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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 (42 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
472.1.k.a	$472$	$1$	472.k	472.k	$58$	$28$	$1$	$0.236$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{58}^{4}q^{2}+(-\zeta_{58}^{5}+\zeta_{58}^{18})q^{3}+\cdots$
649.1.l.a	$649$	$1$	649.l	649.l	$58$	$28$	$1$	$0.324$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(\zeta_{58}^{8}-\zeta_{58}^{11})q^{3}-\zeta_{58}^{23}q^{4}+\cdots$
887.1.b.a	$887$	$1$	887.b	887.b	$2$	$14$	$14$	$0.443$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-887}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q-\beta _{11}q^{2}-\beta _{5}q^{3}+(1-\beta _{7})q^{4}+(\beta _{6}+\cdots)q^{6}+\cdots$
932.1.k.a	$932$	$1$	932.k	932.k	$58$	$28$	$1$	$0.465$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{58}^{21}q^{2}-\zeta_{58}^{13}q^{4}+(-\zeta_{58}^{9}+\cdots)q^{5}+\cdots$
1047.1.p.a	$1047$	$1$	1047.p	1047.p	$58$	$28$	$1$	$0.523$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{58}^{21}q^{3}-\zeta_{58}^{15}q^{4}+(-\zeta_{58}^{7}+\cdots)q^{7}+\cdots$
1357.1.j.a	$1357$	$1$	1357.j	1357.j	$58$	$28$	$1$	$0.677$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-2$	$-2$	$0$	$0$	$1$		$q+(\zeta_{58}^{22}-\zeta_{58}^{27})q^{2}+(\zeta_{58}^{20}-\zeta_{58}^{23}+\cdots)q^{3}+\cdots$
1396.1.p.a	$1396$	$1$	1396.p	1396.p	$58$	$28$	$1$	$0.697$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{58}^{4}q^{2}+\zeta_{58}^{8}q^{4}+(\zeta_{58}^{6}+\zeta_{58}^{12}+\cdots)q^{5}+\cdots$
1416.1.r.a	$1416$	$1$	1416.r	1416.r	$58$	$28$	$1$	$0.707$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$-2$	$-2$	$1$		$q+\zeta_{58}^{20}q^{2}+\zeta_{58}^{14}q^{3}-\zeta_{58}^{11}q^{4}+\cdots$
1416.1.r.b	$1416$	$1$	1416.r	1416.r	$58$	$28$	$1$	$0.707$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$2$	$-2$	$1$		$q-\zeta_{58}^{20}q^{2}-\zeta_{58}^{14}q^{3}-\zeta_{58}^{11}q^{4}+\cdots$
1569.1.p.a	$1569$	$1$	1569.p	1569.p	$58$	$28$	$1$	$0.783$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{58}^{9}q^{3}-\zeta_{58}^{15}q^{4}+(-\zeta_{58}^{13}+\cdots)q^{7}+\cdots$
1631.1.s.a	$1631$	$1$	1631.s	1631.s	$58$	$28$	$1$	$0.814$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(\zeta_{58}^{10}-\zeta_{58}^{23})q^{2}+(\zeta_{58}^{4}-\zeta_{58}^{17}+\cdots)q^{4}+\cdots$
1829.1.r.a	$1829$	$1$	1829.r	1829.r	$58$	$28$	$1$	$0.913$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$-2$	$-2$	$1$		$q+(\zeta_{58}^{8}-\zeta_{58}^{15})q^{2}+(-\zeta_{58}+\zeta_{58}^{16}+\cdots)q^{4}+\cdots$
1864.1.t.a	$1864$	$1$	1864.t	1864.t	$58$	$28$	$1$	$0.930$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{58}^{2}q^{2}+(\zeta_{58}^{8}-\zeta_{58}^{13})q^{3}+\zeta_{58}^{4}q^{4}+\cdots$
1888.1.s.a	$1888$	$1$	1888.s	472.k	$58$	$28$	$1$	$0.942$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(-\zeta_{58}^{24}-\zeta_{58}^{26})q^{3}+(-\zeta_{58}^{19}+\cdots)q^{9}+\cdots$
2231.1.d.a	$2231$	$1$	2231.d	2231.d	$2$	$14$	$14$	$1.113$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-2231}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q+\beta _{2}q^{2}-\beta _{13}q^{3}+(1+\beta _{4})q^{4}-\beta _{11}q^{5}+\cdots$
