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 239 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
300.1.b.a	$2$	$0.150$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q-iq^{3}-iq^{7}-q^{9}+iq^{13}+q^{19}+\cdots$
300.1.g.a	$1$	$0.150$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$0$	$1$		$q-q^{3}+q^{7}+q^{9}+q^{13}-q^{19}-q^{21}+\cdots$
300.1.g.b	$1$	$0.150$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$1$	$0$	$-1$		$q+q^{3}-q^{7}+q^{9}-q^{13}-q^{19}-q^{21}+\cdots$
300.1.l.a	$4$	$0.150$	$\Q(\zeta_{8})$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{3}) $	$0$	$0$	$0$	$0$		$q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots$
300.2.a.a	$1$	$2.396$	$\Q$	None	None	$0$	$-1$	$0$	$-4$	$+$	$q-q^{3}-4q^{7}+q^{9}-4q^{11}-4q^{17}+\cdots$
300.2.a.b	$1$	$2.396$	$\Q$	None	None	$0$	$-1$	$0$	$1$	$-$	$q-q^{3}+q^{7}+q^{9}+6q^{11}-5q^{13}+\cdots$
300.2.a.c	$1$	$2.396$	$\Q$	None	None	$0$	$1$	$0$	$-1$	$-$	$q+q^{3}-q^{7}+q^{9}+6q^{11}+5q^{13}+\cdots$
300.2.a.d	$1$	$2.396$	$\Q$	None	None	$0$	$1$	$0$	$4$	$-$	$q+q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{17}+\cdots$
300.2.d.a	$2$	$2.396$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$0$		$q+iq^{3}+iq^{7}-q^{9}+6q^{11}+5iq^{13}+\cdots$
300.2.e.a	$4$	$2.396$	$\Q(\sqrt{3}, \sqrt{-5})$	$\Q(\sqrt{-15}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots$
300.2.e.b	$4$	$2.396$	$\Q(\sqrt{2}, \sqrt{-5})$	$\Q(\sqrt{-5}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots$
300.2.e.c	$8$	$2.396$	8.0.342102016.5	None	None	$0$	$0$	$0$	$0$		$q+\beta _{5}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
300.2.e.d	$8$	$2.396$	8.0.4521217600.1	None	None	$0$	$0$	$0$	$0$		$q+\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots$
300.2.e.e	$8$	$2.396$	8.0.4521217600.1	None	None	$0$	$0$	$0$	$0$		$q+\beta _{6}q^{2}+\beta _{3}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots$
300.2.h.a	$8$	$2.396$	8.0.342102016.5	None	None	$-2$	$0$	$0$	$0$		$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
300.2.h.b	$8$	$2.396$	8.0.342102016.5	None	None	$2$	$0$	$0$	$0$		$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
300.2.h.c	$16$	$2.396$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}-\beta _{10}q^{3}-\beta _{4}q^{4}-\beta _{12}q^{6}+\cdots$
300.2.i.a	$4$	$2.396$	$\Q(i, \sqrt{5})$	None	None	$0$	$-2$	$0$	$4$		$q+(-1+\beta _{3})q^{3}+(1-\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
300.2.i.b	$4$	$2.396$	$\Q(i, \sqrt{6})$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{3}+2\beta _{3}q^{7}+3\beta _{2}q^{9}+4\beta _{1}q^{13}+\cdots$
300.2.i.c	$4$	$2.396$	$\Q(i, \sqrt{6})$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{3}-3\beta _{3}q^{7}+3\beta _{2}q^{9}-\beta _{1}q^{13}+\cdots$
300.2.j.a	$8$	$2.396$	$\Q(\zeta_{24})$	None	None	$0$	$0$	$0$	$0$		$q+(\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{5})q^{2}+\zeta_{24}q^{3}+\cdots$
300.2.j.b	$8$	$2.396$	8.0.157351936.1	None	None	$0$	$0$	$0$	$0$		$q+(\beta _{2}+\beta _{4})q^{2}+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{4}+\cdots$
300.2.j.c	$8$	$2.396$	$\Q(\zeta_{24})$	None	None	$0$	$0$	$0$	$0$		$q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}-\zeta_{24}^{5}q^{3}+(\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
300.2.j.d	$12$	$2.396$	12.0.$\cdots$.1	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{2}+\beta _{8}+\beta _{9})q^{4}+\cdots$
