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

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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
11.2.a.a	$1$	$0.088$	$\Q$	None	$-2$	$-1$	$1$	$-2$	$-$	$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots$
13.2.e.a	$2$	$0.104$	$\Q(\sqrt{-3}) $	None	$-3$	$-2$	$0$	$0$		$q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
14.2.a.a	$1$	$0.112$	$\Q$	None	$-1$	$-2$	$0$	$1$	$-$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots$
15.2.a.a	$1$	$0.120$	$\Q$	None	$-1$	$-1$	$1$	$0$	$-$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots$
16.2.e.a	$2$	$0.128$	$\Q(\sqrt{-1}) $	None	$-2$	$-2$	$-2$	$0$		$q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots$
17.2.a.a	$1$	$0.136$	$\Q$	None	$-1$	$0$	$-2$	$4$	$-$	$q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots$
17.2.d.a	$4$	$0.136$	$\Q(\zeta_{8})$	None	$-4$	$-4$	$0$	$-4$		$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots$
18.2.c.a	$2$	$0.144$	$\Q(\sqrt{-3}) $	None	$-1$	$-3$	$0$	$-2$		$q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
19.2.a.a	$1$	$0.152$	$\Q$	None	$0$	$-2$	$3$	$-1$	$-$	$q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots$
19.2.e.a	$6$	$0.152$	$\Q(\zeta_{18})$	None	$-6$	$-3$	$-6$	$0$		$q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots$
20.2.a.a	$1$	$0.160$	$\Q$	None	$0$	$-2$	$-1$	$2$	$-$	$q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots$
20.2.e.a	$2$	$0.160$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	$-2$	$0$	$-4$	$0$		$q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots$
21.2.a.a	$1$	$0.168$	$\Q$	None	$-1$	$1$	$-2$	$-1$	$-$	$q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
21.2.e.a	$2$	$0.168$	$\Q(\sqrt{-3}) $	None	$-2$	$-1$	$2$	$-5$		$q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots$
21.2.g.a	$2$	$0.168$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	$0$	$-3$	$0$	$1$		$q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots$
22.2.c.a	$4$	$0.176$	$\Q(\zeta_{10})$	None	$-1$	$-4$	$-6$	$2$		$q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots$
23.2.a.a	$2$	$0.184$	$\Q(\sqrt{5}) $	None	$-1$	$0$	$-2$	$2$	$-$	$q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
23.2.c.a	$10$	$0.184$	$\Q(\zeta_{22})$	None	$-7$	$-7$	$-3$	$-5$		$q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots$
24.2.a.a	$1$	$0.192$	$\Q$	None	$0$	$-1$	$-2$	$0$	$-$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
24.2.d.a	$2$	$0.192$	$\Q(\sqrt{-1}) $	None	$-2$	$0$	$0$	$-4$		$q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots$
24.2.f.a	$2$	$0.192$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $	$0$	$-2$	$0$	$0$		$q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots$
25.2.d.a	$4$	$0.200$	$\Q(\zeta_{10})$	None	$-2$	$-1$	$-5$	$-2$		$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
25.2.e.a	$8$	$0.200$	8.0.58140625.2	None	$-5$	$-5$	$0$	$0$		$q+(-1+\beta _{1})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+\cdots$
26.2.a.a	$1$	$0.208$	$\Q$	None	$-1$	$1$	$-3$	$-1$	$-$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots$
26.2.a.b	$1$	$0.208$	$\Q$	None	$1$	$-3$	$-1$	$1$	$-$	$q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots$
26.2.b.a	$2$	$0.208$	$\Q(\sqrt{-1}) $	None	$0$	$-2$	$0$	$0$		$q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots$
26.2.c.a	$2$	$0.208$	$\Q(\sqrt{-3}) $	None	$-1$	$0$	$-2$	$-4$		$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-4\zeta_{6}q^{7}+\cdots$
