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

Coefficient ring index	Coefficient ring gens.	Only for weight 1:	Projective image	Projective image type
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Results (displaying matches 1-50 of 255) Next

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
900.1.c.a	$1$	$0.449$	$\Q$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{15}) $	$-1$	$0$	$0$	$0$		$q-q^{2}+q^{4}-q^{8}+q^{16}+2q^{17}-q^{32}+\cdots$
900.1.c.b	$1$	$0.449$	$\Q$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{15}) $	$1$	$0$	$0$	$0$		$q+q^{2}+q^{4}+q^{8}+q^{16}-2q^{17}+q^{32}+\cdots$
900.1.l.a	$4$	$0.449$	$\Q(i, \sqrt{6})$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{7}-\beta _{3}q^{13}-\beta _{2}q^{19}+q^{31}+\cdots$
900.1.m.a	$4$	$0.449$	$\Q(\zeta_{8})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{8}+(1-\zeta_{8}^{2}+\cdots)q^{13}+\cdots$
900.1.t.a	$4$	$0.449$	$\Q(\zeta_{12})$	$\Q(\sqrt{-5}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+q^{6}+\cdots$
900.1.x.a	$4$	$0.449$	$\Q(\zeta_{10})$	$\Q(\sqrt{-1}) $	None	$1$	$0$	$1$	$0$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{5}+\cdots$
900.1.bb.a	$8$	$0.449$	$\Q(\zeta_{20})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}+\zeta_{20}^{9}q^{5}+\cdots$
900.1.bd.a	$8$	$0.449$	$\Q(\zeta_{24})$	$\Q(\sqrt{-5}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{24}^{11}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{10}q^{4}+\cdots$
900.1.bh.a	$16$	$0.449$	$\Q(\zeta_{40})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{40}^{11}q^{2}-\zeta_{40}^{2}q^{4}+\zeta_{40}^{3}q^{5}+\cdots$
900.2.a.a	$1$	$7.187$	$\Q$	None	None	$0$	$0$	$0$	$-4$	$-$	$q-4q^{7}+4q^{11}+4q^{17}+4q^{23}+6q^{29}+\cdots$
900.2.a.b	$1$	$7.187$	$\Q$	None	None	$0$	$0$	$0$	$-2$	$+$	$q-2q^{7}-2q^{13}-6q^{17}-4q^{19}+6q^{23}+\cdots$
900.2.a.c	$1$	$7.187$	$\Q$	None	None	$0$	$0$	$0$	$-1$	$-$	$q-q^{7}-6q^{11}+5q^{13}+6q^{17}+5q^{19}+\cdots$
900.2.a.d	$1$	$7.187$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$-1$	$+$	$q-q^{7}-7q^{13}-7q^{19}+11q^{31}-10q^{37}+\cdots$
900.2.a.e	$1$	$7.187$	$\Q$	None	None	$0$	$0$	$0$	$1$	$+$	$q+q^{7}-6q^{11}-5q^{13}-6q^{17}+5q^{19}+\cdots$
900.2.a.f	$1$	$7.187$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$1$	$-$	$q+q^{7}+7q^{13}-7q^{19}+11q^{31}+10q^{37}+\cdots$
900.2.a.g	$1$	$7.187$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$4$	$-$	$q+4q^{7}-2q^{13}+8q^{19}-4q^{31}+10q^{37}+\cdots$
900.2.a.h	$1$	$7.187$	$\Q$	None	None	$0$	$0$	$0$	$4$	$-$	$q+4q^{7}+4q^{11}-4q^{17}-4q^{23}+6q^{29}+\cdots$
900.2.d.a	$2$	$7.187$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$0$		$q+iq^{7}-6q^{11}+5iq^{13}-6iq^{17}+\cdots$
900.2.d.b	$2$	$7.187$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+2iq^{7}+iq^{13}-8q^{19}-4q^{31}+\cdots$
900.2.d.c	$2$	$7.187$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$0$		$q+iq^{7}-iq^{13}+3iq^{17}+4q^{19}+\cdots$
900.2.d.d	$2$	$7.187$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+iq^{7}-7iq^{13}+7q^{19}+11q^{31}+\cdots$
