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 19306 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
23.1.b.a	$1$	$0.011$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	$-1$	$-1$	$0$	$0$	$q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\cdots$
31.1.b.a	$1$	$0.015$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	$-1$	$0$	$-1$	$-1$	$q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots$
39.1.d.a	$1$	$0.019$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	$0$	$-1$	$0$	$0$	$q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
44.1.d.a	$1$	$0.022$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	$0$	$-1$	$-1$	$0$	$q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots$
47.1.b.a	$2$	$0.023$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-47}) $	None	$-1$	$-1$	$0$	$-1$	$q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$
52.1.j.a	$2$	$0.026$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None	$-1$	$0$	$-2$	$0$	$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
55.1.d.a	$1$	$0.027$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	$0$	$0$	$-1$	$0$	$q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots$
56.1.h.a	$1$	$0.028$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	$-1$	$0$	$0$	$-1$	$q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots$
57.1.h.a	$2$	$0.028$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$0$	$-2$	$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots$
59.1.b.a	$1$	$0.029$	$\Q$	$D_{3}$	$\Q(\sqrt{-59}) $	None	$0$	$-1$	$-1$	$-1$	$q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\cdots$
63.1.d.a	$1$	$0.031$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $	$0$	$0$	$0$	$-1$	$q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots$
68.1.d.a	$1$	$0.034$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-17}) $	$\Q(\sqrt{17}) $	$-1$	$0$	$0$	$0$	$q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots$
68.1.f.a	$2$	$0.034$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-2$	$0$	$q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots$
71.1.b.a	$3$	$0.035$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-71}) $	None	$-1$	$-1$	$-1$	$0$	$q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
72.1.p.a	$2$	$0.036$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None	$-1$	$-1$	$0$	$0$	$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$
76.1.c.a	$1$	$0.038$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	$0$	$0$	$-1$	$-1$	$q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$
77.1.j.a	$4$	$0.038$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-7}) $	None	$-2$	$0$	$0$	$-1$	$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
79.1.b.a	$2$	$0.039$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-79}) $	None	$-1$	$0$	$-1$	$0$	$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots$
80.1.h.a	$1$	$0.040$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	$0$	$0$	$-1$	$0$	$q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots$
83.1.b.a	$1$	$0.041$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	$0$	$-1$	$0$	$-1$	$q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots$
84.1.p.a	$2$	$0.042$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$0$	$-1$	$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots$
87.1.d.a	$1$	$0.043$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	$-1$	$1$	$0$	$-1$	$q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots$
87.1.d.b	$1$	$0.043$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	$1$	$-1$	$0$	$-1$	$q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots$
88.1.l.a	$4$	$0.044$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None	$-1$	$-2$	$0$	$0$	$q-\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
93.1.l.a	$4$	$0.046$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$0$	$-2$	$q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
95.1.d.a	$1$	$0.047$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $	$0$	$0$	$1$	$0$	$q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots$
