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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.		Projective image	Projective image type
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Results (1-50 of 205 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
59.1.b.a	$59$	$1$	59.b	59.b	$2$	$1$	$1$	$0.029$	$\Q$	$D_{3}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\cdots$
236.1.d.a	$236$	$1$	236.d	59.b	$2$	$3$	$3$	$0.118$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots$
295.1.d.a	$295$	$1$	295.d	295.d	$2$	$1$	$1$	$0.147$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-295}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-q^{4}+q^{5}+q^{9}+q^{16}-2q^{19}-q^{20}+\cdots$
295.1.d.b	$295$	$1$	295.d	295.d	$2$	$2$	$2$	$0.147$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-q^{4}-\zeta_{6}q^{5}+(\zeta_{6}+\cdots)q^{7}+\cdots$
413.1.g.a	$413$	$1$	413.g	413.g	$6$	$2$	$1$	$0.206$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$-2$	$1$	$2$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{7}+\cdots$
413.1.g.b	$413$	$1$	413.g	413.g	$6$	$2$	$1$	$0.206$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$1$	$-2$	$-1$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}q^{7}+\cdots$
413.1.g.c	$413$	$1$	413.g	413.g	$6$	$2$	$1$	$0.206$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$1$	$1$	$-1$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\cdots$
531.1.c.a	$531$	$1$	531.c	59.b	$2$	$1$	$1$	$0.265$	$\Q$	$D_{3}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$-1$	$1$		$q+q^{4}+q^{5}-q^{7}+q^{16}-2q^{17}-q^{19}+\cdots$
531.1.g.a	$531$	$1$	531.g	531.g	$6$	$6$	$3$	$0.265$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{5}+\cdots$
885.1.k.a	$885$	$1$	885.k	885.k	$4$	$2$	$1$	$0.442$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$-2$	$-2$	$2$	$1$		$q-q^{3}-iq^{4}-q^{5}+(1+i)q^{7}+q^{9}+\cdots$
885.1.k.b	$885$	$1$	885.k	885.k	$4$	$2$	$1$	$0.442$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$2$	$2$	$1$		$q+iq^{3}-iq^{4}+q^{5}+(1+i)q^{7}-q^{9}+\cdots$
885.1.k.c	$885$	$1$	885.k	885.k	$4$	$4$	$2$	$0.442$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{3}q^{4}+\zeta_{12}^{4}q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots$
885.1.k.d	$885$	$1$	885.k	885.k	$4$	$4$	$2$	$0.442$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$2$	$2$	$-2$	$1$		$q+\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{4}-\zeta_{12}^{4}q^{5}+\cdots$
944.1.h.a	$944$	$1$	944.h	59.b	$2$	$1$	$1$	$0.471$	$\Q$	$D_{3}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$1$	$1$		$q+q^{3}-q^{5}+q^{7}-q^{15}+2q^{17}+q^{19}+\cdots$
944.1.h.b	$944$	$1$	944.h	59.b	$2$	$3$	$3$	$0.471$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots$
1003.1.b.a	$1003$	$1$	1003.b	1003.b	$2$	$1$	$1$	$0.501$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-1003}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots$
1003.1.b.b	$1003$	$1$	1003.b	1003.b	$2$	$2$	$2$	$0.501$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots$
1003.1.f.a	$1003$	$1$	1003.f	1003.f	$4$	$2$	$1$	$0.501$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$-2$	$-2$	$-2$	$1$		$q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots$
1003.1.f.b	$1003$	$1$	1003.f	1003.f	$4$	$4$	$2$	$0.501$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$2$	$2$	$2$	$2$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}^{4}+\cdots)q^{5}+\cdots$
1003.1.h.a	$1003$	$1$	1003.h	1003.h	$8$	$4$	$1$	$0.501$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$
1003.1.h.b	$1003$	$1$	1003.h	1003.h	$8$	$8$	$2$	$0.501$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(-\zeta_{24}-\zeta_{24}^{2})q^{3}-\zeta_{24}^{6}q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots$
1121.1.g.a	$1121$	$1$	1121.g	1121.g	$6$	$6$	$3$	$0.559$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}-\zeta_{18}^{3}q^{4}+(-\zeta_{18}+\cdots)q^{5}+\cdots$
1121.1.l.a	$1121$	$1$	1121.l	1121.l	$18$	$18$	$3$	$0.559$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}^{7}-\zeta_{54}^{17})q^{3}+\zeta_{54}^{6}q^{4}+\cdots$
1180.1.b.a	$1180$	$1$	1180.b	295.d	$2$	$6$	$6$	$0.589$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{8})q^{3}-\zeta_{18}^{5}q^{5}+(-\zeta_{18}^{2}+\cdots)q^{7}+\cdots$
1239.1.h.a	$1239$	$1$	1239.h	1239.h	$2$	$1$	$1$	$0.618$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-1239}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$-1$	$2$	$1$	$1$		$q-q^{3}-q^{4}+2q^{5}+q^{7}+q^{9}+q^{12}+\cdots$
1239.1.h.b	$1239$	$1$	1239.h	1239.h	$2$	$1$	$1$	$0.618$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-1239}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$1$	$-2$	$1$	$1$		$q+q^{3}-q^{4}-2q^{5}+q^{7}+q^{9}-q^{12}+\cdots$
