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 214) Next

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
270.2.a.a	$1$	$2.156$	$\Q$	None	$-1$	$0$	$-1$	$2$	$-$	$q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots$
270.2.a.b	$1$	$2.156$	$\Q$	None	$-1$	$0$	$1$	$2$	$-$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
270.2.a.c	$1$	$2.156$	$\Q$	None	$1$	$0$	$-1$	$2$	$-$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
270.2.a.d	$1$	$2.156$	$\Q$	None	$1$	$0$	$1$	$2$	$-$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
270.2.c.a	$2$	$2.156$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-2$	$0$		$q+iq^{2}-q^{4}+(-1-2i)q^{5}-4iq^{7}+\cdots$
270.2.c.b	$2$	$2.156$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$2$	$0$		$q+iq^{2}-q^{4}+(1-2i)q^{5}+4iq^{7}+\cdots$
270.2.c.c	$4$	$2.156$	$\Q(i, \sqrt{19})$	None	$0$	$0$	$0$	$0$		$q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{5}+(1+2\beta _{3})q^{7}+\cdots$
270.2.e.a	$2$	$2.156$	$\Q(\sqrt{-3}) $	None	$-1$	$0$	$1$	$4$		$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots$
270.2.e.b	$2$	$2.156$	$\Q(\sqrt{-3}) $	None	$1$	$0$	$-1$	$1$		$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
270.2.e.c	$4$	$2.156$	$\Q(\sqrt{-3}, \sqrt{-11})$	None	$-2$	$0$	$-2$	$-1$		$q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
270.2.f.a	$8$	$2.156$	$\Q(\zeta_{24})$	None	$0$	$0$	$0$	$-8$		$q+\zeta_{24}^{5}q^{2}-\zeta_{24}^{3}q^{4}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{5}+\cdots$
270.2.f.b	$8$	$2.156$	$\Q(\zeta_{24})$	None	$0$	$0$	$0$	$4$		$q+(\zeta_{24}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{6}q^{4}+(2\zeta_{24}+\cdots)q^{5}+\cdots$
270.2.i.a	$4$	$2.156$	$\Q(\zeta_{12})$	None	$0$	$0$	$-2$	$0$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
270.2.i.b	$8$	$2.156$	$\Q(\zeta_{24})$	None	$0$	$0$	$4$	$0$		$q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots$
270.2.k.a	$6$	$2.156$	$\Q(\zeta_{18})$	None	$0$	$0$	$0$	$6$		$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(\zeta_{18}-2\zeta_{18}^{4}+\cdots)q^{3}+\cdots$
270.2.k.b	$12$	$2.156$	12.0.$\cdots$.1	None	$0$	$3$	$0$	$-12$		$q-\beta _{7}q^{2}+(1-\beta _{5}-\beta _{7}-\beta _{11})q^{3}+\cdots$
270.2.k.c	$12$	$2.156$	12.0.$\cdots$.1	None	$0$	$3$	$0$	$6$		$q+(-\beta _{7}-\beta _{10})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{7}+\cdots)q^{3}+\cdots$
270.2.k.d	$18$	$2.156$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$0$	$-3$	$0$	$-3$		$q+\beta _{2}q^{2}-\beta _{7}q^{3}+\beta _{3}q^{4}+(\beta _{3}-\beta _{8}+\cdots)q^{5}+\cdots$
270.2.k.e	$24$	$2.156$		None	$0$	$-3$	$0$	$3$
270.2.m.a	$8$	$2.156$	$\Q(\zeta_{24})$	None	$0$	$0$	$-12$	$-8$		$q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-1+\zeta_{24}^{3}+\cdots)q^{5}+\cdots$
270.2.m.b	$16$	$2.156$	16.0.$\cdots$.9	None	$0$	$0$	$12$	$8$		$q+\beta _{5}q^{2}-\beta _{6}q^{4}+(-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$
270.2.p.a	$108$	$2.156$		None	$0$	$0$	$6$	$0$
270.2.r.a	$216$	$2.156$		None	$0$	$0$	$0$	$0$
270.3.b.a	$4$	$7.357$	4.0.31744.1	None	$0$	$0$	$-12$	$0$		$q-\beta _{2}q^{2}+2q^{4}+(-3-\beta _{1}-\beta _{2})q^{5}+\cdots$
270.3.b.b	$4$	$7.357$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$		$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(3\zeta_{8}-4\zeta_{8}^{3})q^{5}+\cdots$