95.1.d.b	$2$	$0.047$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None	$0$	$0$	$-2$	$0$	$q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$
99.1.h.a	$2$	$0.049$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None	$0$	$-1$	$1$	$0$	$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots$
100.1.j.a	$4$	$0.050$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None	$-1$	$0$	$-1$	$0$	$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots$
103.1.b.a	$2$	$0.051$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-103}) $	None	$-1$	$0$	$0$	$-1$	$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots$
104.1.h.a	$1$	$0.052$	$\Q$	$D_{3}$	$\Q(\sqrt{-26}) $	None	$-1$	$-1$	$1$	$1$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
104.1.h.b	$1$	$0.052$	$\Q$	$D_{3}$	$\Q(\sqrt{-26}) $	None	$1$	$-1$	$-1$	$-1$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
107.1.b.a	$1$	$0.053$	$\Q$	$D_{3}$	$\Q(\sqrt{-107}) $	None	$0$	$-1$	$0$	$0$	$q-q^{3}+q^{4}-q^{11}-q^{12}-q^{13}+q^{16}+\cdots$
108.1.c.a	$1$	$0.054$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$-1$	$q-q^{7}-q^{13}-q^{19}+q^{25}+2q^{31}+\cdots$
111.1.d.a	$1$	$0.055$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{37}) $	$0$	$1$	$0$	$-2$	$q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots$
111.1.d.b	$2$	$0.055$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-111}) $	None	$0$	$-2$	$0$	$0$	$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots$
111.1.h.a	$2$	$0.055$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$0$	$-1$	$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
111.1.i.a	$2$	$0.055$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$0$	$1$	$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
112.1.l.a	$2$	$0.056$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$	$q+iq^{2}-q^{4}+iq^{7}-iq^{8}-iq^{9}+\cdots$
116.1.d.a	$1$	$0.058$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	$-1$	$1$	$-1$	$0$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
116.1.d.b	$1$	$0.058$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	$1$	$-1$	$-1$	$0$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
116.1.j.a	$6$	$0.058$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-1}) $	None	$-1$	$0$	$-2$	$0$	$q-\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+(\zeta_{14}^{4}-\zeta_{14}^{5}+\cdots)q^{5}+\cdots$
117.1.j.a	$2$	$0.058$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$-2$	$q+iq^{4}+(-1-i)q^{7}-iq^{13}-q^{16}+\cdots$
119.1.d.a	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	$-1$	$-1$	$-1$	$2$	$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
119.1.d.b	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	$-1$	$1$	$1$	$-2$	$q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots$
120.1.i.a	$2$	$0.060$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $	$0$	$0$	$0$	$0$	$q-iq^{2}-iq^{3}-q^{4}+iq^{5}-q^{6}+iq^{8}+\cdots$
124.1.i.a	$4$	$0.062$	$\Q(\zeta_{12})$	$A_{4}$	None	None	$0$	$0$	$-2$	$0$	$q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
127.1.b.a	$2$	$0.063$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-127}) $	None	$-1$	$0$	$0$	$0$	$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-q^{8}+q^{9}+\cdots$
128.1.d.a	$1$	$0.064$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $	$0$	$0$	$0$	$0$	$q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots$
129.1.l.a	$6$	$0.064$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$0$	$-2$	$q-\zeta_{14}^{5}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots$

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Classical	Maass
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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
23.1.b.a	\(1\)	\(0.011\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-23}) \)	None	\(-1\)	\(-1\)	\(0\)	\(0\)	\(q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\cdots\)
31.1.b.a	\(1\)	\(0.015\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-31}) \)	None	\(-1\)	\(0\)	\(-1\)	\(-1\)	\(q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots\)