1239.1.h.d	$1239$	$1$	1239.h	1239.h	$2$	$2$	$2$	$0.618$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$-1$	$2$	$-1$	$1$		$q+\zeta_{6}^{2}q^{3}-q^{4}+q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
1239.1.h.e	$1239$	$1$	1239.h	1239.h	$2$	$2$	$2$	$0.618$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$1$	$-2$	$-1$	$1$		$q-\zeta_{6}^{2}q^{3}-q^{4}-q^{5}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
1239.1.j.a	$1239$	$1$	1239.j	1239.j	$6$	$2$	$1$	$0.618$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$-2$	$-2$	$-1$	$1$		$q-q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\cdots$
1239.1.j.b	$1239$	$1$	1239.j	1239.j	$6$	$2$	$1$	$0.618$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$-1$	$-1$	$2$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
1239.1.j.c	$1239$	$1$	1239.j	1239.j	$6$	$2$	$1$	$0.618$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$-1$	$2$	$-1$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\cdots$
1239.1.j.d	$1239$	$1$	1239.j	1239.j	$6$	$2$	$1$	$0.618$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$1$	$1$	$-1$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
1239.1.j.e	$1239$	$1$	1239.j	1239.j	$6$	$2$	$1$	$0.618$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$1$	$1$	$2$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
1239.1.j.f	$1239$	$1$	1239.j	1239.j	$6$	$2$	$1$	$0.618$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$2$	$-1$	$-1$	$1$		$q+q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+q^{9}+\cdots$
1475.1.c.a	$1475$	$1$	1475.c	59.b	$2$	$1$	$1$	$0.736$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-295}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-q^{9}+q^{16}+2q^{19}+2q^{29}+\cdots$
1475.1.c.b	$1475$	$1$	1475.c	59.b	$2$	$1$	$1$	$0.736$	$\Q$	$D_{3}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$	$1$		$q+q^{3}+q^{4}+q^{7}+q^{12}+q^{16}-2q^{17}+\cdots$
1475.1.c.d	$1475$	$1$	1475.c	59.b	$2$	$2$	$2$	$0.736$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{3}+q^{4}+\beta q^{7}+2q^{9}-\beta q^{12}+\cdots$
1475.1.d.a	$1475$	$1$	1475.d	295.d	$2$	$2$	$2$	$0.736$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-q^{4}+iq^{7}+iq^{12}+q^{16}+\cdots$
1475.1.h.a	$1475$	$1$	1475.h	1475.h	$10$	$4$	$1$	$0.736$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$-5$	$-1$	$0$	$1$		$q+(-1-\zeta_{10})q^{3}+\zeta_{10}^{3}q^{4}+\zeta_{10}^{2}q^{5}+\cdots$
1475.1.h.b	$1475$	$1$	1475.h	1475.h	$10$	$8$	$2$	$0.736$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$5$	$1$	$0$	$1$		$q+(\zeta_{30}^{5}-\zeta_{30}^{13})q^{3}+\zeta_{30}^{9}q^{4}-\zeta_{30}^{11}q^{5}+\cdots$
1475.1.i.a	$1475$	$1$	1475.i	1475.i	$10$	$4$	$1$	$0.736$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$3$	$-1$	$-2$	$1$		$q+(1+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{3}q^{5}+\cdots$
1475.1.i.b	$1475$	$1$	1475.i	1475.i	$10$	$8$	$2$	$0.736$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$-3$	$1$	$2$	$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{10})q^{3}+\zeta_{30}^{6}q^{4}+\zeta_{30}^{4}q^{5}+\cdots$
1593.1.g.a	$1593$	$1$	1593.g	531.g	$6$	$6$	$3$	$0.795$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q-\zeta_{18}^{3}q^{4}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{5}+\cdots$
1593.1.l.a	$1593$	$1$	1593.l	1593.l	$18$	$18$	$3$	$0.795$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{17}q^{3}-\zeta_{54}^{15}q^{4}+(\zeta_{54}^{8}-\zeta_{54}^{13}+\cdots)q^{5}+\cdots$
1652.1.j.a	$1652$	$1$	1652.j	413.g	$6$	$6$	$3$	$0.824$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}^{7}+\zeta_{18}^{8})q^{3}+(-\zeta_{18}^{5}-\zeta_{18}^{7}+\cdots)q^{5}+\cdots$
1652.1.j.b	$1652$	$1$	1652.j	413.g	$6$	$6$	$3$	$0.824$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{3}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{5}+\cdots$
1711.1.d.a	$1711$	$1$	1711.d	1711.d	$2$	$1$	$1$	$0.854$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-1711}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-q^{4}-2q^{5}-2q^{7}+q^{9}+q^{16}+2q^{20}+\cdots$
1711.1.d.b	$1711$	$1$	1711.d	1711.d	$2$	$2$	$2$	$0.854$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$2$	$2$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-q^{4}+q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots$
1711.1.h.a	$1711$	$1$	1711.h	1711.h	$14$	$6$	$1$	$0.854$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$-7$	$2$	$2$	$1$		$q+(-1+\zeta_{14}^{6})q^{3}-\zeta_{14}^{4}q^{4}+(\zeta_{14}^{5}+\cdots)q^{5}+\cdots$
1711.1.h.b	$1711$	$1$	1711.h	1711.h	$14$	$12$	$2$	$0.854$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$7$	$-2$	$-2$	$1$		$q+(-\zeta_{42}^{5}+\zeta_{42}^{7})q^{3}+\zeta_{42}^{15}q^{4}+\cdots$

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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.