900.2.e.a	$2$	$7.187$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-\beta q^{2}-2q^{4}+2\beta q^{8}-6q^{13}+4q^{16}+\cdots$
900.2.e.b	$2$	$7.187$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+\beta q^{2}-2q^{4}-2\beta q^{8}+4q^{13}+4q^{16}+\cdots$
900.2.e.c	$2$	$7.187$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-\beta q^{2}-2q^{4}+2\beta q^{8}+6q^{13}+4q^{16}+\cdots$
900.2.e.d	$8$	$7.187$	8.0.18939904.2	None	None	$0$	$0$	$0$	$0$		$q+\beta _{5}q^{2}+(1-\beta _{3}-\beta _{4}-\beta _{7})q^{4}+(-2+\cdots)q^{7}+\cdots$
900.2.e.e	$8$	$7.187$	8.0.64000000.1	None	None	$0$	$0$	$0$	$0$		$q+\beta _{4}q^{2}-\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
900.2.e.f	$8$	$7.187$	8.0.207360000.2	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+(1-\beta _{5})q^{4}+(\beta _{2}+\beta _{7})q^{7}+\cdots$
900.2.e.g	$8$	$7.187$	8.0.64000000.1	None	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{2}+\beta _{4}q^{4}+(-\beta _{4}+\beta _{7})q^{7}+\cdots$
900.2.h.a	$4$	$7.187$	$\Q(\zeta_{8})$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{8}^{3}q^{2}+2q^{4}-2\zeta_{8}^{3}q^{8}+2\zeta_{8}q^{13}+\cdots$
900.2.h.b	$8$	$7.187$	8.0.18939904.2	None	None	$-4$	$0$	$0$	$0$		$q+(-1-\beta _{3})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(-2\beta _{4}+\cdots)q^{7}+\cdots$
900.2.h.c	$8$	$7.187$	8.0.18939904.2	None	None	$4$	$0$	$0$	$0$		$q+(1+\beta _{3})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(-2\beta _{4}+\cdots)q^{7}+\cdots$
900.2.h.d	$16$	$7.187$	$\Q(\zeta_{40})$	None	None	$0$	$0$	$0$	$0$		$q-\zeta_{40}^{9}q^{2}+\zeta_{40}^{3}q^{4}+(\zeta_{40}^{5}+\zeta_{40}^{10}+\cdots)q^{7}+\cdots$
900.2.i.a	$2$	$7.187$	$\Q(\sqrt{-3}) $	None	None	$0$	$-3$	$0$	$-1$		$q+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots$
900.2.i.b	$2$	$7.187$	$\Q(\sqrt{-3}) $	None	None	$0$	$0$	$0$	$-1$		$q+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{7}-3q^{9}+\cdots$
900.2.i.c	$6$	$7.187$	6.0.954288.1	None	None	$0$	$1$	$0$	$3$		$q-\beta _{4}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{5})q^{7}+\cdots$
900.2.i.d	$8$	$7.187$	8.0.142635249.1	None	None	$0$	$-1$	$0$	$1$		$q+\beta _{3}q^{3}+(-\beta _{3}+\beta _{4}+\beta _{5}+\beta _{7})q^{7}+\cdots$
900.2.i.e	$8$	$7.187$	8.0.142635249.1	None	None	$0$	$1$	$0$	$-1$		$q-\beta _{2}q^{3}+(2\beta _{2}+\beta _{5}-\beta _{6}-\beta _{7})q^{7}+\cdots$
900.2.i.f	$12$	$7.187$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{3}+(\beta _{5}+\beta _{11})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
900.2.j.a	$4$	$7.187$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$0$	$-8$		$q+(-2+2\zeta_{8})q^{7}+2\zeta_{8}^{2}q^{11}+(-3+\cdots)q^{13}+\cdots$
900.2.j.b	$8$	$7.187$	$\Q(\zeta_{24})$	None	None	$0$	$0$	$0$	$0$		$q-\zeta_{24}^{3}q^{7}-\zeta_{24}^{5}q^{11}-\zeta_{24}q^{13}+\cdots$
900.2.k.a	$2$	$7.187$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-5}) $	None	$-2$	$0$	$0$	$-6$		$q+(-1+i)q^{2}-2iq^{4}+(-3+3i)q^{7}+\cdots$