27.2.a.a	$1$	$0.216$	$\Q$	$\Q(\sqrt{-3}) $	$0$	$0$	$0$	$-1$	$-$	$q-2q^{4}-q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots$
27.2.e.a	$12$	$0.216$	12.0.$\cdots$.1	None	$-6$	$-6$	$-3$	$-6$		$q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots$
28.2.d.a	$2$	$0.224$	$\Q(\sqrt{-7}) $	$\Q(\sqrt{-7}) $	$-1$	$0$	$0$	$0$		$q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots$
28.2.e.a	$2$	$0.224$	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$-3$	$-4$		$q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
28.2.f.a	$4$	$0.224$	$\Q(\zeta_{12})$	None	$-2$	$0$	$-6$	$0$		$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots$
29.2.a.a	$2$	$0.232$	$\Q(\sqrt{2}) $	None	$-2$	$2$	$-2$	$0$	$-$	$q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
29.2.b.a	$2$	$0.232$	$\Q(\sqrt{-5}) $	None	$0$	$0$	$-6$	$4$		$q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots$
29.2.d.a	$6$	$0.232$	$\Q(\zeta_{14})$	None	$-2$	$-5$	$1$	$1$		$q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$
29.2.e.a	$12$	$0.232$	12.0.$\cdots$.1	None	$-7$	$-7$	$-1$	$-11$		$q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots$
30.2.a.a	$1$	$0.240$	$\Q$	None	$-1$	$1$	$-1$	$-4$	$-$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots$
30.2.c.a	$2$	$0.240$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-4$	$0$		$q+iq^{2}-iq^{3}-q^{4}+(-2+i)q^{5}+\cdots$
30.2.e.a	$4$	$0.240$	$\Q(\zeta_{8})$	None	$0$	$-4$	$0$	$-4$		$q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
31.2.a.a	$2$	$0.248$	$\Q(\sqrt{5}) $	None	$1$	$-2$	$2$	$-4$	$-$	$q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots$
31.2.c.a	$4$	$0.248$	$\Q(\sqrt{2}, \sqrt{-3})$	None	$-4$	$2$	$-2$	$-2$		$q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots$
31.2.d.a	$4$	$0.248$	$\Q(\zeta_{10})$	None	$-3$	$1$	$-6$	$-3$		$q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
31.2.g.a	$16$	$0.248$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$-6$	$-12$	$-3$	$2$		$q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
32.2.a.a	$1$	$0.256$	$\Q$	$\Q(\sqrt{-1}) $	$0$	$0$	$-2$	$0$	$-$	$q-2q^{5}-3q^{9}+6q^{13}+2q^{17}-q^{25}+\cdots$
32.2.g.a	$4$	$0.256$	$\Q(\zeta_{8})$	None	$0$	$0$	$-4$	$4$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots$
32.2.g.b	$8$	$0.256$	8.0.18939904.2	None	$-4$	$-4$	$0$	$-8$		$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots$
33.2.a.a	$1$	$0.264$	$\Q$	None	$1$	$-1$	$-2$	$4$	$-$	$q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots$
33.2.d.a	$2$	$0.264$	$\Q(\sqrt{-11}) $	$\Q(\sqrt{-11}) $	$0$	$1$	$0$	$0$		$q+\beta q^{3}-2q^{4}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots$
33.2.e.a	$4$	$0.264$	$\Q(\zeta_{10})$	None	$-3$	$-1$	$-1$	$-3$		$q+(-1-\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(\zeta_{10}+\cdots)q^{4}+\cdots$
33.2.e.b	$4$	$0.264$	$\Q(\zeta_{10})$	None	$-1$	$1$	$-3$	$1$		$q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+\cdots$

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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
11.2.a.a	\(1\)	\(0.088\)	\(\Q\)	None	\(-2\)	\(-1\)	\(1\)	\(-2\)	\(-\)	\(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
13.2.e.a	\(2\)	\(0.104\)	\(\Q(\sqrt{-3}) \)	None	\(-3\)	\(-2\)	\(0\)	\(0\)		\(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
14.2.a.a	\(1\)	\(0.112\)	\(\Q\)	None	\(-1\)	\(-2\)	\(0\)	\(1\)	\(-\)	\(q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots\)
