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 240 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
588.1.c.a	$1$	$0.293$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$0$	$0$	$-$	$q-q^{3}+q^{9}+q^{13}+q^{19}+q^{25}-q^{27}+\cdots$
588.1.c.b	$1$	$0.293$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$1$	$0$	$0$	$-$	$q+q^{3}+q^{9}-q^{13}-q^{19}+q^{25}+q^{27}+\cdots$
588.1.p.a	$2$	$0.293$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$1$	$0$	$0$	$-$	$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+q^{13}-\zeta_{6}q^{19}+\cdots$
588.1.z.a	$12$	$0.293$	$\Q(\zeta_{21})$	$\Q(\sqrt{-3}) $	None	$0$	$1$	$0$	$1$	$-$	$q+\zeta_{42}^{10}q^{3}+\zeta_{42}^{8}q^{7}+\zeta_{42}^{20}q^{9}+\cdots$
588.2.a.a	$1$	$4.695$	$\Q$	None	None	$0$	$-1$	$-2$	$0$	$-$	$q-q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots$
588.2.a.b	$1$	$4.695$	$\Q$	None	None	$0$	$-1$	$-2$	$0$	$+$	$q-q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots$
588.2.a.c	$1$	$4.695$	$\Q$	None	None	$0$	$-1$	$0$	$0$	$+$	$q-q^{3}+q^{9}-6q^{11}-2q^{13}+4q^{19}+\cdots$
588.2.a.d	$1$	$4.695$	$\Q$	None	None	$0$	$1$	$-4$	$0$	$-$	$q+q^{3}-4q^{5}+q^{9}+2q^{11}+6q^{13}+\cdots$
588.2.a.e	$1$	$4.695$	$\Q$	None	None	$0$	$1$	$2$	$0$	$-$	$q+q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots$
588.2.a.f	$1$	$4.695$	$\Q$	None	None	$0$	$1$	$2$	$0$	$-$	$q+q^{3}+2q^{5}+q^{9}+2q^{11}+3q^{13}+\cdots$
588.2.b.a	$8$	$4.695$	8.0.562828176.1	None	None	$-2$	$-8$	$0$	$0$	$-$	$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots$
588.2.b.b	$8$	$4.695$	8.0.562828176.1	None	None	$-2$	$8$	$0$	$0$	$-$	$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots$
588.2.b.c	$12$	$4.695$	12.0.$\cdots$.1	None	None	$4$	$-12$	$0$	$0$	$-$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots$
588.2.b.d	$12$	$4.695$	12.0.$\cdots$.1	None	None	$4$	$12$	$0$	$0$	$-$	$q+\beta _{1}q^{2}+q^{3}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
588.2.e.a	$4$	$4.695$	$\Q(\sqrt{2}, \sqrt{-3})$	$\Q(\sqrt{-21}) $	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+\beta _{3}q^{6}+\cdots$
588.2.e.b	$8$	$4.695$	8.0.3317760000.1	None	None	$0$	$0$	$0$	$0$	$-$	$q-\beta _{6}q^{2}-\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
588.2.e.c	$12$	$4.695$	12.0.$\cdots$.2	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{2}q^{2}+\beta _{10}q^{3}+(-\beta _{3}+\beta _{5})q^{4}+\cdots$
588.2.e.d	$12$	$4.695$	12.0.$\cdots$.1	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots$
588.2.e.e	$12$	$4.695$	12.0.$\cdots$.1	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots$
588.2.e.f	$24$	$4.695$		None	None	$0$	$0$	$0$	$0$	$-$
588.2.f.a	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$-3$	$6$	$0$	$-$	$q+(-1-\zeta_{6})q^{3}+3q^{5}+3\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots$
588.2.f.b	$2$	$4.695$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$	$-$	$q-\zeta_{6}q^{3}-3q^{9}-3\zeta_{6}q^{13}-5\zeta_{6}q^{19}+\cdots$
588.2.f.c	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$3$	$-6$	$0$	$-$	$q+(1+\zeta_{6})q^{3}-3q^{5}+3\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots$
588.2.f.d	$8$	$4.695$	8.0.3288334336.2	None	None	$0$	$0$	$0$	$0$	$-$	$q+(-\beta _{1}+\beta _{6})q^{3}+(-\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots$
588.2.i.a	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$-2$	$0$	$-$	$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
