}+\zeta_{6}^{2})q^{19}+\cdots$
1764.1.g.a	$1$	$0.880$	$\Q$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{7}) $	$1$	$0$	$0$	$0$		$q+q^{2}+q^{4}+q^{8}+q^{16}-q^{25}+2q^{29}+\cdots$
1764.1.g.b	$2$	$0.880$	$\Q(\sqrt{2}) $	$\Q(\sqrt{-1}) $	None	$-2$	$0$	$0$	$0$		$q-q^{2}+q^{4}-\beta q^{5}-q^{8}+\beta q^{10}-\beta q^{13}+\cdots$
1764.1.g.c	$2$	$0.880$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{3}) $	$0$	$0$	$0$	$0$		$q-iq^{2}-q^{4}+iq^{8}+iq^{11}+q^{16}+\cdots$
1764.1.g.d	$2$	$0.880$	$\Q(\sqrt{2}) $	$\Q(\sqrt{-1}) $	None	$2$	$0$	$0$	$0$		$q+q^{2}+q^{4}-\beta q^{5}+q^{8}-\beta q^{10}+\beta q^{13}+\cdots$
1764.1.h.a	$8$	$0.880$	$\Q(\zeta_{16})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{16}^{4}q^{2}-q^{4}+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{5}+\cdots$
1764.1.q.a	$8$	$0.880$	$\Q(\zeta_{24})$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{9}q^{8}+\cdots$
1764.1.q.b	$16$	$0.880$	$\Q(\zeta_{48})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{48}^{20}q^{2}-\zeta_{48}^{16}q^{4}+(-\zeta_{48}^{5}+\cdots)q^{5}+\cdots$
1764.1.y.a	$2$	$0.880$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{7}) $	$-1$	$0$	$0$	$0$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}-\zeta_{6}q^{16}+\cdots$
1764.1.y.b	$4$	$0.880$	$\Q(\sqrt{2}, \sqrt{-3})$	$\Q(\sqrt{-1}) $	None	$-2$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
1764.1.y.c	$4$	$0.880$	$\Q(\zeta_{12})$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{3}) $	$0$	$0$	$0$	$0$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{11}+\cdots$
1764.1.y.d	$4$	$0.880$	$\Q(\sqrt{2}, \sqrt{-3})$	$\Q(\sqrt{-1}) $	None	$2$	$0$	$0$	$0$		$q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
1764.1.z.a	$2$	$0.880$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1+\zeta_{6})q^{19}+\cdots$
1764.1.co.a	$12$	$0.880$	$\Q(\zeta_{21})$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$-1$		$q-\zeta_{42}^{16}q^{7}+(-\zeta_{42}^{8}+\zeta_{42}^{10})q^{13}+\cdots$
1764.2.a.a	$1$	$14.086$	$\Q$	None	None	$0$	$0$	$-3$	$0$	$+$	$q-3q^{5}+3q^{11}+2q^{13}-3q^{17}-q^{19}+\cdots$
1764.2.a.b	$1$	$14.086$	$\Q$	None	None	$0$	$0$	$-2$	$0$	$-$	$q-2q^{5}-2q^{11}-4q^{13}-6q^{17}+8q^{19}+\cdots$
1764.2.a.c	$1$	$14.086$	$\Q$	None	None	$0$	$0$	$-2$	$0$	$-$	$q-2q^{5}-2q^{11}+3q^{13}+8q^{17}+q^{19}+\cdots$
1764.2.a.d	$1$	$14.086$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$	$+$	$q-5q^{13}+q^{19}-5q^{25}-11q^{31}+\cdots$
1764.2.a.e	$1$	$14.086$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$	$+$	$q-2q^{13}-8q^{19}-5q^{25}+4q^{31}+\cdots$
1764.2.a.f	$1$	$14.086$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$	$-$	$q+5q^{13}-q^{19}-5q^{25}+11q^{31}+\cdots$
1764.2.a.g	$1$	$14.086$	$\Q$	None	None	$0$	$0$	$0$	$0$	$-$	$q+6q^{11}-2q^{13}+4q^{19}+6q^{23}+\cdots$
1764.2.a.h	$1$	$14.086$	$\Q$	None	None	$0$	$0$	$2$	$0$	$+$	$q+2q^{5}-2q^{11}-3q^{13}-8q^{17}-q^{19}+\cdots$
1764.2.a.i	$1$	$14.086$	$\Q$	None	None	$0$	$0$	$2$	$0$	$-$	$q+2q^{5}-2q^{11}+4q^{13}+6q^{17}-8q^{19}+\cdots$
1764.2.a.j	$1$	$14.086$	$\Q$	None	None	$0$	$0$	$3$	$0$	$-$	$q+3q^{5}+3q^{11}-2q^{13}+3q^{17}+q^{19}+\cdots$
1764.2.a.k	$1$	$14.086$	$\Q$	None	None	$0$	$0$	$4$	$0$	$-$	$q+4q^{5}-2q^{11}+6q^{13}-4q^{17}+4q^{19}+\cdots$
1764.2.a.l	$2$	$14.086$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$0$	$0$	$+$	$q+\beta q^{5}-4q^{11}-3\beta q^{13}+\beta q^{17}+\cdots$
1764.2.a.m	$4$	$14.086$	$\Q(\sqrt{2}, \sqrt{7})$	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{2}q^{5}-\beta _{3}q^{11}-3\beta _{1}q^{13}+\beta _{2}q^{17}+\cdots$
1764.2.b.a	$4$	$14.086$	$\Q(\zeta_{12})$	None	None	$-4$	$0$	$0$	$0$		$q+(-1+\zeta_{12})q^{2}-2\zeta_{12}q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