300.2.m.a	$8$	$2.396$	$\Q(\zeta_{15})$	None	None	$0$	$-2$	$5$	$-8$		$q+\zeta_{15}^{5}q^{3}+(-1-2\zeta_{15}^{2}-\zeta_{15}^{3}+\cdots)q^{5}+\cdots$
300.2.m.b	$8$	$2.396$	8.0.26265625.1	None	None	$0$	$2$	$-5$	$8$		$q+\beta _{3}q^{3}+(-1+\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
300.2.n.a	$224$	$2.396$		None	None	$0$	$0$	$0$	$0$
300.2.o.a	$24$	$2.396$		None	None	$0$	$0$	$-2$	$0$
300.2.r.a	$224$	$2.396$		None	None	$0$	$0$	$0$	$0$
300.2.w.a	$240$	$2.396$		None	None	$0$	$0$	$0$	$0$
300.2.x.a	$80$	$2.396$		None	None	$0$	$-2$	$0$	$4$
300.3.b.a	$2$	$8.174$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+3iq^{3}+2iq^{7}-9q^{9}+22iq^{13}+\cdots$
300.3.b.b	$2$	$8.174$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+3iq^{3}-13iq^{7}-9q^{9}-23iq^{13}+\cdots$
300.3.b.c	$4$	$8.174$	$\Q(i, \sqrt{5})$	None	None	$0$	$0$	$0$	$0$		$q+(-\beta _{1}+\beta _{3})q^{3}+\beta _{1}q^{7}+(1-2\beta _{2}+\cdots)q^{9}+\cdots$
300.3.b.d	$4$	$8.174$	$\Q(i, \sqrt{35})$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{3}-8\beta _{2}q^{7}+(9+\beta _{3})q^{9}+(-3+\cdots)q^{11}+\cdots$
300.3.c.a	$2$	$8.174$	$\Q(\sqrt{-3}) $	None	None	$-2$	$0$	$0$	$0$		$q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
300.3.c.b	$2$	$8.174$	$\Q(\sqrt{-3}) $	None	None	$2$	$0$	$0$	$0$		$q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
300.3.c.c	$2$	$8.174$	$\Q(\sqrt{-3}) $	None	None	$2$	$0$	$0$	$0$		$q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
300.3.c.d	$8$	$8.174$	8.0.85100625.1	None	None	$-4$	$0$	$0$	$0$		$q-\beta _{5}q^{2}+\beta _{6}q^{3}+(1-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.c.e	$8$	$8.174$	8.0.4069419264.1	None	None	$-2$	$0$	$0$	$0$		$q+\beta _{4}q^{2}-\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.c.f	$8$	$8.174$	8.0.6080256576.2	None	None	$0$	$0$	$0$	$0$		$q+\beta _{5}q^{2}-\beta _{2}q^{3}+(1-\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.c.g	$8$	$8.174$	8.0.4069419264.1	None	None	$2$	$0$	$0$	$0$		$q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.f.a	$4$	$8.174$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$0$	$0$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{3}q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
300.3.f.b	$16$	$8.174$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{12}q^{2}-\beta _{9}q^{3}+(-1+\beta _{4})q^{4}+\cdots$
300.3.f.c	$16$	$8.174$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$0$	$0$	$0$	$0$		$q-\beta _{3}q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.g.a	$1$	$8.174$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$-3$	$0$	$-13$		$q-3q^{3}-13q^{7}+9q^{9}+23q^{13}+11q^{19}+\cdots$
300.3.g.b	$1$	$8.174$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$3$	$0$	$-2$		$q+3q^{3}-2q^{7}+9q^{9}+22q^{13}+26q^{19}+\cdots$
300.3.g.c	$1$	$8.174$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$3$	$0$	$13$		$q+3q^{3}+13q^{7}+9q^{9}-23q^{13}+11q^{19}+\cdots$
300.3.g.d	$2$	$8.174$	$\Q(\sqrt{-5}) $	None	None	$0$	$-4$	$0$	$-4$		$q+(-2+\beta )q^{3}-2q^{7}+(-1-4\beta )q^{9}+\cdots$
300.3.g.e	$2$	$8.174$	$\Q(\sqrt{-5}) $	None	None	$0$	$-4$	$0$	$16$		$q+(-2+\beta )q^{3}+8q^{7}+(-1-4\beta )q^{9}+\cdots$

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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
