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 38787 matches)

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Label	Dim.	$A$	Field	Image	CM	RM	Traces				$q$-expansion
Label	Dim.	$A$	Field	Image	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	$q$-expansion
1001.1.r.a	$4$	$0.500$	$\Q(\zeta_{12})$	$A_{4}$	None	None	$0$	$0$	$2$	$0$	$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{8}+\cdots$
1001.1.y.a	$2$	$0.500$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-143}) $	None	$-1$	$1$	$0$	$1$	$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-q^{6}+\zeta_{6}q^{7}-q^{8}+\cdots$
1001.1.y.b	$2$	$0.500$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-143}) $	None	$1$	$1$	$0$	$-1$	$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}+q^{6}-\zeta_{6}q^{7}+q^{8}+\cdots$
1001.1.y.c	$8$	$0.500$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-143}) $	None	$-1$	$-1$	$0$	$1$	$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$
1001.1.y.d	$8$	$0.500$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-143}) $	None	$1$	$-1$	$0$	$-1$	$q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$
1001.1.bo.a	$4$	$0.500$	$\Q(\zeta_{12})$	$A_{4}$	None	None	$0$	$0$	$2$	$0$	$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$
1003.1.b.a	$1$	$0.501$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-1003}) $	$\Q(\sqrt{17}) $	$0$	$0$	$0$	$0$	$q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots$
1003.1.b.b	$2$	$0.501$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None	$0$	$0$	$0$	$0$	$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots$
1003.1.f.a	$2$	$0.501$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-59}) $	None	$0$	$-2$	$-2$	$-2$	$q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots$
1003.1.f.b	$4$	$0.501$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-59}) $	None	$0$	$2$	$2$	$2$	$q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}^{4}+\cdots)q^{5}+\cdots$
1003.1.h.a	$4$	$0.501$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-59}) $	None	$0$	$0$	$0$	$0$	$q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$
1003.1.h.b	$8$	$0.501$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-59}) $	None	$0$	$0$	$0$	$0$	$q+(-\zeta_{24}-\zeta_{24}^{2})q^{3}-\zeta_{24}^{6}q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots$
1004.1.d.a	$1$	$0.501$	$\Q$	$D_{3}$	$\Q(\sqrt{-251}) $	None	$0$	$2$	$-1$	$-1$	$q+2q^{3}-q^{5}-q^{7}+3q^{9}+2q^{13}+\cdots$
1004.1.d.b	$6$	$0.501$	$\Q(\zeta_{21})^+$	$D_{21}$	$\Q(\sqrt{-251}) $	None	$0$	$-2$	$1$	$1$	$q+(-1-\beta _{3}+\beta _{5})q^{3}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
1005.1.p.a	$4$	$0.502$	$\Q(\zeta_{12})$	$A_{4}$	None	None	$-2$	$0$	$0$	$0$	$q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{3}q^{5}+\cdots$
1005.1.p.b	$4$	$0.502$	$\Q(\zeta_{12})$	$A_{4}$	None	None	$2$	$0$	$0$	$0$	$q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{3}q^{5}+\cdots$
1007.1.d.a	$1$	$0.503$	$\Q$	$D_{3}$	$\Q(\sqrt{-1007}) $	None	$-1$	$-1$	$0$	$2$	$q-q^{2}-q^{3}+q^{6}+2q^{7}+q^{8}-q^{11}+\cdots$
1007.1.d.b	$1$	$0.503$	$\Q$	$D_{3}$	$\Q(\sqrt{-1007}) $	None	$1$	$1$	$0$	$2$	$q+q^{2}+q^{3}+q^{6}+2q^{7}-q^{8}-q^{11}+\cdots$
1007.1.d.c	$2$	$0.503$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-1007}) $	None	$-1$	$-1$	$0$	$-1$	$q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$
1007.1.d.d	$2$	$0.503$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-1007}) $	None	$1$	$1$	$0$	$-1$	$q+(1-\beta )q^{2}+\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$