270.3.b.c	$4$	$7.357$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+2q^{4}+5\zeta_{8}q^{5}+5\zeta_{8}^{2}q^{7}+\cdots$
270.3.b.d	$4$	$7.357$	4.0.31744.1	None	$0$	$0$	$12$	$0$		$q+\beta _{2}q^{2}+2q^{4}+(3-\beta _{1}+\beta _{2})q^{5}+\cdots$
270.3.d.a	$4$	$7.357$	$\Q(\sqrt{-2}, \sqrt{-5})$	None	$0$	$0$	$0$	$-4$		$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}-q^{7}+2\beta _{1}q^{8}+\cdots$
270.3.d.b	$8$	$7.357$	8.0.40960000.1	None	$0$	$0$	$0$	$-8$		$q+\beta _{2}q^{2}-2q^{4}-\beta _{1}q^{5}+(-1+\beta _{5}+\cdots)q^{7}+\cdots$
270.3.g.a	$4$	$7.357$	$\Q(i, \sqrt{6})$	None	$-4$	$0$	$-12$	$8$		$q+(-1-\beta _{2})q^{2}+2\beta _{2}q^{4}+(-3-2\beta _{1}+\cdots)q^{5}+\cdots$
270.3.g.b	$4$	$7.357$	$\Q(i, \sqrt{6})$	None	$-4$	$0$	$12$	$-4$		$q+(-1+\beta _{2})q^{2}-2\beta _{2}q^{4}+(3+2\beta _{1}+\cdots)q^{5}+\cdots$
270.3.g.c	$4$	$7.357$	$\Q(i, \sqrt{6})$	None	$4$	$0$	$-12$	$-4$		$q+(1-\beta _{2})q^{2}-2\beta _{2}q^{4}+(-3+2\beta _{1}+\cdots)q^{5}+\cdots$
270.3.g.d	$4$	$7.357$	$\Q(i, \sqrt{6})$	None	$4$	$0$	$12$	$8$		$q+(1+\beta _{2})q^{2}+2\beta _{2}q^{4}+(3+2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
270.3.g.e	$8$	$7.357$	8.0.$\cdots$.38	None	$-8$	$0$	$12$	$-8$		$q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots$
270.3.g.f	$8$	$7.357$	8.0.$\cdots$.38	None	$8$	$0$	$-12$	$-8$		$q+(1+\beta _{1})q^{2}+2\beta _{1}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots$
270.3.h.a	$16$	$7.357$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$0$	$0$	$0$	$-4$		$q+\beta _{6}q^{2}-2\beta _{10}q^{4}+\beta _{12}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$
270.3.j.a	$8$	$7.357$	$\Q(\zeta_{24})$	None	$0$	$0$	$12$	$0$		$q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}-2\zeta_{24}^{2}q^{4}+\cdots$
270.3.j.b	$16$	$7.357$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$0$	$0$	$-30$	$0$		$q+\beta _{1}q^{2}+(-2-2\beta _{2})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots$
270.3.l.a	$24$	$7.357$		None	$-12$	$0$	$0$	$6$
270.3.l.b	$24$	$7.357$		None	$12$	$0$	$0$	$-6$
270.3.n.a	$216$	$7.357$		None	$0$	$0$	$-18$	$0$
270.3.o.a	$144$	$7.357$		None	$0$	$0$	$0$	$0$
270.3.q.a	$216$	$7.357$		None	$0$	$0$	$0$	$18$
270.3.q.b	$216$	$7.357$		None	$0$	$0$	$0$	$-18$
270.4.a.a	$1$	$15.931$	$\Q$	None	$-2$	$0$	$-5$	$-34$	$+$	$q-2q^{2}+4q^{4}-5q^{5}-34q^{7}-8q^{8}+\cdots$
270.4.a.b	$1$	$15.931$	$\Q$	None	$-2$	$0$	$-5$	$8$	$-$	$q-2q^{2}+4q^{4}-5q^{5}+8q^{7}-8q^{8}+\cdots$
270.4.a.c	$1$	$15.931$	$\Q$	None	$-2$	$0$	$5$	$-22$	$+$	$q-2q^{2}+4q^{4}+5q^{5}-22q^{7}-8q^{8}+\cdots$
270.4.a.d	$1$	$15.931$	$\Q$	None	$-2$	$0$	$5$	$-13$	$-$	$q-2q^{2}+4q^{4}+5q^{5}-13q^{7}-8q^{8}+\cdots$
270.4.a.e	$1$	$15.931$	$\Q$	None	$-2$	$0$	$5$	$-4$	$-$	$q-2q^{2}+4q^{4}+5q^{5}-4q^{7}-8q^{8}+\cdots$
270.4.a.f	$1$	$15.931$	$\Q$	None	$-2$	$0$	$5$	$14$	$+$	$q-2q^{2}+4q^{4}+5q^{5}+14q^{7}-8q^{8}+\cdots$

Introduction	Features
Universe	News

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
270.2.a.a	\(1\)	\(2.156\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(2\)	\(-\)	\(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots\)
270.2.a.b	\(1\)	\(2.156\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(2\)	\(-\)	\(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