39.1.d.a	\(1\)	\(0.019\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \)	\(\Q(\sqrt{13}) \)	\(0\)	\(-1\)	\(0\)	\(0\)	\(q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\)
44.1.d.a	\(1\)	\(0.022\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(-1\)	\(-1\)	\(0\)	\(q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots\)
47.1.b.a	\(2\)	\(0.023\)	\(\Q(\sqrt{5}) \)	\(D_{5}\)	\(\Q(\sqrt{-47}) \)	None	\(-1\)	\(-1\)	\(0\)	\(-1\)	\(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
52.1.j.a	\(2\)	\(0.026\)	\(\Q(\sqrt{-3}) \)	\(D_{3}\)	\(\Q(\sqrt{-1}) \)	None	\(-1\)	\(0\)	\(-2\)	\(0\)	\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
55.1.d.a	\(1\)	\(0.027\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{5}) \)	\(0\)	\(0\)	\(-1\)	\(0\)	\(q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots\)
56.1.h.a	\(1\)	\(0.028\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{2}) \)	\(-1\)	\(0\)	\(0\)	\(-1\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots\)
57.1.h.a	\(2\)	\(0.028\)	\(\Q(\sqrt{-3}) \)	\(D_{3}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(0\)	\(-2\)	\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots\)
59.1.b.a	\(1\)	\(0.029\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-59}) \)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\cdots\)
63.1.d.a	\(1\)	\(0.031\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{21}) \)	\(0\)	\(0\)	\(0\)	\(-1\)	\(q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots\)
68.1.d.a	\(1\)	\(0.034\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \)	\(\Q(\sqrt{17}) \)	\(-1\)	\(0\)	\(0\)	\(0\)	\(q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots\)
68.1.f.a	\(2\)	\(0.034\)	\(\Q(\sqrt{-1}) \)	\(D_{4}\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots\)
71.1.b.a	\(3\)	\(0.035\)	\(\Q(\zeta_{14})^+\)	\(D_{7}\)	\(\Q(\sqrt{-71}) \)	None	\(-1\)	\(-1\)	\(-1\)	\(0\)	\(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
72.1.p.a	\(2\)	\(0.036\)	\(\Q(\sqrt{-3}) \)	\(D_{3}\)	\(\Q(\sqrt{-2}) \)	None	\(-1\)	\(-1\)	\(0\)	\(0\)	\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)
76.1.c.a	\(1\)	\(0.038\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(-1\)	\(-1\)	\(q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)
77.1.j.a	\(4\)	\(0.038\)	\(\Q(\zeta_{10})\)	\(D_{5}\)	\(\Q(\sqrt{-7}) \)	None	\(-2\)	\(0\)	\(0\)	\(-1\)	\(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)
79.1.b.a	\(2\)	\(0.039\)	\(\Q(\sqrt{5}) \)	\(D_{5}\)	\(\Q(\sqrt{-79}) \)	None	\(-1\)	\(0\)	\(-1\)	\(0\)	\(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots\)
80.1.h.a	\(1\)	\(0.040\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{5}) \)	\(0\)	\(0\)	\(-1\)	\(0\)	\(q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots\)
83.1.b.a	\(1\)	\(0.041\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-83}) \)	None	\(0\)	\(-1\)	\(0\)	\(-1\)	\(q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots\)
84.1.p.a	\(2\)	\(0.042\)	\(\Q(\sqrt{-3}) \)	\(D_{3}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(0\)	\(-1\)	\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots\)
87.1.d.a	\(1\)	\(0.043\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-87}) \)	None	\(-1\)	\(1\)	\(0\)	\(-1\)	\(q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots\)
87.1.d.b	\(1\)	\(0.043\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-87}) \)	None	\(1\)	\(-1\)	\(0\)	\(-1\)	\(q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots\)
88.1.l.a	\(4\)	\(0.044\)	\(\Q(\zeta_{10})\)	\(D_{5}\)	\(\Q(\sqrt{-2}) \)	None	\(-1\)	\(-2\)	\(0\)	\(0\)	\(q-\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots\)
93.1.l.a	\(4\)	\(0.046\)	\(\Q(\zeta_{10})\)	\(D_{5}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(0\)	\(-2\)	\(q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots\)
95.1.d.a	\(1\)	\(0.047\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \)	\(\Q(\sqrt{5}) \)	\(0\)	\(0\)	\(1\)	\(0\)	\(q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots\)