2231.1.d.b	$2231$	$1$	2231.d	2231.d	$2$	$14$	$14$	$1.113$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-2231}) $	None	✓	$2$	$0$	$-1$	$-1$	$1$	$1$	$1$		$q+\beta _{2}q^{2}-\beta _{13}q^{3}+(1+\beta _{4})q^{4}+\beta _{11}q^{5}+\cdots$
2287.1.b.a	$2287$	$1$	2287.b	2287.b	$2$	$14$	$14$	$1.141$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-2287}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-\beta _{11}q^{2}+(1-\beta _{7})q^{4}-\beta _{5}q^{7}+(\beta _{4}+\cdots)q^{8}+\cdots$
2301.1.z.a	$2301$	$1$	2301.z	2301.z	$58$	$28$	$1$	$1.148$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-2$	$-1$	$-2$	$0$	$1$		$q+(-\zeta_{58}^{7}+\zeta_{58}^{28})q^{2}-\zeta_{58}^{5}q^{3}+\cdots$
2301.1.z.b	$2301$	$1$	2301.z	2301.z	$58$	$28$	$1$	$1.148$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$2$	$-1$	$2$	$0$	$1$		$q+(\zeta_{58}^{7}-\zeta_{58}^{28})q^{2}-\zeta_{58}^{5}q^{3}+(\zeta_{58}^{6}+\cdots)q^{4}+\cdots$
2311.1.b.a	$2311$	$1$	2311.b	2311.b	$2$	$14$	$14$	$1.153$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-2311}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\beta _{11}q^{2}+(1-\beta _{7})q^{4}-\beta _{1}q^{5}+(\beta _{4}+\cdots)q^{8}+\cdots$
2360.1.bh.a	$2360$	$1$	2360.bh	2360.ah	$58$	$28$	$1$	$1.178$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-1$	$0$	$-1$	$-2$	$1$		$q+\zeta_{58}^{20}q^{2}-\zeta_{58}^{11}q^{4}+\zeta_{58}^{4}q^{5}+\cdots$
2360.1.bh.b	$2360$	$1$	2360.bh	2360.ah	$58$	$28$	$1$	$1.178$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$1$	$0$	$1$	$2$	$1$		$q-\zeta_{58}^{20}q^{2}-\zeta_{58}^{11}q^{4}-\zeta_{58}^{4}q^{5}+\cdots$
2383.1.b.a	$2383$	$1$	2383.b	2383.b	$2$	$14$	$14$	$1.189$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-2383}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-\beta _{11}q^{2}+(1-\beta _{7})q^{4}+\beta _{6}q^{7}+(\beta _{4}+\cdots)q^{8}+\cdots$
2537.1.t.a	$2537$	$1$	2537.t	2537.t	$58$	$28$	$1$	$1.266$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{58}^{17}q^{4}-\zeta_{58}^{9}q^{9}+(-\zeta_{58}^{21}+\cdots)q^{11}+\cdots$
2773.1.j.a	$2773$	$1$	2773.j	2773.j	$58$	$28$	$1$	$1.384$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-2$	$-2$	$0$	$-2$	$1$		$q+(\zeta_{58}^{8}-\zeta_{58}^{17})q^{2}+(-\zeta_{58}^{15}-\zeta_{58}^{17}+\cdots)q^{3}+\cdots$
2939.1.b.a	$2939$	$1$	2939.b	2939.b	$2$	$14$	$14$	$1.467$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-2939}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-\beta _{11}q^{3}+q^{4}-\beta _{13}q^{5}+\beta _{12}q^{7}+\cdots$
3068.1.be.a	$3068$	$1$	3068.be	3068.ae	$58$	$28$	$1$	$1.531$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-1$	$0$	$0$	$-2$	$1$		$q+\zeta_{58}^{4}q^{2}+\zeta_{58}^{8}q^{4}+(\zeta_{58}^{10}+\zeta_{58}^{18}+\cdots)q^{7}+\cdots$
3068.1.be.b	$3068$	$1$	3068.be	3068.ae	$58$	$28$	$1$	$1.531$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$1$	$0$	$0$	$2$	$1$		$q-\zeta_{58}^{4}q^{2}+\zeta_{58}^{8}q^{4}+(-\zeta_{58}^{10}+\cdots)q^{7}+\cdots$