1007.1.d.e	$4$	$0.503$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-1007}) $	None	$-1$	$-1$	$0$	$-2$	$q-\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1007.1.d.f	$4$	$0.503$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-1007}) $	None	$1$	$1$	$0$	$-2$	$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
1008.1.f.a	$1$	$0.503$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $	$0$	$0$	$0$	$1$	$q+q^{7}+q^{25}-2q^{37}+2q^{43}+q^{49}+\cdots$
1008.1.u.a	$2$	$0.503$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None	$-2$	$0$	$0$	$0$	$q-q^{2}+q^{4}+iq^{7}-q^{8}+(1-i)q^{11}+\cdots$
1008.1.u.b	$2$	$0.503$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$	$q+iq^{2}-q^{4}-iq^{7}-iq^{8}+(1-i+\cdots)q^{11}+\cdots$
1008.1.u.c	$2$	$0.503$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None	$2$	$0$	$0$	$0$	$q+q^{2}+q^{4}+iq^{7}+q^{8}+(-1+i+\cdots)q^{11}+\cdots$
1008.1.y.a	$4$	$0.503$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$-4$	$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
1008.1.y.b	$4$	$0.503$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$4$	$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+q^{7}-\zeta_{8}q^{8}+\cdots$
1008.1.bw.a	$4$	$0.503$	$\Q(\zeta_{12})$	$A_{4}$	None	None	$0$	$0$	$2$	$0$	$q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots$
1008.1.cd.a	$2$	$0.503$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$-1$	$q+\zeta_{6}^{2}q^{7}+q^{13}+(1+\zeta_{6})q^{19}+\zeta_{6}q^{25}+\cdots$
1008.1.cd.b	$2$	$0.503$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$1$	$q-\zeta_{6}^{2}q^{7}+q^{13}+(-1-\zeta_{6})q^{19}+\cdots$
1008.1.cg.a	$2$	$0.503$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$-1$	$q-\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
1008.1.dc.a	$4$	$0.503$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None	$0$	$0$	$0$	$-2$	$q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots$
1008.1.dd.a	$4$	$0.503$	$\Q(\zeta_{12})$	$A_{4}$	None	None	$0$	$0$	$-4$	$0$	$q+\zeta_{12}^{5}q^{3}-q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\cdots$
1008.1.dt.a	$8$	$0.503$	$\Q(\zeta_{24})$	$S_{4}$	None	None	$0$	$0$	$0$	$-4$	$q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}+\zeta_{24}^{11}q^{5}+\cdots$
1008.1.ed.a	$8$	$0.503$	$\Q(\zeta_{24})$	$S_{4}$	None	None	$0$	$0$	$0$	$0$	$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}q^{5}+\zeta_{24}^{2}q^{7}+\cdots$
1011.1.c.a	$1$	$0.505$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1011}) $	$\Q(\sqrt{337}) $	$0$	$-1$	$0$	$2$	$q-q^{3}+q^{4}+2q^{7}+q^{9}-q^{12}-2q^{13}+\cdots$
1011.1.c.b	$1$	$0.505$	$\Q$	$D_{3}$	$\Q(\sqrt{-1011}) $	None	$0$	$1$	$-1$	$-1$	$q+q^{3}+q^{4}-q^{5}-q^{7}+q^{9}+2q^{11}+\cdots$
1011.1.c.c	$1$	$0.505$	$\Q$	$D_{3}$	$\Q(\sqrt{-1011}) $	None	$0$	$1$	$1$	$-1$	$q+q^{3}+q^{4}+q^{5}-q^{7}+q^{9}-2q^{11}+\cdots$
1011.1.c.d	$2$	$0.505$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-1011}) $	None	$0$	$-2$	$0$	$-2$	$q-q^{3}+q^{4}-\beta q^{5}-q^{7}+q^{9}-q^{12}+\cdots$
1011.1.f.a	$2$	$0.505$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$	$q-iq^{3}+q^{4}-q^{9}-iq^{12}+q^{16}+\cdots$
1011.1.f.b	$4$	$0.505$	$\Q(\zeta_{8})$	$S_{4}$	None	None	$0$	$0$	$0$	$0$	$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots$
1011.1.l.a	$4$	$0.505$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$-4$	$q-\zeta_{8}^{3}q^{3}+q^{4}+(-1-\zeta_{8}^{2})q^{7}-\zeta_{8}^{2}q^{9}+\cdots$