1764.2.b.b	$4$	$14.086$	$\Q(\sqrt{-3}, \sqrt{-7})$	None	None	$-2$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+(-2-\beta _{2})q^{4}+\beta _{3}q^{5}+(2+\cdots)q^{8}+\cdots$
1764.2.b.c	$4$	$14.086$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	None	$0$	$0$	$0$	$0$		$q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
1764.2.b.d	$4$	$14.086$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
1764.2.b.e	$4$	$14.086$	4.0.2048.2	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}+2\beta _{2}q^{8}+\cdots$
1764.2.b.f	$4$	$14.086$	4.0.2048.2	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}+2\beta _{2}q^{8}+\cdots$
1764.2.b.g	$4$	$14.086$	4.0.2048.2	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}-2\beta _{2}q^{8}+\cdots$
1764.2.b.h	$4$	$14.086$	$\Q(\sqrt{-3}, \sqrt{-7})$	None	None	$2$	$0$	$0$	$0$		$q-\beta _{2}q^{2}+(-2-\beta _{2})q^{4}+\beta _{3}q^{5}+(-2+\cdots)q^{8}+\cdots$
1764.2.b.i	$8$	$14.086$	8.0.562828176.1	None	None	$2$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+(\beta _{3}+\cdots)q^{8}+\cdots$
1764.2.b.j	$8$	$14.086$	8.0.562828176.1	None	None	$2$	$0$	$0$	$0$		$q-\beta _{4}q^{2}+\beta _{6}q^{4}+(\beta _{2}-\beta _{6})q^{5}+(-1+\cdots)q^{8}+\cdots$
1764.2.b.k	$8$	$14.086$	8.0.$\cdots$.10	None	None	$4$	$0$	$0$	$0$		$q+(1+\beta _{3})q^{2}+(1+\beta _{3}+\beta _{5}-\beta _{6})q^{4}+\cdots$
1764.2.b.l	$12$	$14.086$	12.0.$\cdots$.1	None	None	$-4$	$0$	$0$	$0$		$q-\beta _{1}q^{2}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots$
1764.2.b.m	$12$	$14.086$	12.0.$\cdots$.1	None	None	$-4$	$0$	$0$	$0$		$q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{11})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots$
1764.2.b.n	$16$	$14.086$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{7}q^{2}+(-1+\beta _{1}-\beta _{10})q^{4}+\beta _{12}q^{5}+\cdots$
1764.2.e.a	$2$	$14.086$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+\beta q^{2}-2q^{4}+3\beta q^{5}-2\beta q^{8}-6q^{10}+\cdots$
1764.2.e.b	$2$	$14.086$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+\beta q^{2}-2q^{4}+\beta q^{5}-2\beta q^{8}-2q^{10}+\cdots$
1764.2.e.c	$2$	$14.086$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-\beta q^{2}-2q^{4}+3\beta q^{5}+2\beta q^{8}+6q^{10}+\cdots$
1764.2.e.d	$4$	$14.086$	$\Q(\zeta_{8})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{8}^{2}q^{2}-2q^{4}+2\zeta_{8}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots$
1764.2.e.e	$4$	$14.086$	$\Q(\zeta_{8})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{8}^{2}q^{2}-2q^{4}-\zeta_{8}q^{5}-2\zeta_{8}^{2}q^{8}+\cdots$
1764.2.e.f	$8$	$14.086$	8.0.157351936.1	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{6}q^{2}-\beta _{1}q^{4}-\beta _{5}q^{8}+(\beta _{5}+\beta _{6}+\cdots)q^{11}+\cdots$
1764.2.e.g	$12$	$14.086$	12.0.$\cdots$.1	None	None	$0$	$0$	$0$	$0$		$q+\beta _{6}q^{2}+(1+\beta _{10})q^{4}-\beta _{4}q^{5}+(\beta _{6}+\cdots)q^{8}+\cdots$
1764.2.e.h	$16$	$14.086$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(\beta _{3}-\beta _{5}+\cdots)q^{8}+\cdots$
1764.2.e.i	$16$	$14.086$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(-\beta _{3}+\beta _{5}+\cdots)q^{8}+\cdots$

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Elliptic curves over $\Q$
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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
1764.1.d.a	\(2\)	\(0.880\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{13}+(\zeta_{6}+\zeta_{6}^{2})q^{19}+\cdots\)
