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 136 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
605.1.f.a	$2$	$0.302$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-11}) $	None	$0$	$2$	$0$	$0$	$-$	$q+(1+i)q^{3}+iq^{4}-iq^{5}+iq^{9}+(-1+\cdots)q^{12}+\cdots$
605.1.h.a	$4$	$0.302$	$\Q(\zeta_{10})$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	$0$	$0$	$1$	$0$	$-$	$q+\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots$
605.1.l.a	$8$	$0.302$	$\Q(\zeta_{20})$	$\Q(\sqrt{-11}) $	None	$0$	$-2$	$0$	$0$	$-$	$q+(-\zeta_{20}-\zeta_{20}^{6})q^{3}-\zeta_{20}^{9}q^{4}-\zeta_{20}^{3}q^{5}+\cdots$
605.2.a.a	$1$	$4.831$	$\Q$	None	None	$-1$	$-3$	$1$	$-3$	$+$	$q-q^{2}-3q^{3}-q^{4}+q^{5}+3q^{6}-3q^{7}+\cdots$
605.2.a.b	$1$	$4.831$	$\Q$	None	None	$-1$	$0$	$1$	$0$	$+$	$q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots$
605.2.a.c	$1$	$4.831$	$\Q$	None	None	$1$	$-3$	$1$	$3$	$+$	$q+q^{2}-3q^{3}-q^{4}+q^{5}-3q^{6}+3q^{7}+\cdots$
605.2.a.d	$2$	$4.831$	$\Q(\sqrt{2}) $	None	None	$-2$	$0$	$-2$	$4$	$-$	$q+(-1+\beta )q^{2}+2\beta q^{3}+(1-2\beta )q^{4}+\cdots$
605.2.a.e	$2$	$4.831$	$\Q(\sqrt{3}) $	None	None	$0$	$-2$	$-2$	$0$	$+$	$q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}-\beta q^{7}+\cdots$
605.2.a.f	$2$	$4.831$	$\Q(\sqrt{3}) $	None	None	$0$	$4$	$2$	$0$	$-$	$q+\beta q^{2}+2q^{3}+q^{4}+q^{5}+2\beta q^{6}+\cdots$
605.2.a.g	$3$	$4.831$	3.3.404.1	None	None	$-1$	$1$	$-3$	$1$	$-$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots$
605.2.a.h	$3$	$4.831$	3.3.404.1	None	None	$1$	$1$	$-3$	$-1$	$-$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots$
605.2.a.i	$4$	$4.831$	4.4.2525.1	None	None	$-3$	$-2$	$4$	$-11$	$+$	$q+(-1-\beta _{3})q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
605.2.a.j	$4$	$4.831$	4.4.725.1	None	None	$-1$	$0$	$-4$	$-3$	$+$	$q-\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
605.2.a.k	$4$	$4.831$	4.4.725.1	None	None	$1$	$0$	$-4$	$3$	$-$	$q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
605.2.a.l	$4$	$4.831$	4.4.2525.1	None	None	$3$	$-2$	$4$	$11$	$-$	$q+(1+\beta _{2}-\beta _{3})q^{2}+(-1+\beta _{1})q^{3}+\cdots$
605.2.a.m	$6$	$4.831$	6.6.27433728.1	None	None	$0$	$6$	$6$	$0$	$-$	$q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
605.2.b.a	$2$	$4.831$	$\Q(\sqrt{-11}) $	$\Q(\sqrt{-11}) $	None	$0$	$0$	$3$	$0$	$-$	$q+(-1+2\beta )q^{3}+2q^{4}+(1+\beta )q^{5}+\cdots$
605.2.b.b	$4$	$4.831$	4.0.4400.1	$\Q(\sqrt{-55}) $	None	$0$	$0$	$0$	$0$	$-$	$q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}+\beta _{3}q^{5}-\beta _{1}q^{7}+\cdots$
605.2.b.c	$4$	$4.831$	$\Q(\sqrt{-3}, \sqrt{-11})$	None	None	$0$	$0$	$-3$	$0$	$-$	$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots$
605.2.b.d	$4$	$4.831$	$\Q(\sqrt{-2}, \sqrt{3})$	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
605.2.b.e	$4$	$4.831$	$\Q(\sqrt{-2}, \sqrt{3})$	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