15.2.a.a	\(1\)	\(0.120\)	\(\Q\)	None	\(-1\)	\(-1\)	\(1\)	\(0\)	\(-\)	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)
16.2.e.a	\(2\)	\(0.128\)	\(\Q(\sqrt{-1}) \)	None	\(-2\)	\(-2\)	\(-2\)	\(0\)		\(q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots\)
17.2.a.a	\(1\)	\(0.136\)	\(\Q\)	None	\(-1\)	\(0\)	\(-2\)	\(4\)	\(-\)	\(q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)
17.2.d.a	\(4\)	\(0.136\)	\(\Q(\zeta_{8})\)	None	\(-4\)	\(-4\)	\(0\)	\(-4\)		\(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
18.2.c.a	\(2\)	\(0.144\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(-3\)	\(0\)	\(-2\)		\(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
19.2.a.a	\(1\)	\(0.152\)	\(\Q\)	None	\(0\)	\(-2\)	\(3\)	\(-1\)	\(-\)	\(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots\)
19.2.e.a	\(6\)	\(0.152\)	\(\Q(\zeta_{18})\)	None	\(-6\)	\(-3\)	\(-6\)	\(0\)		\(q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
20.2.a.a	\(1\)	\(0.160\)	\(\Q\)	None	\(0\)	\(-2\)	\(-1\)	\(2\)	\(-\)	\(q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
20.2.e.a	\(2\)	\(0.160\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	\(-2\)	\(0\)	\(-4\)	\(0\)		\(q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots\)
21.2.a.a	\(1\)	\(0.168\)	\(\Q\)	None	\(-1\)	\(1\)	\(-2\)	\(-1\)	\(-\)	\(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
21.2.e.a	\(2\)	\(0.168\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(-1\)	\(2\)	\(-5\)		\(q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots\)
21.2.g.a	\(2\)	\(0.168\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	\(0\)	\(-3\)	\(0\)	\(1\)		\(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots\)
22.2.c.a	\(4\)	\(0.176\)	\(\Q(\zeta_{10})\)	None	\(-1\)	\(-4\)	\(-6\)	\(2\)		\(q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
23.2.a.a	\(2\)	\(0.184\)	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(0\)	\(-2\)	\(2\)	\(-\)	\(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
23.2.c.a	\(10\)	\(0.184\)	\(\Q(\zeta_{22})\)	None	\(-7\)	\(-7\)	\(-3\)	\(-5\)		\(q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
24.2.a.a	\(1\)	\(0.192\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(-\)	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
24.2.d.a	\(2\)	\(0.192\)	\(\Q(\sqrt{-1}) \)	None	\(-2\)	\(0\)	\(0\)	\(-4\)		\(q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots\)
24.2.f.a	\(2\)	\(0.192\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)	\(0\)	\(-2\)	\(0\)	\(0\)		\(q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots\)
25.2.d.a	\(4\)	\(0.200\)	\(\Q(\zeta_{10})\)	None	\(-2\)	\(-1\)	\(-5\)	\(-2\)		\(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
25.2.e.a	\(8\)	\(0.200\)	8.0.58140625.2	None	\(-5\)	\(-5\)	\(0\)	\(0\)		\(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+\cdots\)
26.2.a.a	\(1\)	\(0.208\)	\(\Q\)	None	\(-1\)	\(1\)	\(-3\)	\(-1\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
26.2.a.b	\(1\)	\(0.208\)	\(\Q\)	None	\(1\)	\(-3\)	\(-1\)	\(1\)	\(-\)	\(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
26.2.b.a	\(2\)	\(0.208\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)		\(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)
26.2.c.a	\(2\)	\(0.208\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(0\)	\(-2\)	\(-4\)		\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-4\zeta_{6}q^{7}+\cdots\)