95.1.d.b	\(2\)	\(0.047\)	\(\Q(\sqrt{2}) \)	\(D_{4}\)	\(\Q(\sqrt{-95}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
99.1.h.a	\(2\)	\(0.049\)	\(\Q(\sqrt{-3}) \)	\(D_{3}\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(-1\)	\(1\)	\(0\)	\(q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots\)
100.1.j.a	\(4\)	\(0.050\)	\(\Q(\zeta_{10})\)	\(D_{5}\)	\(\Q(\sqrt{-1}) \)	None	\(-1\)	\(0\)	\(-1\)	\(0\)	\(q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots\)
103.1.b.a	\(2\)	\(0.051\)	\(\Q(\sqrt{5}) \)	\(D_{5}\)	\(\Q(\sqrt{-103}) \)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots\)
104.1.h.a	\(1\)	\(0.052\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-26}) \)	None	\(-1\)	\(-1\)	\(1\)	\(1\)	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
104.1.h.b	\(1\)	\(0.052\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-26}) \)	None	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
107.1.b.a	\(1\)	\(0.053\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-107}) \)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(q-q^{3}+q^{4}-q^{11}-q^{12}-q^{13}+q^{16}+\cdots\)
108.1.c.a	\(1\)	\(0.054\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(-1\)	\(q-q^{7}-q^{13}-q^{19}+q^{25}+2q^{31}+\cdots\)
111.1.d.a	\(1\)	\(0.055\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \)	\(\Q(\sqrt{37}) \)	\(0\)	\(1\)	\(0\)	\(-2\)	\(q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots\)
111.1.d.b	\(2\)	\(0.055\)	\(\Q(\sqrt{2}) \)	\(D_{4}\)	\(\Q(\sqrt{-111}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots\)
111.1.h.a	\(2\)	\(0.055\)	\(\Q(\sqrt{-3}) \)	\(D_{6}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(0\)	\(-1\)	\(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
111.1.i.a	\(2\)	\(0.055\)	\(\Q(\sqrt{-3}) \)	\(D_{3}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(0\)	\(1\)	\(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
112.1.l.a	\(2\)	\(0.056\)	\(\Q(\sqrt{-1}) \)	\(D_{4}\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-iq^{9}+\cdots\)
116.1.d.a	\(1\)	\(0.058\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-29}) \)	None	\(-1\)	\(1\)	\(-1\)	\(0\)	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
116.1.d.b	\(1\)	\(0.058\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-29}) \)	None	\(1\)	\(-1\)	\(-1\)	\(0\)	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
116.1.j.a	\(6\)	\(0.058\)	\(\Q(\zeta_{14})\)	\(D_{7}\)	\(\Q(\sqrt{-1}) \)	None	\(-1\)	\(0\)	\(-2\)	\(0\)	\(q-\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+(\zeta_{14}^{4}-\zeta_{14}^{5}+\cdots)q^{5}+\cdots\)
117.1.j.a	\(2\)	\(0.058\)	\(\Q(\sqrt{-1}) \)	\(D_{4}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(-2\)	\(q+iq^{4}+(-1-i)q^{7}-iq^{13}-q^{16}+\cdots\)
119.1.d.a	\(2\)	\(0.059\)	\(\Q(\sqrt{5}) \)	\(D_{5}\)	\(\Q(\sqrt{-119}) \)	None	\(-1\)	\(-1\)	\(-1\)	\(2\)	\(q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
119.1.d.b	\(2\)	\(0.059\)	\(\Q(\sqrt{5}) \)	\(D_{5}\)	\(\Q(\sqrt{-119}) \)	None	\(-1\)	\(1\)	\(1\)	\(-2\)	\(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
120.1.i.a	\(2\)	\(0.060\)	\(\Q(\sqrt{-1}) \)	\(D_{2}\)	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{10}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q-iq^{2}-iq^{3}-q^{4}+iq^{5}-q^{6}+iq^{8}+\cdots\)
124.1.i.a	\(4\)	\(0.062\)	\(\Q(\zeta_{12})\)	\(A_{4}\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
127.1.b.a	\(2\)	\(0.063\)	\(\Q(\sqrt{5}) \)	\(D_{5}\)	\(\Q(\sqrt{-127}) \)	None	\(-1\)	\(0\)	\(0\)	\(0\)	\(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-q^{8}+q^{9}+\cdots\)
128.1.d.a	\(1\)	\(0.064\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{2}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots\)
129.1.l.a	\(6\)	\(0.064\)	\(\Q(\zeta_{14})\)	\(D_{7}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(0\)	\(-2\)	\(q-\zeta_{14}^{5}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots\)

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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.