270.2.a.c	\(1\)	\(2.156\)	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(2\)	\(-\)	\(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
270.2.a.d	\(1\)	\(2.156\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(2\)	\(-\)	\(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
270.2.c.a	\(2\)	\(2.156\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+iq^{2}-q^{4}+(-1-2i)q^{5}-4iq^{7}+\cdots\)
270.2.c.b	\(2\)	\(2.156\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+iq^{2}-q^{4}+(1-2i)q^{5}+4iq^{7}+\cdots\)
270.2.c.c	\(4\)	\(2.156\)	\(\Q(i, \sqrt{19})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{5}+(1+2\beta _{3})q^{7}+\cdots\)
270.2.e.a	\(2\)	\(2.156\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(0\)	\(1\)	\(4\)		\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
270.2.e.b	\(2\)	\(2.156\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(0\)	\(-1\)	\(1\)		\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
270.2.e.c	\(4\)	\(2.156\)	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None	\(-2\)	\(0\)	\(-2\)	\(-1\)		\(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
270.2.f.a	\(8\)	\(2.156\)	\(\Q(\zeta_{24})\)	None	\(0\)	\(0\)	\(0\)	\(-8\)		\(q+\zeta_{24}^{5}q^{2}-\zeta_{24}^{3}q^{4}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
270.2.f.b	\(8\)	\(2.156\)	\(\Q(\zeta_{24})\)	None	\(0\)	\(0\)	\(0\)	\(4\)		\(q+(\zeta_{24}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{6}q^{4}+(2\zeta_{24}+\cdots)q^{5}+\cdots\)
270.2.i.a	\(4\)	\(2.156\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
270.2.i.b	\(8\)	\(2.156\)	\(\Q(\zeta_{24})\)	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots\)
270.2.k.a	\(6\)	\(2.156\)	\(\Q(\zeta_{18})\)	None	\(0\)	\(0\)	\(0\)	\(6\)		\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(\zeta_{18}-2\zeta_{18}^{4}+\cdots)q^{3}+\cdots\)
270.2.k.b	\(12\)	\(2.156\)	12.0.\(\cdots\).1	None	\(0\)	\(3\)	\(0\)	\(-12\)		\(q-\beta _{7}q^{2}+(1-\beta _{5}-\beta _{7}-\beta _{11})q^{3}+\cdots\)
270.2.k.c	\(12\)	\(2.156\)	12.0.\(\cdots\).1	None	\(0\)	\(3\)	\(0\)	\(6\)		\(q+(-\beta _{7}-\beta _{10})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{7}+\cdots)q^{3}+\cdots\)
270.2.k.d	\(18\)	\(2.156\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(0\)	\(-3\)	\(0\)	\(-3\)		\(q+\beta _{2}q^{2}-\beta _{7}q^{3}+\beta _{3}q^{4}+(\beta _{3}-\beta _{8}+\cdots)q^{5}+\cdots\)
270.2.k.e	\(24\)	\(2.156\)		None	\(0\)	\(-3\)	\(0\)	\(3\)
270.2.m.a	\(8\)	\(2.156\)	\(\Q(\zeta_{24})\)	None	\(0\)	\(0\)	\(-12\)	\(-8\)		\(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-1+\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
270.2.m.b	\(16\)	\(2.156\)	16.0.\(\cdots\).9	None	\(0\)	\(0\)	\(12\)	\(8\)		\(q+\beta _{5}q^{2}-\beta _{6}q^{4}+(-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
270.2.p.a	\(108\)	\(2.156\)		None	\(0\)	\(0\)	\(6\)	\(0\)
270.2.r.a	\(216\)	\(2.156\)		None	\(0\)	\(0\)	\(0\)	\(0\)
270.3.b.a	\(4\)	\(7.357\)	4.0.31744.1	None	\(0\)	\(0\)	\(-12\)	\(0\)		\(q-\beta _{2}q^{2}+2q^{4}+(-3-\beta _{1}-\beta _{2})q^{5}+\cdots\)
270.3.b.b	\(4\)	\(7.357\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(3\zeta_{8}-4\zeta_{8}^{3})q^{5}+\cdots\)