1764.1.g.a	\(1\)	\(0.880\)	\(\Q\)	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{7}) \)	\(1\)	\(0\)	\(0\)	\(0\)		\(q+q^{2}+q^{4}+q^{8}+q^{16}-q^{25}+2q^{29}+\cdots\)
1764.1.g.b	\(2\)	\(0.880\)	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-1}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q-q^{2}+q^{4}-\beta q^{5}-q^{8}+\beta q^{10}-\beta q^{13}+\cdots\)
1764.1.g.c	\(2\)	\(0.880\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{3}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{2}-q^{4}+iq^{8}+iq^{11}+q^{16}+\cdots\)
1764.1.g.d	\(2\)	\(0.880\)	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-1}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q+q^{2}+q^{4}-\beta q^{5}+q^{8}-\beta q^{10}+\beta q^{13}+\cdots\)
1764.1.h.a	\(8\)	\(0.880\)	\(\Q(\zeta_{16})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{16}^{4}q^{2}-q^{4}+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{5}+\cdots\)
1764.1.q.a	\(8\)	\(0.880\)	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{9}q^{8}+\cdots\)
1764.1.q.b	\(16\)	\(0.880\)	\(\Q(\zeta_{48})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{48}^{20}q^{2}-\zeta_{48}^{16}q^{4}+(-\zeta_{48}^{5}+\cdots)q^{5}+\cdots\)
1764.1.y.a	\(2\)	\(0.880\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{7}) \)	\(-1\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}-\zeta_{6}q^{16}+\cdots\)
1764.1.y.b	\(4\)	\(0.880\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-1}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.1.y.c	\(4\)	\(0.880\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{3}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{11}+\cdots\)
1764.1.y.d	\(4\)	\(0.880\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-1}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.1.z.a	\(2\)	\(0.880\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1+\zeta_{6})q^{19}+\cdots\)
1764.1.co.a	\(12\)	\(0.880\)	\(\Q(\zeta_{21})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(-1\)		\(q-\zeta_{42}^{16}q^{7}+(-\zeta_{42}^{8}+\zeta_{42}^{10})q^{13}+\cdots\)
1764.2.a.a	\(1\)	\(14.086\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-3\)	\(0\)	\(+\)	\(q-3q^{5}+3q^{11}+2q^{13}-3q^{17}-q^{19}+\cdots\)
1764.2.a.b	\(1\)	\(14.086\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(q-2q^{5}-2q^{11}-4q^{13}-6q^{17}+8q^{19}+\cdots\)
1764.2.a.c	\(1\)	\(14.086\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(q-2q^{5}-2q^{11}+3q^{13}+8q^{17}+q^{19}+\cdots\)
1764.2.a.d	\(1\)	\(14.086\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(q-5q^{13}+q^{19}-5q^{25}-11q^{31}+\cdots\)
1764.2.a.e	\(1\)	\(14.086\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(q-2q^{13}-8q^{19}-5q^{25}+4q^{31}+\cdots\)
1764.2.a.f	\(1\)	\(14.086\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(q+5q^{13}-q^{19}-5q^{25}+11q^{31}+\cdots\)
1764.2.a.g	\(1\)	\(14.086\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(q+6q^{11}-2q^{13}+4q^{19}+6q^{23}+\cdots\)
1764.2.a.h	\(1\)	\(14.086\)	\(\Q\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	\(+\)	\(q+2q^{5}-2q^{11}-3q^{13}-8q^{17}-q^{19}+\cdots\)
1764.2.a.i	\(1\)	\(14.086\)	\(\Q\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	\(-\)	\(q+2q^{5}-2q^{11}+4q^{13}+6q^{17}-8q^{19}+\cdots\)
1764.2.a.j	\(1\)	\(14.086\)	\(\Q\)	None	None	\(0\)	\(0\)	\(3\)	\(0\)	\(-\)	\(q+3q^{5}+3q^{11}-2q^{13}+3q^{17}+q^{19}+\cdots\)
1764.2.a.k	\(1\)	\(14.086\)	\(\Q\)	None	None	\(0\)	\(0\)	\(4\)	\(0\)	\(-\)	\(q+4q^{5}-2q^{11}+6q^{13}-4q^{17}+4q^{19}+\cdots\)
1764.2.a.l	\(2\)	\(14.086\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(q+\beta q^{5}-4q^{11}-3\beta q^{13}+\beta q^{17}+\cdots\)
