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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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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
460.1.d.a	$460$	$1$	460.d	115.c	$2$	$1$	$1$	$0.230$	$\Q$	$D_{3}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$1$	$1$		$q-q^{5}+q^{7}+q^{9}+q^{17}-q^{23}+q^{25}+\cdots$
460.1.d.b	$460$	$1$	460.d	115.c	$2$	$1$	$1$	$0.230$	$\Q$	$D_{3}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$-1$	$1$		$q+q^{5}-q^{7}+q^{9}-q^{17}+q^{23}+q^{25}+\cdots$
805.1.t.a	$805$	$1$	805.t	805.t	$6$	$2$	$1$	$0.402$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
805.1.t.b	$805$	$1$	805.t	805.t	$6$	$2$	$1$	$0.402$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$1$	$1$	$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
1035.1.d.a	$1035$	$1$	1035.d	115.c	$2$	$1$	$1$	$0.517$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-115}) $	$\Q(\sqrt{69}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+q^{4}-q^{5}+q^{16}+2q^{17}-q^{20}+\cdots$
1035.1.d.b	$1035$	$1$	1035.d	115.c	$2$	$1$	$1$	$0.517$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-115}) $	$\Q(\sqrt{69}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{4}+q^{5}+q^{16}-2q^{17}+q^{20}+\cdots$
1840.1.g.a	$1840$	$1$	1840.g	115.c	$2$	$1$	$1$	$0.918$	$\Q$	$D_{3}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q-q^{5}-q^{7}+q^{9}+q^{17}+q^{23}+q^{25}+\cdots$
1840.1.g.b	$1840$	$1$	1840.g	115.c	$2$	$1$	$1$	$0.918$	$\Q$	$D_{3}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$1$	$1$		$q+q^{5}+q^{7}+q^{9}-q^{17}-q^{23}+q^{25}+\cdots$
1955.1.d.e	$1955$	$1$	1955.d	1955.d	$2$	$2$	$2$	$0.976$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-115}) $, $\Q(\sqrt{-391}) $	$\Q(\sqrt{85}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-iq^{5}-iq^{7}-q^{9}+q^{16}+iq^{17}+\cdots$
1955.1.t.a	$1955$	$1$	1955.t	1955.t	$4$	$4$	$2$	$0.976$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{2}q^{9}+q^{16}-\zeta_{8}q^{17}+\cdots$
1955.1.z.a	$1955$	$1$	1955.z	1955.z	$8$	$8$	$2$	$0.976$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{4}q^{4}+\zeta_{16}^{5}q^{5}+(\zeta_{16}+\zeta_{16}^{5}+\cdots)q^{7}+\cdots$
2300.1.f.a	$2300$	$1$	2300.f	23.b	$2$	$2$	$2$	$1.148$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{7}-q^{9}-iq^{17}-iq^{23}+q^{29}+\cdots$
2875.1.c.a	$2875$	$1$	2875.c	115.c	$2$	$2$	$2$	$1.435$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-1$	$1$		$q+q^{4}+(-1+\beta )q^{7}+q^{9}+q^{16}-\beta q^{17}+\cdots$
2875.1.c.b	$2875$	$1$	2875.c	115.c	$2$	$2$	$2$	$1.435$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$1$	$1$		$q+q^{4}+(1-\beta )q^{7}+q^{9}+q^{16}+\beta q^{17}+\cdots$
2875.1.d.a	$2875$	$1$	2875.d	23.b	$2$	$4$	$4$	$1.435$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}-\beta _{1}q^{7}-q^{9}+q^{16}+(\beta _{1}+\beta _{3})q^{17}+\cdots$
3220.1.bl.a	$3220$	$1$	3220.bl	805.t	$6$	$2$	$1$	$1.607$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{17}+\cdots$
3220.1.bl.b	$3220$	$1$	3220.bl	805.t	$6$	$2$	$1$	$1.607$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$-1$	$2$	$1$		$q+\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{17}+\cdots$
3220.1.bl.c	$3220$	$1$	3220.bl	805.t	$6$	$2$	$1$	$1.607$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$1$	$-2$	$1$		$q-\zeta_{6}^{2}q^{5}-q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{17}+\cdots$