588.2.i.b	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$-2$	$0$	$-$	$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
588.2.i.c	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$0$	$0$	$-$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots$
588.2.i.d	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$4$	$0$	$-$	$q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
588.2.i.e	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$-4$	$0$	$-$	$q+(1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots$
588.2.i.f	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$0$	$0$	$-$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots$
588.2.i.g	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$2$	$0$	$-$	$q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots$
588.2.k.a	$2$	$4.695$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$-3$	$0$	$0$	$-$	$q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(4-8\zeta_{6})q^{13}+\cdots$
588.2.k.b	$2$	$4.695$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$-3$	$0$	$0$	$-$	$q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(-3+6\zeta_{6})q^{13}+\cdots$
588.2.k.c	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$0$	$3$	$0$	$-$	$q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}-3q^{9}+\cdots$
588.2.k.d	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$3$	$-3$	$0$	$-$	$q+(2-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-3\zeta_{6})q^{9}+\cdots$
588.2.k.e	$2$	$4.695$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$3$	$0$	$0$	$-$	$q+(1+\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(-4+8\zeta_{6})q^{13}+\cdots$
588.2.k.f	$16$	$4.695$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$0$	$0$	$0$	$0$	$-$	$q+(-\beta _{1}-\beta _{5}-\beta _{8})q^{3}+(\beta _{1}-2\beta _{7}+\cdots)q^{5}+\cdots$
588.2.n.a	$4$	$4.695$	$\Q(\sqrt{2}, \sqrt{-3})$	$\Q(\sqrt{-21}) $	None	$0$	$-6$	$0$	$0$	$-$	$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
588.2.n.b	$4$	$4.695$	$\Q(\sqrt{2}, \sqrt{-3})$	$\Q(\sqrt{-21}) $	None	$0$	$6$	$0$	$0$	$-$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
588.2.n.c	$16$	$4.695$	16.0.$\cdots$.1	None	None	$0$	$0$	$0$	$0$	$-$	$q-\beta _{9}q^{2}+(-\beta _{1}+\beta _{5}+\beta _{15})q^{3}-\beta _{3}q^{4}+\cdots$
588.2.n.d	$24$	$4.695$		None	None	$0$	$0$	$0$	$0$	$-$
588.2.n.e	$24$	$4.695$		None	None	$0$	$0$	$0$	$0$	$-$
588.2.n.f	$24$	$4.695$		None	None	$0$	$0$	$0$	$0$	$-$
588.2.n.g	$24$	$4.695$		None	None	$0$	$0$	$0$	$0$	$-$
588.2.n.h	$24$	$4.695$		None	None	$0$	$0$	$0$	$0$	$-$
588.2.o.a	$8$	$4.695$	8.0.432972864.2	None	None	$1$	$-4$	$0$	$0$	$-$	$q+(-\beta _{1}-\beta _{6})q^{2}+\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots$
588.2.o.b	$8$	$4.695$	8.0.562828176.1	None	None	$1$	$-4$	$0$	$0$	$-$	$q+\beta _{6}q^{2}-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
588.2.o.c	$8$	$4.695$	8.0.432972864.2	None	None	$1$	$4$	$0$	$0$	$-$	$q+(-\beta _{1}-\beta _{6})q^{2}-\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots$
588.2.o.d	$8$	$4.695$	8.0.562828176.1	None	None	$1$	$4$	$0$	$0$	$-$	$q-\beta _{4}q^{2}+(1-\beta _{3})q^{3}+(\beta _{2}+\beta _{5}-\beta _{7})q^{4}+\cdots$
588.2.o.e	$24$	$4.695$		None	None	$-4$	$-12$	$0$	$0$	$-$

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Results (1-50 of 240 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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
588.1.c.a	$1$	$0.293$	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(0\)	\(0\)	$-$	\(q-q^{3}+q^{9}+q^{13}+q^{19}+q^{25}-q^{27}+\cdots\)