1011.1.q.a	$6$	$0.505$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None	$0$	$1$	$0$	$-2$	$q-\zeta_{14}^{6}q^{3}+\zeta_{14}^{6}q^{4}+(-\zeta_{14}-\zeta_{14}^{5}+\cdots)q^{7}+\cdots$
1011.1.r.a	$6$	$0.505$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$0$	$-2$	$q-\zeta_{14}^{3}q^{3}-\zeta_{14}^{3}q^{4}+(\zeta_{14}^{4}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots$
1011.1.y.a	$12$	$0.505$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$	$q-\zeta_{28}^{3}q^{3}-\zeta_{28}^{10}q^{4}+(-\zeta_{28}^{4}+\cdots)q^{7}+\cdots$
1011.1.bf.a	$24$	$0.505$	$\Q(\zeta_{56})$	$D_{56}$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$4$	$q-\zeta_{56}^{15}q^{3}+\zeta_{56}^{8}q^{4}+(\zeta_{56}^{6}-\zeta_{56}^{16}+\cdots)q^{7}+\cdots$
1012.1.r.a	$20$	$0.505$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-11}) $	None	$0$	$2$	$2$	$0$	$q+(\zeta_{66}^{2}-\zeta_{66}^{19})q^{3}+(-\zeta_{66}^{25}+\zeta_{66}^{32}+\cdots)q^{5}+\cdots$
1015.1.f.a	$1$	$0.507$	$\Q$	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-1015}) $	$\Q(\sqrt{29}) $	$0$	$0$	$-1$	$-1$	$q-q^{4}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{16}+\cdots$
1015.1.f.b	$1$	$0.507$	$\Q$	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-1015}) $	$\Q(\sqrt{29}) $	$0$	$0$	$1$	$1$	$q-q^{4}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{16}+\cdots$

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$\zeta$ zeros

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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	Image	CM	RM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	Image	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
1001.1.r.a	\(4\)	\(0.500\)	\(\Q(\zeta_{12})\)	\(A_{4}\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	\(q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
1001.1.y.a	\(2\)	\(0.500\)	\(\Q(\sqrt{-3}) \)	\(D_{3}\)	\(\Q(\sqrt{-143}) \)	None	\(-1\)	\(1\)	\(0\)	\(1\)	\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-q^{6}+\zeta_{6}q^{7}-q^{8}+\cdots\)
1001.1.y.b	\(2\)	\(0.500\)	\(\Q(\sqrt{-3}) \)	\(D_{3}\)	\(\Q(\sqrt{-143}) \)	None	\(1\)	\(1\)	\(0\)	\(-1\)	\(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}+q^{6}-\zeta_{6}q^{7}+q^{8}+\cdots\)
1001.1.y.c	\(8\)	\(0.500\)	\(\Q(\zeta_{15})\)	\(D_{15}\)	\(\Q(\sqrt{-143}) \)	None	\(-1\)	\(-1\)	\(0\)	\(1\)	\(q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots\)
1001.1.y.d	\(8\)	\(0.500\)	\(\Q(\zeta_{15})\)	\(D_{15}\)	\(\Q(\sqrt{-143}) \)	None	\(1\)	\(-1\)	\(0\)	\(-1\)	\(q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots\)
1001.1.bo.a	\(4\)	\(0.500\)	\(\Q(\zeta_{12})\)	\(A_{4}\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1003.1.b.a	\(1\)	\(0.501\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1003}) \)	\(\Q(\sqrt{17}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots\)
1003.1.b.b	\(2\)	\(0.501\)	\(\Q(\sqrt{-3}) \)	\(D_{6}\)	\(\Q(\sqrt{-59}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots\)
1003.1.f.a	\(2\)	\(0.501\)	\(\Q(\sqrt{-1}) \)	\(D_{4}\)	\(\Q(\sqrt{-59}) \)	None	\(0\)	\(-2\)	\(-2\)	\(-2\)	\(q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots\)
1003.1.f.b	\(4\)	\(0.501\)	\(\Q(\zeta_{12})\)	\(D_{12}\)	\(\Q(\sqrt{-59}) \)	None	\(0\)	\(2\)	\(2\)	\(2\)	\(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
1003.1.h.a	\(4\)	\(0.501\)	\(\Q(\zeta_{8})\)	\(D_{8}\)	\(\Q(\sqrt{-59}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
1003.1.h.b	\(8\)	\(0.501\)	\(\Q(\zeta_{24})\)	\(D_{24}\)	\(\Q(\sqrt{-59}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+(-\zeta_{24}-\zeta_{24}^{2})q^{3}-\zeta_{24}^{6}q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