3220.1.bl.d	$3220$	$1$	3220.bl	805.t	$6$	$2$	$1$	$1.607$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$1$	$1$	$1$		$q-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{17}+\cdots$
3335.1.h.a	$3335$	$1$	3335.h	3335.h	$2$	$1$	$1$	$1.664$	$\Q$	$D_{2}$	$\Q(\sqrt{-115}) $, $\Q(\sqrt{-3335}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$-1$	$2$	$1$		$q-q^{4}-q^{5}+2q^{7}-q^{9}+q^{16}+q^{20}+\cdots$
3335.1.h.b	$3335$	$1$	3335.h	3335.h	$2$	$1$	$1$	$1.664$	$\Q$	$D_{2}$	$\Q(\sqrt{-115}) $, $\Q(\sqrt{-3335}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$1$	$-2$	$1$		$q-q^{4}+q^{5}-2q^{7}-q^{9}+q^{16}-q^{20}+\cdots$
3335.1.w.a	$3335$	$1$	3335.w	3335.w	$14$	$6$	$1$	$1.664$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$-1$	$2$	$1$		$q-\zeta_{14}^{6}q^{4}-\zeta_{14}^{3}q^{5}+(\zeta_{14}^{3}-\zeta_{14}^{6}+\cdots)q^{7}+\cdots$
3335.1.w.b	$3335$	$1$	3335.w	3335.w	$14$	$6$	$1$	$1.664$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$1$	$-2$	$1$		$q-\zeta_{14}^{6}q^{4}+\zeta_{14}^{3}q^{5}+(-\zeta_{14}^{3}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots$
3335.1.ba.a	$3335$	$1$	3335.ba	3335.aa	$14$	$6$	$1$	$1.664$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$-1$	$-2$	$1$		$q-\zeta_{14}q^{4}+\zeta_{14}^{4}q^{5}+(-\zeta_{14}+\zeta_{14}^{4}+\cdots)q^{7}+\cdots$
3335.1.ba.b	$3335$	$1$	3335.ba	3335.aa	$14$	$6$	$1$	$1.664$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$1$	$2$	$1$		$q-\zeta_{14}q^{4}-\zeta_{14}^{4}q^{5}+(\zeta_{14}-\zeta_{14}^{4}+\cdots)q^{7}+\cdots$
3565.1.q.a	$3565$	$1$	3565.q	3565.q	$6$	$2$	$1$	$1.779$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$-1$	$-2$	$1$		$q+q^{4}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+q^{16}+\cdots$
3565.1.q.b	$3565$	$1$	3565.q	3565.q	$6$	$2$	$1$	$1.779$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$1$	$2$	$1$		$q+q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+q^{16}+\cdots$
3565.1.ba.a	$3565$	$1$	3565.ba	3565.aa	$10$	$4$	$1$	$1.779$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$-4$	$-3$	$1$		$q+\zeta_{10}^{4}q^{4}-q^{5}+(-1+\zeta_{10}^{3})q^{7}+\cdots$
3565.1.ba.b	$3565$	$1$	3565.ba	3565.aa	$10$	$4$	$1$	$1.779$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$4$	$3$	$1$		$q+\zeta_{10}^{4}q^{4}+q^{5}+(1-\zeta_{10}^{3})q^{7}-\zeta_{10}q^{9}+\cdots$
3565.1.bx.a	$3565$	$1$	3565.bx	3565.ax	$30$	$8$	$1$	$1.779$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$-4$	$-3$	$1$		$q-\zeta_{30}^{9}q^{4}+\zeta_{30}^{10}q^{5}+(-\zeta_{30}^{5}+\cdots)q^{7}+\cdots$
3565.1.bx.b	$3565$	$1$	3565.bx	3565.ax	$30$	$8$	$1$	$1.779$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$4$	$3$	$1$		$q-\zeta_{30}^{9}q^{4}-\zeta_{30}^{10}q^{5}+(\zeta_{30}^{5}-\zeta_{30}^{8}+\cdots)q^{7}+\cdots$
115.3.c.a	$115$	$3$	115.c	115.c	$2$	$1$	$1$	$3.134$	$\Q$	$_{}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$-5$	$9$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}-5q^{5}+9q^{7}+9q^{9}+2^{4}q^{16}+\cdots$
115.3.c.b	$115$	$3$	115.c	115.c	$2$	$1$	$1$	$3.134$	$\Q$	$_{}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$5$	$-9$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+5q^{5}-9q^{7}+9q^{9}+2^{4}q^{16}+\cdots$
575.2.e.a	$575$	$2$	575.e	115.e	$4$	$4$	$2$	$4.591$	$\Q(i, \sqrt{46})$	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{4}]$	$q+2\beta _{2}q^{4}+\beta _{1}q^{7}-3\beta _{2}q^{9}-4q^{16}+\cdots$