270.3.b.c	\(4\)	\(7.357\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+2q^{4}+5\zeta_{8}q^{5}+5\zeta_{8}^{2}q^{7}+\cdots\)
270.3.b.d	\(4\)	\(7.357\)	4.0.31744.1	None	\(0\)	\(0\)	\(12\)	\(0\)		\(q+\beta _{2}q^{2}+2q^{4}+(3-\beta _{1}+\beta _{2})q^{5}+\cdots\)
270.3.d.a	\(4\)	\(7.357\)	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}-q^{7}+2\beta _{1}q^{8}+\cdots\)
270.3.d.b	\(8\)	\(7.357\)	8.0.40960000.1	None	\(0\)	\(0\)	\(0\)	\(-8\)		\(q+\beta _{2}q^{2}-2q^{4}-\beta _{1}q^{5}+(-1+\beta _{5}+\cdots)q^{7}+\cdots\)
270.3.g.a	\(4\)	\(7.357\)	\(\Q(i, \sqrt{6})\)	None	\(-4\)	\(0\)	\(-12\)	\(8\)		\(q+(-1-\beta _{2})q^{2}+2\beta _{2}q^{4}+(-3-2\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.g.b	\(4\)	\(7.357\)	\(\Q(i, \sqrt{6})\)	None	\(-4\)	\(0\)	\(12\)	\(-4\)		\(q+(-1+\beta _{2})q^{2}-2\beta _{2}q^{4}+(3+2\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.g.c	\(4\)	\(7.357\)	\(\Q(i, \sqrt{6})\)	None	\(4\)	\(0\)	\(-12\)	\(-4\)		\(q+(1-\beta _{2})q^{2}-2\beta _{2}q^{4}+(-3+2\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.g.d	\(4\)	\(7.357\)	\(\Q(i, \sqrt{6})\)	None	\(4\)	\(0\)	\(12\)	\(8\)		\(q+(1+\beta _{2})q^{2}+2\beta _{2}q^{4}+(3+2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
270.3.g.e	\(8\)	\(7.357\)	8.0.\(\cdots\).38	None	\(-8\)	\(0\)	\(12\)	\(-8\)		\(q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.g.f	\(8\)	\(7.357\)	8.0.\(\cdots\).38	None	\(8\)	\(0\)	\(-12\)	\(-8\)		\(q+(1+\beta _{1})q^{2}+2\beta _{1}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.h.a	\(16\)	\(7.357\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q+\beta _{6}q^{2}-2\beta _{10}q^{4}+\beta _{12}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
270.3.j.a	\(8\)	\(7.357\)	\(\Q(\zeta_{24})\)	None	\(0\)	\(0\)	\(12\)	\(0\)		\(q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}-2\zeta_{24}^{2}q^{4}+\cdots\)
270.3.j.b	\(16\)	\(7.357\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(0\)	\(0\)	\(-30\)	\(0\)		\(q+\beta _{1}q^{2}+(-2-2\beta _{2})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
270.3.l.a	\(24\)	\(7.357\)		None	\(-12\)	\(0\)	\(0\)	\(6\)
270.3.l.b	\(24\)	\(7.357\)		None	\(12\)	\(0\)	\(0\)	\(-6\)
270.3.n.a	\(216\)	\(7.357\)		None	\(0\)	\(0\)	\(-18\)	\(0\)
270.3.o.a	\(144\)	\(7.357\)		None	\(0\)	\(0\)	\(0\)	\(0\)
270.3.q.a	\(216\)	\(7.357\)		None	\(0\)	\(0\)	\(0\)	\(18\)
270.3.q.b	\(216\)	\(7.357\)		None	\(0\)	\(0\)	\(0\)	\(-18\)
270.4.a.a	\(1\)	\(15.931\)	\(\Q\)	None	\(-2\)	\(0\)	\(-5\)	\(-34\)	\(+\)	\(q-2q^{2}+4q^{4}-5q^{5}-34q^{7}-8q^{8}+\cdots\)
270.4.a.b	\(1\)	\(15.931\)	\(\Q\)	None	\(-2\)	\(0\)	\(-5\)	\(8\)	\(-\)	\(q-2q^{2}+4q^{4}-5q^{5}+8q^{7}-8q^{8}+\cdots\)
270.4.a.c	\(1\)	\(15.931\)	\(\Q\)	None	\(-2\)	\(0\)	\(5\)	\(-22\)	\(+\)	\(q-2q^{2}+4q^{4}+5q^{5}-22q^{7}-8q^{8}+\cdots\)
270.4.a.d	\(1\)	\(15.931\)	\(\Q\)	None	\(-2\)	\(0\)	\(5\)	\(-13\)	\(-\)	\(q-2q^{2}+4q^{4}+5q^{5}-13q^{7}-8q^{8}+\cdots\)
270.4.a.e	\(1\)	\(15.931\)	\(\Q\)	None	\(-2\)	\(0\)	\(5\)	\(-4\)	\(-\)	\(q-2q^{2}+4q^{4}+5q^{5}-4q^{7}-8q^{8}+\cdots\)
270.4.a.f	\(1\)	\(15.931\)	\(\Q\)	None	\(-2\)	\(0\)	\(5\)	\(14\)	\(+\)	\(q-2q^{2}+4q^{4}+5q^{5}+14q^{7}-8q^{8}+\cdots\)

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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.