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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
44.1.d.a	$44$	$1$	44.d	11.b	$2$	$1$	$1$	$0.022$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots$
55.1.d.a	$55$	$1$	55.d	55.d	$2$	$1$	$1$	$0.027$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots$
99.1.h.a	$99$	$1$	99.h	99.h	$6$	$2$	$1$	$0.049$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots$
165.1.l.a	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-q^{3}+iq^{4}+iq^{5}+q^{9}-iq^{11}+\cdots$
165.1.l.b	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}+iq^{4}-iq^{5}-q^{9}+iq^{11}+\cdots$
176.1.h.a	$176$	$1$	176.h	11.b	$2$	$1$	$1$	$0.088$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$0$	$1$		$q+q^{3}-q^{5}-q^{11}-q^{15}+q^{23}-q^{27}+\cdots$
220.1.e.a	$220$	$1$	220.e	55.d	$2$	$2$	$2$	$0.110$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-\zeta_{6}^{2}q^{5}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots$
253.1.k.a	$253$	$1$	253.k	253.k	$22$	$10$	$1$	$0.126$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(\zeta_{22}^{8}+\zeta_{22}^{10})q^{3}-\zeta_{22}^{5}q^{4}+(-\zeta_{22}+\cdots)q^{5}+\cdots$
275.1.c.a	$275$	$1$	275.c	11.b	$2$	$1$	$1$	$0.137$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-q^{9}-q^{11}+q^{16}-2q^{31}+\cdots$
275.1.s.a	$275$	$1$	275.s	275.s	$10$	$4$	$1$	$0.137$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+(\zeta_{10}-\zeta_{10}^{3})q^{3}-\zeta_{10}^{2}q^{4}-q^{5}+\cdots$
275.1.v.a	$275$	$1$	275.v	275.v	$10$	$4$	$1$	$0.137$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$4$	$0$	$1$		$q+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}+q^{5}+\cdots$
297.1.h.a	$297$	$1$	297.h	99.h	$6$	$2$	$1$	$0.148$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}-\zeta_{6}q^{16}+\cdots$
297.1.q.a	$297$	$1$	297.q	297.q	$18$	$6$	$1$	$0.148$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{2}q^{4}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{5}+\cdots$
341.1.l.a	$341$	$1$	341.l	341.l	$6$	$2$	$1$	$0.170$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$1$	$0$	$1$		$q-\zeta_{6}q^{3}+q^{4}-\zeta_{6}^{2}q^{5}+3\zeta_{6}^{2}q^{9}+\cdots$
341.1.z.a	$341$	$1$	341.z	341.z	$10$	$4$	$1$	$0.170$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}-\zeta_{10}q^{4}+(\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
341.1.by.a	$341$	$1$	341.by	341.ay	$30$	$8$	$1$	$0.170$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$-1$	$0$	$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{14})q^{3}-\zeta_{30}^{9}q^{4}+(\zeta_{30}^{8}+\cdots)q^{5}+\cdots$
363.1.b.a	$363$	$1$	363.b	3.b	$2$	$1$	$1$	$0.181$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}+q^{25}+\cdots$
363.1.h.a	$363$	$1$	363.h	33.h	$10$	$4$	$1$	$0.181$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{33}) $		$16$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}-\zeta_{10}^{3}q^{9}-q^{12}+\cdots$
396.1.f.a	$396$	$1$	396.f	11.b	$2$	$1$	$1$	$0.198$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{5}-q^{11}+q^{23}-q^{31}-q^{37}+\cdots$
396.1.m.a	$396$	$1$	396.m	99.h	$6$	$2$	$1$	$0.198$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$1$	$0$	$1$		$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+\cdots$
396.1.m.b	$396$	$1$	396.m	99.h	$6$	$2$	$1$	$0.198$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$-2$	$0$	$1$		$q+q^{3}+\zeta_{6}^{2}q^{5}+q^{9}-\zeta_{6}q^{11}+2\zeta_{6}^{2}q^{15}+\cdots$
407.1.d.a	$407$	$1$	407.d	407.d	$2$	$1$	$1$	$0.203$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-407}) $	$\Q(\sqrt{37}) $	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-2q^{3}-q^{4}+3q^{9}+q^{11}+2q^{12}+\cdots$
407.1.i.a	$407$	$1$	407.i	407.i	$6$	$2$	$1$	$0.203$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+q^{11}-\zeta_{6}^{2}q^{12}+\cdots$