1004.1.d.a	\(1\)	\(0.501\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-251}) \)	None	\(0\)	\(2\)	\(-1\)	\(-1\)	\(q+2q^{3}-q^{5}-q^{7}+3q^{9}+2q^{13}+\cdots\)
1004.1.d.b	\(6\)	\(0.501\)	\(\Q(\zeta_{21})^+\)	\(D_{21}\)	\(\Q(\sqrt{-251}) \)	None	\(0\)	\(-2\)	\(1\)	\(1\)	\(q+(-1-\beta _{3}+\beta _{5})q^{3}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1005.1.p.a	\(4\)	\(0.502\)	\(\Q(\zeta_{12})\)	\(A_{4}\)	None	None	\(-2\)	\(0\)	\(0\)	\(0\)	\(q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{3}q^{5}+\cdots\)
1005.1.p.b	\(4\)	\(0.502\)	\(\Q(\zeta_{12})\)	\(A_{4}\)	None	None	\(2\)	\(0\)	\(0\)	\(0\)	\(q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{3}q^{5}+\cdots\)
1007.1.d.a	\(1\)	\(0.503\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-1007}) \)	None	\(-1\)	\(-1\)	\(0\)	\(2\)	\(q-q^{2}-q^{3}+q^{6}+2q^{7}+q^{8}-q^{11}+\cdots\)
1007.1.d.b	\(1\)	\(0.503\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-1007}) \)	None	\(1\)	\(1\)	\(0\)	\(2\)	\(q+q^{2}+q^{3}+q^{6}+2q^{7}-q^{8}-q^{11}+\cdots\)
1007.1.d.c	\(2\)	\(0.503\)	\(\Q(\sqrt{5}) \)	\(D_{5}\)	\(\Q(\sqrt{-1007}) \)	None	\(-1\)	\(-1\)	\(0\)	\(-1\)	\(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
1007.1.d.d	\(2\)	\(0.503\)	\(\Q(\sqrt{5}) \)	\(D_{5}\)	\(\Q(\sqrt{-1007}) \)	None	\(1\)	\(1\)	\(0\)	\(-1\)	\(q+(1-\beta )q^{2}+\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
1007.1.d.e	\(4\)	\(0.503\)	\(\Q(\zeta_{15})^+\)	\(D_{15}\)	\(\Q(\sqrt{-1007}) \)	None	\(-1\)	\(-1\)	\(0\)	\(-2\)	\(q-\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1007.1.d.f	\(4\)	\(0.503\)	\(\Q(\zeta_{15})^+\)	\(D_{15}\)	\(\Q(\sqrt{-1007}) \)	None	\(1\)	\(1\)	\(0\)	\(-2\)	\(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
1008.1.f.a	\(1\)	\(0.503\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{21}) \)	\(0\)	\(0\)	\(0\)	\(1\)	\(q+q^{7}+q^{25}-2q^{37}+2q^{43}+q^{49}+\cdots\)
1008.1.u.a	\(2\)	\(0.503\)	\(\Q(\sqrt{-1}) \)	\(D_{4}\)	\(\Q(\sqrt{-7}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)	\(q-q^{2}+q^{4}+iq^{7}-q^{8}+(1-i)q^{11}+\cdots\)
1008.1.u.b	\(2\)	\(0.503\)	\(\Q(\sqrt{-1}) \)	\(D_{4}\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+(1-i+\cdots)q^{11}+\cdots\)
1008.1.u.c	\(2\)	\(0.503\)	\(\Q(\sqrt{-1}) \)	\(D_{4}\)	\(\Q(\sqrt{-7}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)	\(q+q^{2}+q^{4}+iq^{7}+q^{8}+(-1+i+\cdots)q^{11}+\cdots\)
1008.1.y.a	\(4\)	\(0.503\)	\(\Q(\zeta_{8})\)	\(D_{4}\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(-4\)	\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
1008.1.y.b	\(4\)	\(0.503\)	\(\Q(\zeta_{8})\)	\(D_{4}\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(4\)	\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+q^{7}-\zeta_{8}q^{8}+\cdots\)
1008.1.bw.a	\(4\)	\(0.503\)	\(\Q(\zeta_{12})\)	\(A_{4}\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	\(q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1008.1.cd.a	\(2\)	\(0.503\)	\(\Q(\sqrt{-3}) \)	\(D_{6}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(-1\)	\(q+\zeta_{6}^{2}q^{7}+q^{13}+(1+\zeta_{6})q^{19}+\zeta_{6}q^{25}+\cdots\)
1008.1.cd.b	\(2\)	\(0.503\)	\(\Q(\sqrt{-3}) \)	\(D_{6}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(1\)	\(q-\zeta_{6}^{2}q^{7}+q^{13}+(-1-\zeta_{6})q^{19}+\cdots\)
1008.1.cg.a	\(2\)	\(0.503\)	\(\Q(\sqrt{-3}) \)	\(D_{6}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(-1\)	\(q-\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1008.1.dc.a	\(4\)	\(0.503\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(S_{4}\)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)	\(q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots\)