588.1.c.b	$1$	$0.293$	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(1\)	\(0\)	\(0\)	$-$	\(q+q^{3}+q^{9}-q^{13}-q^{19}+q^{25}+q^{27}+\cdots\)
588.1.p.a	$2$	$0.293$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(1\)	\(0\)	\(0\)	$-$	\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+q^{13}-\zeta_{6}q^{19}+\cdots\)
588.1.z.a	$12$	$0.293$	\(\Q(\zeta_{21})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(1\)	\(0\)	\(1\)	$-$	\(q+\zeta_{42}^{10}q^{3}+\zeta_{42}^{8}q^{7}+\zeta_{42}^{20}q^{9}+\cdots\)
588.2.a.a	$1$	$4.695$	\(\Q\)	None	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$-$	\(q-q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots\)
588.2.a.b	$1$	$4.695$	\(\Q\)	None	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$+$	\(q-q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
588.2.a.c	$1$	$4.695$	\(\Q\)	None	None	\(0\)	\(-1\)	\(0\)	\(0\)	$+$	\(q-q^{3}+q^{9}-6q^{11}-2q^{13}+4q^{19}+\cdots\)
588.2.a.d	$1$	$4.695$	\(\Q\)	None	None	\(0\)	\(1\)	\(-4\)	\(0\)	$-$	\(q+q^{3}-4q^{5}+q^{9}+2q^{11}+6q^{13}+\cdots\)
588.2.a.e	$1$	$4.695$	\(\Q\)	None	None	\(0\)	\(1\)	\(2\)	\(0\)	$-$	\(q+q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
588.2.a.f	$1$	$4.695$	\(\Q\)	None	None	\(0\)	\(1\)	\(2\)	\(0\)	$-$	\(q+q^{3}+2q^{5}+q^{9}+2q^{11}+3q^{13}+\cdots\)
588.2.b.a	$8$	$4.695$	8.0.562828176.1	None	None	\(-2\)	\(-8\)	\(0\)	\(0\)	$-$	\(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots\)
588.2.b.b	$8$	$4.695$	8.0.562828176.1	None	None	\(-2\)	\(8\)	\(0\)	\(0\)	$-$	\(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
588.2.b.c	$12$	$4.695$	12.0.\(\cdots\).1	None	None	\(4\)	\(-12\)	\(0\)	\(0\)	$-$	\(q+\beta _{1}q^{2}-q^{3}+(\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
588.2.b.d	$12$	$4.695$	12.0.\(\cdots\).1	None	None	\(4\)	\(12\)	\(0\)	\(0\)	$-$	\(q+\beta _{1}q^{2}+q^{3}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
588.2.e.a	$4$	$4.695$	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-21}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+\beta _{3}q^{6}+\cdots\)
588.2.e.b	$8$	$4.695$	8.0.3317760000.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\beta _{6}q^{2}-\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
588.2.e.c	$12$	$4.695$	12.0.\(\cdots\).2	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{2}q^{2}+\beta _{10}q^{3}+(-\beta _{3}+\beta _{5})q^{4}+\cdots\)
588.2.e.d	$12$	$4.695$	12.0.\(\cdots\).1	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
588.2.e.e	$12$	$4.695$	12.0.\(\cdots\).1	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots\)
588.2.e.f	$24$	$4.695$		None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$
588.2.f.a	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-3\)	\(6\)	\(0\)	$-$	\(q+(-1-\zeta_{6})q^{3}+3q^{5}+3\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
588.2.f.b	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\zeta_{6}q^{3}-3q^{9}-3\zeta_{6}q^{13}-5\zeta_{6}q^{19}+\cdots\)
588.2.f.c	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(3\)	\(-6\)	\(0\)	$-$	\(q+(1+\zeta_{6})q^{3}-3q^{5}+3\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
588.2.f.d	$8$	$4.695$	8.0.3288334336.2	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+(-\beta _{1}+\beta _{6})q^{3}+(-\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
588.2.i.a	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$-$	\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
