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 162 matches)

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Label	Dim.	$A$	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
570.2.a.a	$1$	$4.551$	$\Q$	None	$-1$	$-1$	$-1$	$-2$	$-$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
570.2.a.b	$1$	$4.551$	$\Q$	None	$-1$	$-1$	$-1$	$2$	$+$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
570.2.a.c	$1$	$4.551$	$\Q$	None	$-1$	$-1$	$1$	$-2$	$+$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
570.2.a.d	$1$	$4.551$	$\Q$	None	$-1$	$1$	$-1$	$4$	$-$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots$
570.2.a.e	$1$	$4.551$	$\Q$	None	$-1$	$1$	$1$	$-4$	$+$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots$
570.2.a.f	$1$	$4.551$	$\Q$	None	$-1$	$1$	$1$	$2$	$-$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots$
570.2.a.g	$1$	$4.551$	$\Q$	None	$1$	$-1$	$-1$	$0$	$-$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
570.2.a.h	$1$	$4.551$	$\Q$	None	$1$	$-1$	$1$	$-2$	$-$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
570.2.a.i	$1$	$4.551$	$\Q$	None	$1$	$-1$	$1$	$4$	$-$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots$
570.2.a.j	$1$	$4.551$	$\Q$	None	$1$	$1$	$-1$	$2$	$-$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
570.2.a.k	$1$	$4.551$	$\Q$	None	$1$	$1$	$-1$	$2$	$-$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
570.2.a.l	$1$	$4.551$	$\Q$	None	$1$	$1$	$1$	$-2$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
570.2.a.m	$1$	$4.551$	$\Q$	None	$1$	$1$	$1$	$4$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
570.2.c.a	$4$	$4.551$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
570.2.c.b	$4$	$4.551$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
570.2.c.c	$8$	$4.551$	8.0.1499238400.2	None	$0$	$-4$	$0$	$0$		$q+\beta _{6}q^{2}+(-1-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots$
570.2.c.d	$8$	$4.551$	$\Q(\zeta_{24})$	None	$0$	$0$	$0$	$0$		$q-\zeta_{24}q^{2}-\zeta_{24}^{4}q^{3}-q^{4}+(-\zeta_{24}^{2}+\cdots)q^{5}+\cdots$
570.2.c.e	$8$	$4.551$	$\Q(\zeta_{24})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{24}q^{2}+(-\zeta_{24}-\zeta_{24}^{6})q^{3}-q^{4}+\cdots$
570.2.c.f	$8$	$4.551$	8.0.1499238400.2	None	$0$	$4$	$0$	$0$		$q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots$
570.2.d.a	$2$	$4.551$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-2$	$0$		$q+iq^{2}+iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots$
570.2.d.b	$2$	$4.551$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$4$	$0$		$q+iq^{2}+iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\cdots$
570.2.d.c	$6$	$4.551$	6.0.350464.1	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-q^{6}+\cdots$
570.2.d.d	$6$	$4.551$	6.0.350464.1	None	$0$	$0$	$2$	$0$		$q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{5}q^{5}+q^{6}+\cdots$
570.2.f.a	$4$	$4.551$	$\Q(\zeta_{8})$	None	$-4$	$-4$	$0$	$8$		$q-q^{2}+(-1-\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots$
570.2.f.b	$4$	$4.551$	$\Q(\zeta_{8})$	None	$4$	$4$	$0$	$8$		$q+q^{2}+(1+\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots$
570.2.f.c	$8$	$4.551$	8.0.7278137344.1	None	$-8$	$2$	$0$	$4$		$q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
570.2.f.d	$8$	$4.551$	8.0.7278137344.1	None	$8$	$-2$	$0$	$4$		$q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
570.2.i.a	$2$	$4.551$	$\Q(\sqrt{-3}) $	None	$-1$	$-1$	$1$	$-2$		$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
570.2.i.b	$2$	$4.551$	$\Q(\sqrt{-3}) $	None	$-1$	$-1$	$1$	$-2$		$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
570.2.i.c	$2$	$4.551$	$\Q(\sqrt{-3}) $	None	$-1$	$1$	$1$	$6$		$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
570.2.i.d	$2$	$4.551$	$\Q(\sqrt{-3}) $	None	$1$	$-1$	$1$	$-2$		$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
570.2.i.e	$2$	$4.551$	$\Q(\sqrt{-3}) $	None	$1$	$1$	$-1$	$-10$		$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
570.2.i.f	$4$	$4.551$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	$-2$	$2$	$-2$	$4$		$q+(-1+\beta _{1})q^{2}+(1-\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots$