27.2.a.a	\(1\)	\(0.216\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	\(0\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(q-2q^{4}-q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\)
27.2.e.a	\(12\)	\(0.216\)	12.0.\(\cdots\).1	None	\(-6\)	\(-6\)	\(-3\)	\(-6\)		\(q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots\)
28.2.d.a	\(2\)	\(0.224\)	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)	\(-1\)	\(0\)	\(0\)	\(0\)		\(q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)
28.2.e.a	\(2\)	\(0.224\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(-3\)	\(-4\)		\(q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
28.2.f.a	\(4\)	\(0.224\)	\(\Q(\zeta_{12})\)	None	\(-2\)	\(0\)	\(-6\)	\(0\)		\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots\)
29.2.a.a	\(2\)	\(0.232\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(2\)	\(-2\)	\(0\)	\(-\)	\(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
29.2.b.a	\(2\)	\(0.232\)	\(\Q(\sqrt{-5}) \)	None	\(0\)	\(0\)	\(-6\)	\(4\)		\(q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots\)
29.2.d.a	\(6\)	\(0.232\)	\(\Q(\zeta_{14})\)	None	\(-2\)	\(-5\)	\(1\)	\(1\)		\(q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
29.2.e.a	\(12\)	\(0.232\)	12.0.\(\cdots\).1	None	\(-7\)	\(-7\)	\(-1\)	\(-11\)		\(q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots\)
30.2.a.a	\(1\)	\(0.240\)	\(\Q\)	None	\(-1\)	\(1\)	\(-1\)	\(-4\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
30.2.c.a	\(2\)	\(0.240\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+iq^{2}-iq^{3}-q^{4}+(-2+i)q^{5}+\cdots\)
30.2.e.a	\(4\)	\(0.240\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(-4\)	\(0\)	\(-4\)		\(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
31.2.a.a	\(2\)	\(0.248\)	\(\Q(\sqrt{5}) \)	None	\(1\)	\(-2\)	\(2\)	\(-4\)	\(-\)	\(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)
31.2.c.a	\(4\)	\(0.248\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	\(-4\)	\(2\)	\(-2\)	\(-2\)		\(q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
31.2.d.a	\(4\)	\(0.248\)	\(\Q(\zeta_{10})\)	None	\(-3\)	\(1\)	\(-6\)	\(-3\)		\(q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
31.2.g.a	\(16\)	\(0.248\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(-6\)	\(-12\)	\(-3\)	\(2\)		\(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
32.2.a.a	\(1\)	\(0.256\)	\(\Q\)	\(\Q(\sqrt{-1}) \)	\(0\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(q-2q^{5}-3q^{9}+6q^{13}+2q^{17}-q^{25}+\cdots\)
32.2.g.a	\(4\)	\(0.256\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(-4\)	\(4\)		\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots\)
32.2.g.b	\(8\)	\(0.256\)	8.0.18939904.2	None	\(-4\)	\(-4\)	\(0\)	\(-8\)		\(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots\)
33.2.a.a	\(1\)	\(0.264\)	\(\Q\)	None	\(1\)	\(-1\)	\(-2\)	\(4\)	\(-\)	\(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots\)
33.2.d.a	\(2\)	\(0.264\)	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)	\(0\)	\(1\)	\(0\)	\(0\)		\(q+\beta q^{3}-2q^{4}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
33.2.e.a	\(4\)	\(0.264\)	\(\Q(\zeta_{10})\)	None	\(-3\)	\(-1\)	\(-1\)	\(-3\)		\(q+(-1-\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(\zeta_{10}+\cdots)q^{4}+\cdots\)
33.2.e.b	\(4\)	\(0.264\)	\(\Q(\zeta_{10})\)	None	\(-1\)	\(1\)	\(-3\)	\(1\)		\(q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)

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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.