605.2.b.f	$8$	$4.831$	8.0.1480160000.1	None	None	$0$	$0$	$4$	$0$	$-$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{6}+\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots$
605.2.b.g	$8$	$4.831$	8.0.1480160000.1	None	None	$0$	$0$	$4$	$0$	$-$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{6}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots$
605.2.b.h	$12$	$4.831$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$0$	$0$	$-6$	$0$	$-$	$q+\beta _{9}q^{2}-\beta _{8}q^{3}+(-2-\beta _{6})q^{4}+\beta _{4}q^{5}+\cdots$
605.2.e.a	$20$	$4.831$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	None	$0$	$4$	$4$	$0$	$-$	$q+\beta _{1}q^{2}-\beta _{12}q^{3}+(-\beta _{4}+\beta _{10}-\beta _{13}+\cdots)q^{4}+\cdots$
605.2.e.b	$32$	$4.831$		None	None	$0$	$-4$	$8$	$0$	$-$
605.2.e.c	$40$	$4.831$		None	None	$0$	$8$	$-4$	$0$	$-$
605.2.g.a	$4$	$4.831$	$\Q(\zeta_{10})$	None	None	$-1$	$0$	$-1$	$0$	$-$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
605.2.g.b	$4$	$4.831$	$\Q(\zeta_{10})$	None	None	$-1$	$3$	$-1$	$-3$	$-$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
605.2.g.c	$4$	$4.831$	$\Q(\zeta_{10})$	None	None	$1$	$0$	$-1$	$0$	$-$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots$
605.2.g.d	$4$	$4.831$	$\Q(\zeta_{10})$	None	None	$1$	$3$	$-1$	$3$	$-$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-3\zeta_{10}^{2}q^{3}+\cdots$
605.2.g.e	$8$	$4.831$	8.0.13140625.1	None	None	$-3$	$5$	$2$	$-4$	$-$	$q-\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots$
605.2.g.f	$8$	$4.831$	8.0.64000000.2	None	None	$-2$	$0$	$2$	$4$	$-$	$q+(-1-\beta _{2}+\beta _{3}-\beta _{4}-\beta _{6})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots$
605.2.g.g	$8$	$4.831$	8.0.159390625.1	None	None	$-1$	$1$	$-2$	$8$	$-$	$q+(1-\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots$
605.2.g.h	$8$	$4.831$	8.0.324000000.3	None	None	$0$	$-4$	$-2$	$0$	$-$	$q+\beta _{7}q^{2}+2\beta _{6}q^{3}+\beta _{4}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$
605.2.g.i	$8$	$4.831$	8.0.324000000.3	None	None	$0$	$2$	$2$	$0$	$-$	$q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
605.2.g.j	$8$	$4.831$	8.0.159390625.1	None	None	$1$	$1$	$-2$	$-8$	$-$	$q+(-1+\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots$
605.2.g.k	$8$	$4.831$	8.0.13140625.1	None	None	$2$	$-5$	$2$	$1$	$-$	$q+\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
605.2.g.l	$8$	$4.831$	8.0.64000000.2	None	None	$2$	$0$	$2$	$-4$	$-$	$q+(-\beta _{2}+\beta _{7})q^{2}+2\beta _{1}q^{3}+(2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots$
605.2.g.m	$8$	$4.831$	8.0.13140625.1	None	None	$3$	$5$	$2$	$4$	$-$	$q+\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots$
605.2.g.n	$8$	$4.831$	8.0.159390625.1	None	None	$4$	$1$	$-2$	$3$	$-$	$q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots$
605.2.g.o	$12$	$4.831$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$-1$	$-1$	$3$	$1$	$-$	$q-\beta _{11}q^{2}+\beta _{8}q^{3}+(-\beta _{1}-3\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