900.2.k.b	$2$	$7.187$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	None	$-2$	$0$	$0$	$0$		$q+(-1-i)q^{2}+2iq^{4}+(2-2i)q^{8}+\cdots$
900.2.k.c	$2$	$7.187$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	None	$-2$	$0$	$0$	$0$		$q+(-1-i)q^{2}+2iq^{4}+(2-2i)q^{8}+\cdots$
900.2.k.d	$2$	$7.187$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	None	$2$	$0$	$0$	$0$		$q+(1+i)q^{2}+2iq^{4}+(-2+2i)q^{8}+\cdots$
900.2.k.e	$2$	$7.187$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-5}) $	None	$2$	$0$	$0$	$6$		$q+(1-i)q^{2}-2iq^{4}+(3-3i)q^{7}+(-2+\cdots)q^{8}+\cdots$
900.2.k.f	$8$	$7.187$	$\Q(\zeta_{24})$	None	None	$-4$	$0$	$0$	$0$		$q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(\zeta_{24}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots$
900.2.k.g	$8$	$7.187$	$\Q(\zeta_{24})$	None	None	$0$	$0$	$0$	$0$		$q-\zeta_{24}^{4}q^{2}+(-2+\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots$
900.2.k.h	$8$	$7.187$	8.0.157351936.1	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
900.2.k.i	$8$	$7.187$	8.0.3317760000.5	$\Q(\sqrt{-15}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{5}q^{2}+(\beta _{2}-\beta _{4})q^{4}+(\beta _{1}-\beta _{3})q^{8}+\cdots$
900.2.k.j	$8$	$7.187$	8.0.3317760000.5	None	None	$0$	$0$	$0$	$0$		$q-\beta _{5}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+(\beta _{4}+2\beta _{6}+\cdots)q^{8}+\cdots$

Introduction	Features
Universe	News

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
900.1.c.a	\(1\)	\(0.449\)	\(\Q\)	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \)	\(\Q(\sqrt{15}) \)	\(-1\)	\(0\)	\(0\)	\(0\)		\(q-q^{2}+q^{4}-q^{8}+q^{16}+2q^{17}-q^{32}+\cdots\)
900.1.c.b	\(1\)	\(0.449\)	\(\Q\)	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \)	\(\Q(\sqrt{15}) \)	\(1\)	\(0\)	\(0\)	\(0\)		\(q+q^{2}+q^{4}+q^{8}+q^{16}-2q^{17}+q^{32}+\cdots\)
900.1.l.a	\(4\)	\(0.449\)	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{7}-\beta _{3}q^{13}-\beta _{2}q^{19}+q^{31}+\cdots\)
900.1.m.a	\(4\)	\(0.449\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{8}+(1-\zeta_{8}^{2}+\cdots)q^{13}+\cdots\)
900.1.t.a	\(4\)	\(0.449\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-5}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+q^{6}+\cdots\)
900.1.x.a	\(4\)	\(0.449\)	\(\Q(\zeta_{10})\)	\(\Q(\sqrt{-1}) \)	None	\(1\)	\(0\)	\(1\)	\(0\)		\(q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{5}+\cdots\)
900.1.bb.a	\(8\)	\(0.449\)	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}+\zeta_{20}^{9}q^{5}+\cdots\)
900.1.bd.a	\(8\)	\(0.449\)	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-5}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{24}^{11}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
900.1.bh.a	\(16\)	\(0.449\)	\(\Q(\zeta_{40})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{40}^{11}q^{2}-\zeta_{40}^{2}q^{4}+\zeta_{40}^{3}q^{5}+\cdots\)
900.2.a.a	\(1\)	\(7.187\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)	\(-\)	\(q-4q^{7}+4q^{11}+4q^{17}+4q^{23}+6q^{29}+\cdots\)