588.2.i.b	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$-$	\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
588.2.i.c	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(0\)	\(0\)	$-$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots\)
588.2.i.d	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(4\)	\(0\)	$-$	\(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
588.2.i.e	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(-4\)	\(0\)	$-$	\(q+(1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
588.2.i.f	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(0\)	\(0\)	$-$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots\)
588.2.i.g	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(2\)	\(0\)	$-$	\(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
588.2.k.a	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-3\)	\(0\)	\(0\)	$-$	\(q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(4-8\zeta_{6})q^{13}+\cdots\)
588.2.k.b	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-3\)	\(0\)	\(0\)	$-$	\(q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(-3+6\zeta_{6})q^{13}+\cdots\)
588.2.k.c	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(0\)	\(3\)	\(0\)	$-$	\(q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}-3q^{9}+\cdots\)
588.2.k.d	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(3\)	\(-3\)	\(0\)	$-$	\(q+(2-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-3\zeta_{6})q^{9}+\cdots\)
588.2.k.e	$2$	$4.695$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(3\)	\(0\)	\(0\)	$-$	\(q+(1+\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(-4+8\zeta_{6})q^{13}+\cdots\)
588.2.k.f	$16$	$4.695$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+(-\beta _{1}-\beta _{5}-\beta _{8})q^{3}+(\beta _{1}-2\beta _{7}+\cdots)q^{5}+\cdots\)
588.2.n.a	$4$	$4.695$	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-21}) \)	None	\(0\)	\(-6\)	\(0\)	\(0\)	$-$	\(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
588.2.n.b	$4$	$4.695$	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-21}) \)	None	\(0\)	\(6\)	\(0\)	\(0\)	$-$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
588.2.n.c	$16$	$4.695$	16.0.\(\cdots\).1	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\beta _{9}q^{2}+(-\beta _{1}+\beta _{5}+\beta _{15})q^{3}-\beta _{3}q^{4}+\cdots\)
588.2.n.d	$24$	$4.695$		None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$
588.2.n.e	$24$	$4.695$		None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$
588.2.n.f	$24$	$4.695$		None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$
588.2.n.g	$24$	$4.695$		None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$
588.2.n.h	$24$	$4.695$		None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$
588.2.o.a	$8$	$4.695$	8.0.432972864.2	None	None	\(1\)	\(-4\)	\(0\)	\(0\)	$-$	\(q+(-\beta _{1}-\beta _{6})q^{2}+\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots\)
588.2.o.b	$8$	$4.695$	8.0.562828176.1	None	None	\(1\)	\(-4\)	\(0\)	\(0\)	$-$	\(q+\beta _{6}q^{2}-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
588.2.o.c	$8$	$4.695$	8.0.432972864.2	None	None	\(1\)	\(4\)	\(0\)	\(0\)	$-$	\(q+(-\beta _{1}-\beta _{6})q^{2}-\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots\)
588.2.o.d	$8$	$4.695$	8.0.562828176.1	None	None	\(1\)	\(4\)	\(0\)	\(0\)	$-$	\(q-\beta _{4}q^{2}+(1-\beta _{3})q^{3}+(\beta _{2}+\beta _{5}-\beta _{7})q^{4}+\cdots\)
588.2.o.e	$24$	$4.695$		None	None	\(-4\)	\(-12\)	\(0\)	\(0\)	$-$