1764.2.a.m	\(4\)	\(14.086\)	\(\Q(\sqrt{2}, \sqrt{7})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(q+\beta _{2}q^{5}-\beta _{3}q^{11}-3\beta _{1}q^{13}+\beta _{2}q^{17}+\cdots\)
1764.2.b.a	\(4\)	\(14.086\)	\(\Q(\zeta_{12})\)	None	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q+(-1+\zeta_{12})q^{2}-2\zeta_{12}q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
1764.2.b.b	\(4\)	\(14.086\)	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+(-2-\beta _{2})q^{4}+\beta _{3}q^{5}+(2+\cdots)q^{8}+\cdots\)
1764.2.b.c	\(4\)	\(14.086\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.2.b.d	\(4\)	\(14.086\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.2.b.e	\(4\)	\(14.086\)	4.0.2048.2	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}+2\beta _{2}q^{8}+\cdots\)
1764.2.b.f	\(4\)	\(14.086\)	4.0.2048.2	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}+2\beta _{2}q^{8}+\cdots\)
1764.2.b.g	\(4\)	\(14.086\)	4.0.2048.2	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}-2\beta _{2}q^{8}+\cdots\)
1764.2.b.h	\(4\)	\(14.086\)	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{2}+(-2-\beta _{2})q^{4}+\beta _{3}q^{5}+(-2+\cdots)q^{8}+\cdots\)
1764.2.b.i	\(8\)	\(14.086\)	8.0.562828176.1	None	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+(\beta _{3}+\cdots)q^{8}+\cdots\)
1764.2.b.j	\(8\)	\(14.086\)	8.0.562828176.1	None	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{4}q^{2}+\beta _{6}q^{4}+(\beta _{2}-\beta _{6})q^{5}+(-1+\cdots)q^{8}+\cdots\)
1764.2.b.k	\(8\)	\(14.086\)	8.0.\(\cdots\).10	None	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q+(1+\beta _{3})q^{2}+(1+\beta _{3}+\beta _{5}-\beta _{6})q^{4}+\cdots\)
1764.2.b.l	\(12\)	\(14.086\)	12.0.\(\cdots\).1	None	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{2}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
1764.2.b.m	\(12\)	\(14.086\)	12.0.\(\cdots\).1	None	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{11})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
1764.2.b.n	\(16\)	\(14.086\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{7}q^{2}+(-1+\beta _{1}-\beta _{10})q^{4}+\beta _{12}q^{5}+\cdots\)
1764.2.e.a	\(2\)	\(14.086\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta q^{2}-2q^{4}+3\beta q^{5}-2\beta q^{8}-6q^{10}+\cdots\)
1764.2.e.b	\(2\)	\(14.086\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta q^{2}-2q^{4}+\beta q^{5}-2\beta q^{8}-2q^{10}+\cdots\)
1764.2.e.c	\(2\)	\(14.086\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta q^{2}-2q^{4}+3\beta q^{5}+2\beta q^{8}+6q^{10}+\cdots\)
1764.2.e.d	\(4\)	\(14.086\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{8}^{2}q^{2}-2q^{4}+2\zeta_{8}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots\)
1764.2.e.e	\(4\)	\(14.086\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{8}^{2}q^{2}-2q^{4}-\zeta_{8}q^{5}-2\zeta_{8}^{2}q^{8}+\cdots\)
1764.2.e.f	\(8\)	\(14.086\)	8.0.157351936.1	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{6}q^{2}-\beta _{1}q^{4}-\beta _{5}q^{8}+(\beta _{5}+\beta _{6}+\cdots)q^{11}+\cdots\)
1764.2.e.g	\(12\)	\(14.086\)	12.0.\(\cdots\).1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{6}q^{2}+(1+\beta _{10})q^{4}-\beta _{4}q^{5}+(\beta _{6}+\cdots)q^{8}+\cdots\)
1764.2.e.h	\(16\)	\(14.086\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(\beta _{3}-\beta _{5}+\cdots)q^{8}+\cdots\)
1764.2.e.i	\(16\)	\(14.086\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(-\beta _{3}+\beta _{5}+\cdots)q^{8}+\cdots\)

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L-functions

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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.