900.2.a.b	\(1\)	\(7.187\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(q-2q^{7}-2q^{13}-6q^{17}-4q^{19}+6q^{23}+\cdots\)
900.2.a.c	\(1\)	\(7.187\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(q-q^{7}-6q^{11}+5q^{13}+6q^{17}+5q^{19}+\cdots\)
900.2.a.d	\(1\)	\(7.187\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(q-q^{7}-7q^{13}-7q^{19}+11q^{31}-10q^{37}+\cdots\)
900.2.a.e	\(1\)	\(7.187\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(1\)	\(+\)	\(q+q^{7}-6q^{11}-5q^{13}-6q^{17}+5q^{19}+\cdots\)
900.2.a.f	\(1\)	\(7.187\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(1\)	\(-\)	\(q+q^{7}+7q^{13}-7q^{19}+11q^{31}+10q^{37}+\cdots\)
900.2.a.g	\(1\)	\(7.187\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(4\)	\(-\)	\(q+4q^{7}-2q^{13}+8q^{19}-4q^{31}+10q^{37}+\cdots\)
900.2.a.h	\(1\)	\(7.187\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(4\)	\(-\)	\(q+4q^{7}+4q^{11}-4q^{17}-4q^{23}+6q^{29}+\cdots\)
900.2.d.a	\(2\)	\(7.187\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{7}-6q^{11}+5iq^{13}-6iq^{17}+\cdots\)
900.2.d.b	\(2\)	\(7.187\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+2iq^{7}+iq^{13}-8q^{19}-4q^{31}+\cdots\)
900.2.d.c	\(2\)	\(7.187\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{7}-iq^{13}+3iq^{17}+4q^{19}+\cdots\)
900.2.d.d	\(2\)	\(7.187\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{7}-7iq^{13}+7q^{19}+11q^{31}+\cdots\)
900.2.e.a	\(2\)	\(7.187\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta q^{2}-2q^{4}+2\beta q^{8}-6q^{13}+4q^{16}+\cdots\)
900.2.e.b	\(2\)	\(7.187\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta q^{2}-2q^{4}-2\beta q^{8}+4q^{13}+4q^{16}+\cdots\)
900.2.e.c	\(2\)	\(7.187\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta q^{2}-2q^{4}+2\beta q^{8}+6q^{13}+4q^{16}+\cdots\)
900.2.e.d	\(8\)	\(7.187\)	8.0.18939904.2	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{5}q^{2}+(1-\beta _{3}-\beta _{4}-\beta _{7})q^{4}+(-2+\cdots)q^{7}+\cdots\)
900.2.e.e	\(8\)	\(7.187\)	8.0.64000000.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{4}q^{2}-\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
900.2.e.f	\(8\)	\(7.187\)	8.0.207360000.2	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(1-\beta _{5})q^{4}+(\beta _{2}+\beta _{7})q^{7}+\cdots\)
900.2.e.g	\(8\)	\(7.187\)	8.0.64000000.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{2}+\beta _{4}q^{4}+(-\beta _{4}+\beta _{7})q^{7}+\cdots\)
900.2.h.a	\(4\)	\(7.187\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{8}^{3}q^{2}+2q^{4}-2\zeta_{8}^{3}q^{8}+2\zeta_{8}q^{13}+\cdots\)
900.2.h.b	\(8\)	\(7.187\)	8.0.18939904.2	None	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q+(-1-\beta _{3})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(-2\beta _{4}+\cdots)q^{7}+\cdots\)
900.2.h.c	\(8\)	\(7.187\)	8.0.18939904.2	None	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q+(1+\beta _{3})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(-2\beta _{4}+\cdots)q^{7}+\cdots\)