605.2.g.p	$12$	$4.831$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$1$	$-1$	$3$	$-1$	$-$	$q+\beta _{9}q^{2}-\beta _{1}q^{3}+(-3+\beta _{3}+3\beta _{4}+\cdots)q^{4}+\cdots$
605.2.g.q	$24$	$4.831$		None	None	$0$	$-6$	$-6$	$0$	$-$
605.2.j.a	$8$	$4.831$	8.0.484000000.6	$\Q(\sqrt{-55}) $	None	$0$	$0$	$-10$	$0$	$-$	$q+(\beta _{1}-\beta _{4})q^{2}+(1+\beta _{2}-3\beta _{3}+3\beta _{5}+\cdots)q^{4}+\cdots$
605.2.j.b	$8$	$4.831$	8.0.228765625.1	$\Q(\sqrt{-11}) $	None	$0$	$0$	$-3$	$0$	$-$	$q+(-\beta _{4}-2\beta _{5})q^{3}+(-2+2\beta _{3}+2\beta _{4}+\cdots)q^{4}+\cdots$
605.2.j.c	$8$	$4.831$	8.0.484000000.6	$\Q(\sqrt{-55}) $	None	$0$	$0$	$10$	$0$	$-$	$q+(\beta _{1}-\beta _{6})q^{2}+(-2\beta _{2}+2\beta _{3}-3\beta _{5}+\cdots)q^{4}+\cdots$
605.2.j.d	$16$	$4.831$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$0$	$0$	$-2$	$0$	$-$	$q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(-\beta _{5}-\beta _{13}+\cdots)q^{3}+\cdots$
605.2.j.e	$16$	$4.831$	16.0.$\cdots$.7	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{12}q^{2}+\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
605.2.j.f	$16$	$4.831$	16.0.$\cdots$.7	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{12}q^{2}-\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$

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Results (1-50 of 136 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
605.1.f.a	$2$	$0.302$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	$-$	\(q+(1+i)q^{3}+iq^{4}-iq^{5}+iq^{9}+(-1+\cdots)q^{12}+\cdots\)
605.1.h.a	$4$	$0.302$	\(\Q(\zeta_{10})\)	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{5}) \)	\(0\)	\(0\)	\(1\)	\(0\)	$-$	\(q+\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots\)
605.1.l.a	$8$	$0.302$	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	$-$	\(q+(-\zeta_{20}-\zeta_{20}^{6})q^{3}-\zeta_{20}^{9}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)
605.2.a.a	$1$	$4.831$	\(\Q\)	None	None	\(-1\)	\(-3\)	\(1\)	\(-3\)	$+$	\(q-q^{2}-3q^{3}-q^{4}+q^{5}+3q^{6}-3q^{7}+\cdots\)
605.2.a.b	$1$	$4.831$	\(\Q\)	None	None	\(-1\)	\(0\)	\(1\)	\(0\)	$+$	\(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\)
605.2.a.c	$1$	$4.831$	\(\Q\)	None	None	\(1\)	\(-3\)	\(1\)	\(3\)	$+$	\(q+q^{2}-3q^{3}-q^{4}+q^{5}-3q^{6}+3q^{7}+\cdots\)
605.2.a.d	$2$	$4.831$	\(\Q(\sqrt{2}) \)	None	None	\(-2\)	\(0\)	\(-2\)	\(4\)	$-$	\(q+(-1+\beta )q^{2}+2\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
605.2.a.e	$2$	$4.831$	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(-2\)	\(-2\)	\(0\)	$+$	\(q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}-\beta q^{7}+\cdots\)
605.2.a.f	$2$	$4.831$	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(4\)	\(2\)	\(0\)	$-$	\(q+\beta q^{2}+2q^{3}+q^{4}+q^{5}+2\beta q^{6}+\cdots\)
605.2.a.g	$3$	$4.831$	3.3.404.1	None	None	\(-1\)	\(1\)	\(-3\)	\(1\)	$-$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots\)