3245.1.ba.a	$3245$	$1$	3245.ba	3245.aa	$58$	$28$	$1$	$1.619$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$-2$	$0$	$-1$	$-2$	$1$		$q+(-\zeta_{58}^{5}+\zeta_{58}^{28})q^{2}+(\zeta_{58}^{4}+\zeta_{58}^{10}+\cdots)q^{4}+\cdots$
3245.1.ba.d	$3245$	$1$	3245.ba	3245.aa	$58$	$28$	$1$	$1.619$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$2$	$0$	$-1$	$2$	$1$		$q+(\zeta_{58}^{5}-\zeta_{58}^{28})q^{2}+(\zeta_{58}^{4}+\zeta_{58}^{10}+\cdots)q^{4}+\cdots$
3304.1.bi.a	$3304$	$1$	3304.bi	3304.ai	$58$	$28$	$1$	$1.649$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$-1$	$-2$	$-2$	$-1$	$1$		$q+\zeta_{58}^{24}q^{2}+(-\zeta_{58}^{3}-\zeta_{58}^{19})q^{3}+\cdots$
3304.1.bi.b	$3304$	$1$	3304.bi	3304.ai	$58$	$28$	$1$	$1.649$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$-1$	$2$	$2$	$-1$	$1$		$q+\zeta_{58}^{24}q^{2}+(\zeta_{58}^{3}+\zeta_{58}^{19})q^{3}+\cdots$
3364.1.p.a	$3364$	$1$	3364.p	3364.p	$58$	$28$	$1$	$1.679$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{58}^{15}q^{2}-\zeta_{58}q^{4}+(\zeta_{58}^{2}+\zeta_{58}^{10}+\cdots)q^{5}+\cdots$
3495.1.bf.a	$3495$	$1$	3495.bf	3495.af	$58$	$28$	$1$	$1.744$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(\zeta_{58}^{20}-\zeta_{58}^{21})q^{2}-\zeta_{58}^{17}q^{3}+\cdots$
3495.1.bf.b	$3495$	$1$	3495.bf	3495.af	$58$	$28$	$1$	$1.744$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(-\zeta_{58}^{20}+\zeta_{58}^{21})q^{2}+\zeta_{58}^{17}q^{3}+\cdots$
3551.1.d.a	$3551$	$1$	3551.d	3551.d	$2$	$14$	$14$	$1.772$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-3551}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q-\beta _{11}q^{2}-\beta _{5}q^{3}+(1-\beta _{7})q^{4}-\beta _{13}q^{5}+\cdots$
3551.1.d.b	$3551$	$1$	3551.d	3551.d	$2$	$14$	$14$	$1.772$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-3551}) $	None	✓	$2$	$0$	$1$	$1$	$1$	$0$	$1$		$q+\beta _{11}q^{2}+\beta _{5}q^{3}+(1-\beta _{7})q^{4}+\beta _{13}q^{5}+\cdots$
3583.1.b.a	$3583$	$1$	3583.b	3583.b	$2$	$14$	$14$	$1.788$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-3583}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-\beta _{11}q^{2}+(1-\beta _{7})q^{4}+\beta _{10}q^{7}+(\beta _{4}+\cdots)q^{8}+\cdots$
3659.1.b.a	$3659$	$1$	3659.b	3659.b	$2$	$14$	$14$	$1.826$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-3659}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-\beta _{11}q^{3}+q^{4}+\beta _{12}q^{5}+\beta _{8}q^{7}+\cdots$
3716.1.p.a	$3716$	$1$	3716.p	3716.p	$58$	$28$	$1$	$1.855$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{58}^{14}q^{2}+\zeta_{58}^{28}q^{4}+(\zeta_{58}^{6}+\zeta_{58}^{26}+\cdots)q^{5}+\cdots$
3823.1.b.a	$3823$	$1$	3823.b	3823.b	$2$	$14$	$14$	$1.908$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-3823}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\beta _{11}q^{2}+(1-\beta _{7})q^{4}+(\beta _{4}-\beta _{11}+\cdots)q^{8}+\cdots$
3953.1.q.a	$3953$	$1$	3953.q	3953.q	$58$	$28$	$1$	$1.973$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{58}^{19}q^{4}+\zeta_{58}^{22}q^{9}-\zeta_{58}^{9}q^{16}+\cdots$

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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.