570.2.i.g	$4$	$4.551$	$\Q(\sqrt{-3}, \sqrt{73})$	None	$2$	$-2$	$-2$	$-4$		$q+(1-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots$
570.2.i.h	$4$	$4.551$	$\Q(\sqrt{-3}, \sqrt{19})$	None	$2$	$-2$	$2$	$0$		$q+(1+\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
570.2.i.i	$4$	$4.551$	$\Q(\sqrt{-3}, \sqrt{7})$	None	$2$	$2$	$2$	$0$		$q+(1+\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
570.2.i.j	$6$	$4.551$	6.0.29654208.1	None	$-3$	$-3$	$-3$	$2$		$q+(-1+\beta _{1})q^{2}+(-1+\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots$
570.2.k.a	$36$	$4.551$		None	$0$	$4$	$0$	$-12$
570.2.k.b	$36$	$4.551$		None	$0$	$4$	$0$	$20$
570.2.m.a	$20$	$4.551$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	$0$	$0$	$-4$	$-4$		$q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots$
570.2.m.b	$20$	$4.551$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	$0$	$0$	$12$	$-4$		$q+\beta _{7}q^{2}-\beta _{10}q^{3}+\beta _{2}q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots$
570.2.n.a	$80$	$4.551$		None	$0$	$0$	$0$	$0$
570.2.q.a	$8$	$4.551$	$\Q(\zeta_{24})$	None	$0$	$0$	$4$	$0$		$q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(\zeta_{24}-\zeta_{24}^{4})q^{3}+\cdots$
570.2.q.b	$12$	$4.551$	12.0.$\cdots$.1	None	$0$	$0$	$0$	$0$		$q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+\cdots$
570.2.q.c	$20$	$4.551$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$0$	$0$	$0$	$0$		$q-\beta _{11}q^{2}+\beta _{11}q^{3}+(1-\beta _{12})q^{4}+\cdots$
570.2.s.a	$24$	$4.551$		None	$-12$	$4$	$0$	$-12$
570.2.s.b	$24$	$4.551$		None	$12$	$2$	$0$	$-12$
570.2.u.a	$6$	$4.551$	$\Q(\zeta_{18})$	None	$0$	$0$	$0$	$-6$		$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
570.2.u.b	$6$	$4.551$	$\Q(\zeta_{18})$	None	$0$	$0$	$0$	$-6$		$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
570.2.u.c	$6$	$4.551$	$\Q(\zeta_{18})$	None	$0$	$0$	$0$	$-3$		$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Label	Dim.	\(A\)	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
570.2.a.a	\(1\)	\(4.551\)	\(\Q\)	None	\(-1\)	\(-1\)	\(-1\)	\(-2\)	\(-\)	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
570.2.a.b	\(1\)	\(4.551\)	\(\Q\)	None	\(-1\)	\(-1\)	\(-1\)	\(2\)	\(+\)	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
570.2.a.c	\(1\)	\(4.551\)	\(\Q\)	None	\(-1\)	\(-1\)	\(1\)	\(-2\)	\(+\)	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
570.2.a.d	\(1\)	\(4.551\)	\(\Q\)	None	\(-1\)	\(1\)	\(-1\)	\(4\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
570.2.a.e	\(1\)	\(4.551\)	\(\Q\)	None	\(-1\)	\(1\)	\(1\)	\(-4\)	\(+\)	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
570.2.a.f	\(1\)	\(4.551\)	\(\Q\)	None	\(-1\)	\(1\)	\(1\)	\(2\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
570.2.a.g	\(1\)	\(4.551\)	\(\Q\)	None	\(1\)	\(-1\)	\(-1\)	\(0\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
570.2.a.h	\(1\)	\(4.551\)	\(\Q\)	None	\(1\)	\(-1\)	\(1\)	\(-2\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
570.2.a.i	\(1\)	\(4.551\)	\(\Q\)	None	\(1\)	\(-1\)	\(1\)	\(4\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
570.2.a.j	\(1\)	\(4.551\)	\(\Q\)	None	\(1\)	\(1\)	\(-1\)	\(2\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
570.2.a.k	\(1\)	\(4.551\)	\(\Q\)	None	\(1\)	\(1\)	\(-1\)	\(2\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
570.2.a.l	\(1\)	\(4.551\)	\(\Q\)	None	\(1\)	\(1\)	\(1\)	\(-2\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
570.2.a.m	\(1\)	\(4.551\)	\(\Q\)	None	\(1\)	\(1\)	\(1\)	\(4\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
570.2.c.a	\(4\)	\(4.551\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
570.2.c.b	\(4\)	\(4.551\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
570.2.c.c	\(8\)	\(4.551\)	8.0.1499238400.2	None	\(0\)	\(-4\)	\(0\)	\(0\)		\(q+\beta _{6}q^{2}+(-1-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
570.2.c.d	\(8\)	\(4.551\)	\(\Q(\zeta_{24})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{24}q^{2}-\zeta_{24}^{4}q^{3}-q^{4}+(-\zeta_{24}^{2}+\cdots)q^{5}+\cdots\)
570.2.c.e	\(8\)	\(4.551\)	\(\Q(\zeta_{24})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{24}q^{2}+(-\zeta_{24}-\zeta_{24}^{6})q^{3}-q^{4}+\cdots\)