605.2.a.h	$3$	$4.831$	3.3.404.1	None	None	\(1\)	\(1\)	\(-3\)	\(-1\)	$-$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots\)
605.2.a.i	$4$	$4.831$	4.4.2525.1	None	None	\(-3\)	\(-2\)	\(4\)	\(-11\)	$+$	\(q+(-1-\beta _{3})q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
605.2.a.j	$4$	$4.831$	4.4.725.1	None	None	\(-1\)	\(0\)	\(-4\)	\(-3\)	$+$	\(q-\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
605.2.a.k	$4$	$4.831$	4.4.725.1	None	None	\(1\)	\(0\)	\(-4\)	\(3\)	$-$	\(q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
605.2.a.l	$4$	$4.831$	4.4.2525.1	None	None	\(3\)	\(-2\)	\(4\)	\(11\)	$-$	\(q+(1+\beta _{2}-\beta _{3})q^{2}+(-1+\beta _{1})q^{3}+\cdots\)
605.2.a.m	$6$	$4.831$	6.6.27433728.1	None	None	\(0\)	\(6\)	\(6\)	\(0\)	$-$	\(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
605.2.b.a	$2$	$4.831$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(0\)	\(3\)	\(0\)	$-$	\(q+(-1+2\beta )q^{3}+2q^{4}+(1+\beta )q^{5}+\cdots\)
605.2.b.b	$4$	$4.831$	4.0.4400.1	\(\Q(\sqrt{-55}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}+\beta _{3}q^{5}-\beta _{1}q^{7}+\cdots\)
605.2.b.c	$4$	$4.831$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None	None	\(0\)	\(0\)	\(-3\)	\(0\)	$-$	\(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
605.2.b.d	$4$	$4.831$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.b.e	$4$	$4.831$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.b.f	$8$	$4.831$	8.0.1480160000.1	None	None	\(0\)	\(0\)	\(4\)	\(0\)	$-$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{6}+\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
605.2.b.g	$8$	$4.831$	8.0.1480160000.1	None	None	\(0\)	\(0\)	\(4\)	\(0\)	$-$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{6}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
605.2.b.h	$12$	$4.831$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(0\)	\(0\)	\(-6\)	\(0\)	$-$	\(q+\beta _{9}q^{2}-\beta _{8}q^{3}+(-2-\beta _{6})q^{4}+\beta _{4}q^{5}+\cdots\)
605.2.e.a	$20$	$4.831$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	None	\(0\)	\(4\)	\(4\)	\(0\)	$-$	\(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(-\beta _{4}+\beta _{10}-\beta _{13}+\cdots)q^{4}+\cdots\)
605.2.e.b	$32$	$4.831$		None	None	\(0\)	\(-4\)	\(8\)	\(0\)	$-$
605.2.e.c	$40$	$4.831$		None	None	\(0\)	\(8\)	\(-4\)	\(0\)	$-$
605.2.g.a	$4$	$4.831$	\(\Q(\zeta_{10})\)	None	None	\(-1\)	\(0\)	\(-1\)	\(0\)	$-$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
605.2.g.b	$4$	$4.831$	\(\Q(\zeta_{10})\)	None	None	\(-1\)	\(3\)	\(-1\)	\(-3\)	$-$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
605.2.g.c	$4$	$4.831$	\(\Q(\zeta_{10})\)	None	None	\(1\)	\(0\)	\(-1\)	\(0\)	$-$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots\)
605.2.g.d	$4$	$4.831$	\(\Q(\zeta_{10})\)	None	None	\(1\)	\(3\)	\(-1\)	\(3\)	$-$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-3\zeta_{10}^{2}q^{3}+\cdots\)
605.2.g.e	$8$	$4.831$	8.0.13140625.1	None	None	\(-3\)	\(5\)	\(2\)	\(-4\)	$-$	\(q-\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