1008.1.dd.a	\(4\)	\(0.503\)	\(\Q(\zeta_{12})\)	\(A_{4}\)	None	None	\(0\)	\(0\)	\(-4\)	\(0\)	\(q+\zeta_{12}^{5}q^{3}-q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\cdots\)
1008.1.dt.a	\(8\)	\(0.503\)	\(\Q(\zeta_{24})\)	\(S_{4}\)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)	\(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}+\zeta_{24}^{11}q^{5}+\cdots\)
1008.1.ed.a	\(8\)	\(0.503\)	\(\Q(\zeta_{24})\)	\(S_{4}\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}q^{5}+\zeta_{24}^{2}q^{7}+\cdots\)
1011.1.c.a	\(1\)	\(0.505\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1011}) \)	\(\Q(\sqrt{337}) \)	\(0\)	\(-1\)	\(0\)	\(2\)	\(q-q^{3}+q^{4}+2q^{7}+q^{9}-q^{12}-2q^{13}+\cdots\)
1011.1.c.b	\(1\)	\(0.505\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-1011}) \)	None	\(0\)	\(1\)	\(-1\)	\(-1\)	\(q+q^{3}+q^{4}-q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
1011.1.c.c	\(1\)	\(0.505\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-1011}) \)	None	\(0\)	\(1\)	\(1\)	\(-1\)	\(q+q^{3}+q^{4}+q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
1011.1.c.d	\(2\)	\(0.505\)	\(\Q(\sqrt{3}) \)	\(D_{6}\)	\(\Q(\sqrt{-1011}) \)	None	\(0\)	\(-2\)	\(0\)	\(-2\)	\(q-q^{3}+q^{4}-\beta q^{5}-q^{7}+q^{9}-q^{12}+\cdots\)
1011.1.f.a	\(2\)	\(0.505\)	\(\Q(\sqrt{-1}) \)	\(D_{4}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-iq^{3}+q^{4}-q^{9}-iq^{12}+q^{16}+\cdots\)
1011.1.f.b	\(4\)	\(0.505\)	\(\Q(\zeta_{8})\)	\(S_{4}\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots\)
1011.1.l.a	\(4\)	\(0.505\)	\(\Q(\zeta_{8})\)	\(D_{8}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(-4\)	\(q-\zeta_{8}^{3}q^{3}+q^{4}+(-1-\zeta_{8}^{2})q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
1011.1.q.a	\(6\)	\(0.505\)	\(\Q(\zeta_{14})\)	\(D_{14}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(1\)	\(0\)	\(-2\)	\(q-\zeta_{14}^{6}q^{3}+\zeta_{14}^{6}q^{4}+(-\zeta_{14}-\zeta_{14}^{5}+\cdots)q^{7}+\cdots\)
1011.1.r.a	\(6\)	\(0.505\)	\(\Q(\zeta_{14})\)	\(D_{7}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(0\)	\(-2\)	\(q-\zeta_{14}^{3}q^{3}-\zeta_{14}^{3}q^{4}+(\zeta_{14}^{4}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots\)
1011.1.y.a	\(12\)	\(0.505\)	\(\Q(\zeta_{28})\)	\(D_{28}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\zeta_{28}^{3}q^{3}-\zeta_{28}^{10}q^{4}+(-\zeta_{28}^{4}+\cdots)q^{7}+\cdots\)
1011.1.bf.a	\(24\)	\(0.505\)	\(\Q(\zeta_{56})\)	\(D_{56}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(4\)	\(q-\zeta_{56}^{15}q^{3}+\zeta_{56}^{8}q^{4}+(\zeta_{56}^{6}-\zeta_{56}^{16}+\cdots)q^{7}+\cdots\)
1012.1.r.a	\(20\)	\(0.505\)	\(\Q(\zeta_{33})\)	\(D_{33}\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(2\)	\(2\)	\(0\)	\(q+(\zeta_{66}^{2}-\zeta_{66}^{19})q^{3}+(-\zeta_{66}^{25}+\zeta_{66}^{32}+\cdots)q^{5}+\cdots\)
1015.1.f.a	\(1\)	\(0.507\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-1015}) \)	\(\Q(\sqrt{29}) \)	\(0\)	\(0\)	\(-1\)	\(-1\)	\(q-q^{4}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{16}+\cdots\)
1015.1.f.b	\(1\)	\(0.507\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-1015}) \)	\(\Q(\sqrt{29}) \)	\(0\)	\(0\)	\(1\)	\(1\)	\(q-q^{4}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{16}+\cdots\)

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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.