300.1.b.a	\(2\)	\(0.150\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{3}-iq^{7}-q^{9}+iq^{13}+q^{19}+\cdots\)
300.1.g.a	\(1\)	\(0.150\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(0\)	\(1\)		\(q-q^{3}+q^{7}+q^{9}+q^{13}-q^{19}-q^{21}+\cdots\)
300.1.g.b	\(1\)	\(0.150\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(1\)	\(0\)	\(-1\)		\(q+q^{3}-q^{7}+q^{9}-q^{13}-q^{19}-q^{21}+\cdots\)
300.1.l.a	\(4\)	\(0.150\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{3}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots\)
300.2.a.a	\(1\)	\(2.396\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(0\)	\(-4\)	\(+\)	\(q-q^{3}-4q^{7}+q^{9}-4q^{11}-4q^{17}+\cdots\)
300.2.a.b	\(1\)	\(2.396\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(0\)	\(1\)	\(-\)	\(q-q^{3}+q^{7}+q^{9}+6q^{11}-5q^{13}+\cdots\)
300.2.a.c	\(1\)	\(2.396\)	\(\Q\)	None	None	\(0\)	\(1\)	\(0\)	\(-1\)	\(-\)	\(q+q^{3}-q^{7}+q^{9}+6q^{11}+5q^{13}+\cdots\)
300.2.a.d	\(1\)	\(2.396\)	\(\Q\)	None	None	\(0\)	\(1\)	\(0\)	\(4\)	\(-\)	\(q+q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{17}+\cdots\)
300.2.d.a	\(2\)	\(2.396\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{3}+iq^{7}-q^{9}+6q^{11}+5iq^{13}+\cdots\)
300.2.e.a	\(4\)	\(2.396\)	\(\Q(\sqrt{3}, \sqrt{-5})\)	\(\Q(\sqrt{-15}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots\)
300.2.e.b	\(4\)	\(2.396\)	\(\Q(\sqrt{2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.2.e.c	\(8\)	\(2.396\)	8.0.342102016.5	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{5}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
300.2.e.d	\(8\)	\(2.396\)	8.0.4521217600.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
300.2.e.e	\(8\)	\(2.396\)	8.0.4521217600.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{6}q^{2}+\beta _{3}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
300.2.h.a	\(8\)	\(2.396\)	8.0.342102016.5	None	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
300.2.h.b	\(8\)	\(2.396\)	8.0.342102016.5	None	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
300.2.h.c	\(16\)	\(2.396\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}-\beta _{10}q^{3}-\beta _{4}q^{4}-\beta _{12}q^{6}+\cdots\)
300.2.i.a	\(4\)	\(2.396\)	\(\Q(i, \sqrt{5})\)	None	None	\(0\)	\(-2\)	\(0\)	\(4\)		\(q+(-1+\beta _{3})q^{3}+(1-\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
300.2.i.b	\(4\)	\(2.396\)	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{3}+2\beta _{3}q^{7}+3\beta _{2}q^{9}+4\beta _{1}q^{13}+\cdots\)
300.2.i.c	\(4\)	\(2.396\)	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{3}-3\beta _{3}q^{7}+3\beta _{2}q^{9}-\beta _{1}q^{13}+\cdots\)
300.2.j.a	\(8\)	\(2.396\)	\(\Q(\zeta_{24})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{5})q^{2}+\zeta_{24}q^{3}+\cdots\)
300.2.j.b	\(8\)	\(2.396\)	8.0.157351936.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\beta _{2}+\beta _{4})q^{2}+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{4}+\cdots\)
300.2.j.c	\(8\)	\(2.396\)	\(\Q(\zeta_{24})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}-\zeta_{24}^{5}q^{3}+(\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
300.2.j.d	\(12\)	\(2.396\)	12.0.\(\cdots\).1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{2}+\beta _{8}+\beta _{9})q^{4}+\cdots\)