605.2.g.f	$8$	$4.831$	8.0.64000000.2	None	None	\(-2\)	\(0\)	\(2\)	\(4\)	$-$	\(q+(-1-\beta _{2}+\beta _{3}-\beta _{4}-\beta _{6})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots\)
605.2.g.g	$8$	$4.831$	8.0.159390625.1	None	None	\(-1\)	\(1\)	\(-2\)	\(8\)	$-$	\(q+(1-\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
605.2.g.h	$8$	$4.831$	8.0.324000000.3	None	None	\(0\)	\(-4\)	\(-2\)	\(0\)	$-$	\(q+\beta _{7}q^{2}+2\beta _{6}q^{3}+\beta _{4}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.g.i	$8$	$4.831$	8.0.324000000.3	None	None	\(0\)	\(2\)	\(2\)	\(0\)	$-$	\(q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.g.j	$8$	$4.831$	8.0.159390625.1	None	None	\(1\)	\(1\)	\(-2\)	\(-8\)	$-$	\(q+(-1+\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
605.2.g.k	$8$	$4.831$	8.0.13140625.1	None	None	\(2\)	\(-5\)	\(2\)	\(1\)	$-$	\(q+\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
605.2.g.l	$8$	$4.831$	8.0.64000000.2	None	None	\(2\)	\(0\)	\(2\)	\(-4\)	$-$	\(q+(-\beta _{2}+\beta _{7})q^{2}+2\beta _{1}q^{3}+(2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots\)
605.2.g.m	$8$	$4.831$	8.0.13140625.1	None	None	\(3\)	\(5\)	\(2\)	\(4\)	$-$	\(q+\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
605.2.g.n	$8$	$4.831$	8.0.159390625.1	None	None	\(4\)	\(1\)	\(-2\)	\(3\)	$-$	\(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots\)
605.2.g.o	$12$	$4.831$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(-1\)	\(-1\)	\(3\)	\(1\)	$-$	\(q-\beta _{11}q^{2}+\beta _{8}q^{3}+(-\beta _{1}-3\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
605.2.g.p	$12$	$4.831$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(1\)	\(-1\)	\(3\)	\(-1\)	$-$	\(q+\beta _{9}q^{2}-\beta _{1}q^{3}+(-3+\beta _{3}+3\beta _{4}+\cdots)q^{4}+\cdots\)
605.2.g.q	$24$	$4.831$		None	None	\(0\)	\(-6\)	\(-6\)	\(0\)	$-$
605.2.j.a	$8$	$4.831$	8.0.484000000.6	\(\Q(\sqrt{-55}) \)	None	\(0\)	\(0\)	\(-10\)	\(0\)	$-$	\(q+(\beta _{1}-\beta _{4})q^{2}+(1+\beta _{2}-3\beta _{3}+3\beta _{5}+\cdots)q^{4}+\cdots\)
605.2.j.b	$8$	$4.831$	8.0.228765625.1	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(0\)	\(-3\)	\(0\)	$-$	\(q+(-\beta _{4}-2\beta _{5})q^{3}+(-2+2\beta _{3}+2\beta _{4}+\cdots)q^{4}+\cdots\)
605.2.j.c	$8$	$4.831$	8.0.484000000.6	\(\Q(\sqrt{-55}) \)	None	\(0\)	\(0\)	\(10\)	\(0\)	$-$	\(q+(\beta _{1}-\beta _{6})q^{2}+(-2\beta _{2}+2\beta _{3}-3\beta _{5}+\cdots)q^{4}+\cdots\)
605.2.j.d	$16$	$4.831$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	\(q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(-\beta _{5}-\beta _{13}+\cdots)q^{3}+\cdots\)
605.2.j.e	$16$	$4.831$	16.0.\(\cdots\).7	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{12}q^{2}+\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.j.f	$16$	$4.831$	16.0.\(\cdots\).7	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{12}q^{2}-\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)