805.2.d.a	$805$	$2$	805.d	805.d	$2$	$4$	$4$	$6.428$	$\Q(\sqrt{-5}, \sqrt{23})$	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}-3q^{9}+\cdots$
805.2.r.a	$805$	$2$	805.r	805.r	$6$	$8$	$4$	$6.428$	8.0.$\cdots$.4	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+2\beta _{3}q^{4}+(\beta _{4}+\beta _{5})q^{5}+\beta _{1}q^{7}+(3+\cdots)q^{9}+\cdots$
1035.2.h.a	$1035$	$2$	1035.h	345.h	$2$	$8$	$8$	$8.265$	8.0.$\cdots$.5	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{4}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}+\beta _{1}q^{5}+\beta _{4}q^{7}+4q^{16}-\beta _{5}q^{17}+\cdots$
115.5.c.a	$115$	$5$	115.c	115.c	$2$	$1$	$1$	$11.888$	$\Q$	$_{}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$-25$	$17$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}-5^{2}q^{5}+17q^{7}+3^{4}q^{9}+\cdots$
115.5.c.b	$115$	$5$	115.c	115.c	$2$	$1$	$1$	$11.888$	$\Q$	$_{}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$25$	$-17$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+5^{2}q^{5}-17q^{7}+3^{4}q^{9}+\cdots$
460.3.d.a	$460$	$3$	460.d	115.c	$2$	$2$	$2$	$12.534$	$\Q(\sqrt{345}) $	$_{}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$-10$	$-9$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-5q^{5}+(-4-\beta )q^{7}+9q^{9}+(4+3\beta )q^{17}+\cdots$
460.3.d.b	$460$	$3$	460.d	115.c	$2$	$2$	$2$	$12.534$	$\Q(\sqrt{345}) $	$_{}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$10$	$9$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+5q^{5}+(4+\beta )q^{7}+9q^{9}+(-4-3\beta )q^{17}+\cdots$
1840.2.m.b	$1840$	$2$	1840.m	460.g	$2$	$4$	$4$	$14.692$	$\Q(\sqrt{5}, \sqrt{-23})$	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}-\beta _{2}q^{7}-3q^{9}+3\beta _{1}q^{17}+\cdots$
1840.2.m.e	$1840$	$2$	1840.m	460.g	$2$	$8$	$8$	$14.692$	8.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}+\beta _{7}q^{7}-3q^{9}+(-\beta _{1}+\beta _{4}+\cdots)q^{17}+\cdots$
575.3.d.a	$575$	$3$	575.d	23.b	$2$	$2$	$2$	$15.668$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{4}+9iq^{7}-9q^{9}+2^{4}q^{16}-11iq^{17}+\cdots$
2300.2.i.a	$2300$	$2$	2300.i	115.e	$4$	$8$	$4$	$18.366$	8.0.$\cdots$.122	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{1}q^{7}-3\beta _{2}q^{9}+(\beta _{1}-2\beta _{5})q^{17}+\cdots$
3220.2.m.a	$3220$	$2$	3220.m	805.d	$2$	$8$	$8$	$25.712$	8.0.$\cdots$.4	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{4}q^{5}-\beta _{1}q^{7}-3q^{9}+(\beta _{1}-2\beta _{4}+\cdots)q^{17}+\cdots$
115.7.c.a	$115$	$7$	115.c	115.c	$2$	$1$	$1$	$26.456$	$\Q$	$_{}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$-125$	$-594$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{6}q^{4}-5^{3}q^{5}-594q^{7}+3^{6}q^{9}+\cdots$
115.7.c.b	$115$	$7$	115.c	115.c	$2$	$1$	$1$	$26.456$	$\Q$	$_{}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$125$	$594$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{6}q^{4}+5^{3}q^{5}+594q^{7}+3^{6}q^{9}+\cdots$
4140.2.n.a	$4140$	$2$	4140.n	345.h	$2$	$16$	$16$	$33.058$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{10}\cdot 3^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{5}-\beta _{12}q^{7}+(\beta _{5}-\beta _{7})q^{17}+\cdots$
115.9.c.a	$115$	$9$	115.c	115.c	$2$	$1$	$1$	$46.849$	$\Q$	$_{}$	$\Q(\sqrt{-115}) $	None	✓	$2$	$0$	$0$	$0$	$-625$	$4513$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{8}q^{4}-5^{4}q^{5}+4513q^{7}+3^{8}q^{9}+\cdots$

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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.