300.2.m.a	\(8\)	\(2.396\)	\(\Q(\zeta_{15})\)	None	None	\(0\)	\(-2\)	\(5\)	\(-8\)		\(q+\zeta_{15}^{5}q^{3}+(-1-2\zeta_{15}^{2}-\zeta_{15}^{3}+\cdots)q^{5}+\cdots\)
300.2.m.b	\(8\)	\(2.396\)	8.0.26265625.1	None	None	\(0\)	\(2\)	\(-5\)	\(8\)		\(q+\beta _{3}q^{3}+(-1+\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
300.2.n.a	\(224\)	\(2.396\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
300.2.o.a	\(24\)	\(2.396\)		None	None	\(0\)	\(0\)	\(-2\)	\(0\)
300.2.r.a	\(224\)	\(2.396\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
300.2.w.a	\(240\)	\(2.396\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
300.2.x.a	\(80\)	\(2.396\)		None	None	\(0\)	\(-2\)	\(0\)	\(4\)
300.3.b.a	\(2\)	\(8.174\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+3iq^{3}+2iq^{7}-9q^{9}+22iq^{13}+\cdots\)
300.3.b.b	\(2\)	\(8.174\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+3iq^{3}-13iq^{7}-9q^{9}-23iq^{13}+\cdots\)
300.3.b.c	\(4\)	\(8.174\)	\(\Q(i, \sqrt{5})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{1}+\beta _{3})q^{3}+\beta _{1}q^{7}+(1-2\beta _{2}+\cdots)q^{9}+\cdots\)
300.3.b.d	\(4\)	\(8.174\)	\(\Q(i, \sqrt{35})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{3}-8\beta _{2}q^{7}+(9+\beta _{3})q^{9}+(-3+\cdots)q^{11}+\cdots\)
300.3.c.a	\(2\)	\(8.174\)	\(\Q(\sqrt{-3}) \)	None	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
300.3.c.b	\(2\)	\(8.174\)	\(\Q(\sqrt{-3}) \)	None	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
300.3.c.c	\(2\)	\(8.174\)	\(\Q(\sqrt{-3}) \)	None	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
300.3.c.d	\(8\)	\(8.174\)	8.0.85100625.1	None	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{5}q^{2}+\beta _{6}q^{3}+(1-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.c.e	\(8\)	\(8.174\)	8.0.4069419264.1	None	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{4}q^{2}-\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.c.f	\(8\)	\(8.174\)	8.0.6080256576.2	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{5}q^{2}-\beta _{2}q^{3}+(1-\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.c.g	\(8\)	\(8.174\)	8.0.4069419264.1	None	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.f.a	\(4\)	\(8.174\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{3}q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
300.3.f.b	\(16\)	\(8.174\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{12}q^{2}-\beta _{9}q^{3}+(-1+\beta _{4})q^{4}+\cdots\)
300.3.f.c	\(16\)	\(8.174\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{3}q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.g.a	\(1\)	\(8.174\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-3\)	\(0\)	\(-13\)		\(q-3q^{3}-13q^{7}+9q^{9}+23q^{13}+11q^{19}+\cdots\)
300.3.g.b	\(1\)	\(8.174\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(3\)	\(0\)	\(-2\)		\(q+3q^{3}-2q^{7}+9q^{9}+22q^{13}+26q^{19}+\cdots\)
300.3.g.c	\(1\)	\(8.174\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(3\)	\(0\)	\(13\)		\(q+3q^{3}+13q^{7}+9q^{9}-23q^{13}+11q^{19}+\cdots\)
300.3.g.d	\(2\)	\(8.174\)	\(\Q(\sqrt{-5}) \)	None	None	\(0\)	\(-4\)	\(0\)	\(-4\)		\(q+(-2+\beta )q^{3}-2q^{7}+(-1-4\beta )q^{9}+\cdots\)
300.3.g.e	\(2\)	\(8.174\)	\(\Q(\sqrt{-5}) \)	None	None	\(0\)	\(-4\)	\(0\)	\(16\)		\(q+(-2+\beta )q^{3}+8q^{7}+(-1-4\beta )q^{9}+\cdots\)

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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.