900.2.h.d	\(16\)	\(7.187\)	\(\Q(\zeta_{40})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{40}^{9}q^{2}+\zeta_{40}^{3}q^{4}+(\zeta_{40}^{5}+\zeta_{40}^{10}+\cdots)q^{7}+\cdots\)
900.2.i.a	\(2\)	\(7.187\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-3\)	\(0\)	\(-1\)		\(q+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots\)
900.2.i.b	\(2\)	\(7.187\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-1\)		\(q+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{7}-3q^{9}+\cdots\)
900.2.i.c	\(6\)	\(7.187\)	6.0.954288.1	None	None	\(0\)	\(1\)	\(0\)	\(3\)		\(q-\beta _{4}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{5})q^{7}+\cdots\)
900.2.i.d	\(8\)	\(7.187\)	8.0.142635249.1	None	None	\(0\)	\(-1\)	\(0\)	\(1\)		\(q+\beta _{3}q^{3}+(-\beta _{3}+\beta _{4}+\beta _{5}+\beta _{7})q^{7}+\cdots\)
900.2.i.e	\(8\)	\(7.187\)	8.0.142635249.1	None	None	\(0\)	\(1\)	\(0\)	\(-1\)		\(q-\beta _{2}q^{3}+(2\beta _{2}+\beta _{5}-\beta _{6}-\beta _{7})q^{7}+\cdots\)
900.2.i.f	\(12\)	\(7.187\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{3}+(\beta _{5}+\beta _{11})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
900.2.j.a	\(4\)	\(7.187\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(0\)	\(-8\)		\(q+(-2+2\zeta_{8})q^{7}+2\zeta_{8}^{2}q^{11}+(-3+\cdots)q^{13}+\cdots\)
900.2.j.b	\(8\)	\(7.187\)	\(\Q(\zeta_{24})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{24}^{3}q^{7}-\zeta_{24}^{5}q^{11}-\zeta_{24}q^{13}+\cdots\)
900.2.k.a	\(2\)	\(7.187\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-5}) \)	None	\(-2\)	\(0\)	\(0\)	\(-6\)		\(q+(-1+i)q^{2}-2iq^{4}+(-3+3i)q^{7}+\cdots\)
900.2.k.b	\(2\)	\(7.187\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q+(-1-i)q^{2}+2iq^{4}+(2-2i)q^{8}+\cdots\)
900.2.k.c	\(2\)	\(7.187\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q+(-1-i)q^{2}+2iq^{4}+(2-2i)q^{8}+\cdots\)
900.2.k.d	\(2\)	\(7.187\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q+(1+i)q^{2}+2iq^{4}+(-2+2i)q^{8}+\cdots\)
900.2.k.e	\(2\)	\(7.187\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-5}) \)	None	\(2\)	\(0\)	\(0\)	\(6\)		\(q+(1-i)q^{2}-2iq^{4}+(3-3i)q^{7}+(-2+\cdots)q^{8}+\cdots\)
900.2.k.f	\(8\)	\(7.187\)	\(\Q(\zeta_{24})\)	None	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(\zeta_{24}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
900.2.k.g	\(8\)	\(7.187\)	\(\Q(\zeta_{24})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{24}^{4}q^{2}+(-2+\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
900.2.k.h	\(8\)	\(7.187\)	8.0.157351936.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
900.2.k.i	\(8\)	\(7.187\)	8.0.3317760000.5	\(\Q(\sqrt{-15}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{5}q^{2}+(\beta _{2}-\beta _{4})q^{4}+(\beta _{1}-\beta _{3})q^{8}+\cdots\)
900.2.k.j	\(8\)	\(7.187\)	8.0.3317760000.5	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{5}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+(\beta _{4}+2\beta _{6}+\cdots)q^{8}+\cdots\)

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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.