570.2.c.f	\(8\)	\(4.551\)	8.0.1499238400.2	None	\(0\)	\(4\)	\(0\)	\(0\)		\(q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
570.2.d.a	\(2\)	\(4.551\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+iq^{2}+iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
570.2.d.b	\(2\)	\(4.551\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q+iq^{2}+iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\cdots\)
570.2.d.c	\(6\)	\(4.551\)	6.0.350464.1	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-q^{6}+\cdots\)
570.2.d.d	\(6\)	\(4.551\)	6.0.350464.1	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{5}q^{5}+q^{6}+\cdots\)
570.2.f.a	\(4\)	\(4.551\)	\(\Q(\zeta_{8})\)	None	\(-4\)	\(-4\)	\(0\)	\(8\)		\(q-q^{2}+(-1-\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots\)
570.2.f.b	\(4\)	\(4.551\)	\(\Q(\zeta_{8})\)	None	\(4\)	\(4\)	\(0\)	\(8\)		\(q+q^{2}+(1+\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots\)
570.2.f.c	\(8\)	\(4.551\)	8.0.7278137344.1	None	\(-8\)	\(2\)	\(0\)	\(4\)		\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
570.2.f.d	\(8\)	\(4.551\)	8.0.7278137344.1	None	\(8\)	\(-2\)	\(0\)	\(4\)		\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
570.2.i.a	\(2\)	\(4.551\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(-1\)	\(1\)	\(-2\)		\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.b	\(2\)	\(4.551\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(-1\)	\(1\)	\(-2\)		\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.c	\(2\)	\(4.551\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(1\)	\(1\)	\(6\)		\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.d	\(2\)	\(4.551\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(-1\)	\(1\)	\(-2\)		\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.e	\(2\)	\(4.551\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(1\)	\(-1\)	\(-10\)		\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.f	\(4\)	\(4.551\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	\(-2\)	\(2\)	\(-2\)	\(4\)		\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots\)
570.2.i.g	\(4\)	\(4.551\)	\(\Q(\sqrt{-3}, \sqrt{73})\)	None	\(2\)	\(-2\)	\(-2\)	\(-4\)		\(q+(1-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
570.2.i.h	\(4\)	\(4.551\)	\(\Q(\sqrt{-3}, \sqrt{19})\)	None	\(2\)	\(-2\)	\(2\)	\(0\)		\(q+(1+\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
570.2.i.i	\(4\)	\(4.551\)	\(\Q(\sqrt{-3}, \sqrt{7})\)	None	\(2\)	\(2\)	\(2\)	\(0\)		\(q+(1+\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
570.2.i.j	\(6\)	\(4.551\)	6.0.29654208.1	None	\(-3\)	\(-3\)	\(-3\)	\(2\)		\(q+(-1+\beta _{1})q^{2}+(-1+\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots\)
570.2.k.a	\(36\)	\(4.551\)		None	\(0\)	\(4\)	\(0\)	\(-12\)
570.2.k.b	\(36\)	\(4.551\)		None	\(0\)	\(4\)	\(0\)	\(20\)
570.2.m.a	\(20\)	\(4.551\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	\(0\)	\(0\)	\(-4\)	\(-4\)		\(q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots\)
570.2.m.b	\(20\)	\(4.551\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	\(0\)	\(0\)	\(12\)	\(-4\)		\(q+\beta _{7}q^{2}-\beta _{10}q^{3}+\beta _{2}q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\)
570.2.n.a	\(80\)	\(4.551\)		None	\(0\)	\(0\)	\(0\)	\(0\)
570.2.q.a	\(8\)	\(4.551\)	\(\Q(\zeta_{24})\)	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(\zeta_{24}-\zeta_{24}^{4})q^{3}+\cdots\)
570.2.q.b	\(12\)	\(4.551\)	12.0.\(\cdots\).1	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+\cdots\)
570.2.q.c	\(20\)	\(4.551\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{11}q^{2}+\beta _{11}q^{3}+(1-\beta _{12})q^{4}+\cdots\)
570.2.s.a	\(24\)	\(4.551\)		None	\(-12\)	\(4\)	\(0\)	\(-12\)
570.2.s.b	\(24\)	\(4.551\)		None	\(12\)	\(2\)	\(0\)	\(-12\)
570.2.u.a	\(6\)	\(4.551\)	\(\Q(\zeta_{18})\)	None	\(0\)	\(0\)	\(0\)	\(-6\)		\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.b	\(6\)	\(4.551\)	\(\Q(\zeta_{18})\)	None	\(0\)	\(0\)	\(0\)	\(-6\)		\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.c	\(6\)	\(4.551\)	\(\Q(\zeta_{18})\)	None	\(0\)	\(0\)	\(0\)	\(-3\)		\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)

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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.