407.1.j.a	$407$	$1$	407.j	407.j	$6$	$2$	$1$	$0.203$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$-2$	$0$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+q^{11}+\cdots$
407.1.t.a	$407$	$1$	407.t	407.t	$18$	$6$	$1$	$0.203$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+(\zeta_{18}^{2}+\zeta_{18}^{6})q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{5}+\cdots$
407.1.u.a	$407$	$1$	407.u	407.u	$18$	$6$	$1$	$0.203$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(-\zeta_{18}^{6}-\zeta_{18}^{8})q^{3}-\zeta_{18}^{4}q^{4}+\cdots$
484.1.f.a	$484$	$1$	484.f	11.d	$10$	$4$	$1$	$0.242$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$1$	$1$	$0$	$1$		$q-\zeta_{10}^{4}q^{3}-\zeta_{10}^{2}q^{5}-\zeta_{10}q^{15}+\cdots$
495.1.h.a	$495$	$1$	495.h	55.d	$2$	$1$	$1$	$0.247$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-q^{4}+q^{5}+q^{11}+q^{16}-q^{20}+q^{25}+\cdots$
495.1.o.a	$495$	$1$	495.o	495.o	$6$	$2$	$1$	$0.247$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$1$	$0$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
495.1.o.b	$495$	$1$	495.o	495.o	$6$	$2$	$1$	$0.247$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$-2$	$0$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}q^{4}-q^{5}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
495.1.bd.a	$495$	$1$	495.bd	495.ad	$12$	$4$	$1$	$0.247$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}q^{3}-\zeta_{12}q^{4}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{2}q^{9}+\cdots$
495.1.bd.b	$495$	$1$	495.bd	495.ad	$12$	$4$	$1$	$0.247$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\zeta_{12}^{4}q^{3}-\zeta_{12}q^{4}-\zeta_{12}^{5}q^{5}-\zeta_{12}^{2}q^{9}+\cdots$
517.1.k.a	$517$	$1$	517.k	517.k	$46$	$22$	$1$	$0.258$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(\zeta_{46}^{16}+\zeta_{46}^{20})q^{3}+\zeta_{46}^{14}q^{4}+\cdots$
33.2.d.a	$33$	$2$	33.d	33.d	$2$	$2$	$2$	$0.264$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}-2q^{4}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots$
528.1.g.a	$528$	$1$	528.g	132.d	$2$	$1$	$1$	$0.264$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-33}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{9}+q^{11}+2q^{23}+q^{25}+\cdots$
528.1.g.b	$528$	$1$	528.g	132.d	$2$	$1$	$1$	$0.264$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-33}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}-q^{11}-2q^{23}+q^{25}+\cdots$
528.1.g.c	$528$	$1$	528.g	132.d	$2$	$2$	$2$	$0.264$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots$
528.1.g.d	$528$	$1$	528.g	132.d	$2$	$2$	$2$	$0.264$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots$
539.1.c.a	$539$	$1$	539.c	11.b	$2$	$1$	$1$	$0.269$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{77}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-q^{9}+q^{11}+q^{16}-2q^{23}+\cdots$
539.1.c.b	$539$	$1$	539.c	11.b	$2$	$2$	$2$	$0.269$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{3}+q^{4}+\beta q^{5}+q^{9}-q^{11}-\beta q^{12}+\cdots$
539.1.h.a	$539$	$1$	539.h	77.h	$6$	$2$	$1$	$0.269$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{77}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}-\zeta_{6}q^{16}+\cdots$
539.1.h.b	$539$	$1$	539.h	77.h	$6$	$4$	$2$	$0.269$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
583.1.d.a	$583$	$1$	583.d	583.d	$2$	$1$	$1$	$0.291$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-583}) $	$\Q(\sqrt{53}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+q^{9}+q^{11}+q^{16}+q^{25}-q^{36}+\cdots$
583.1.n.a	$583$	$1$	583.n	583.n	$26$	$12$	$1$	$0.291$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{26}^{6}-\zeta_{26}^{11})q^{3}+\zeta_{26}q^{4}+\cdots$
583.1.o.a	$583$	$1$	583.o	583.o	$26$	$12$	$1$	$0.291$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(-\zeta_{26}^{9}+\zeta_{26}^{10})q^{3}+\zeta_{26}^{8}q^{4}+\cdots$
11.3.b.a	$11$	$3$	11.b	11.b	$2$	$1$	$1$	$0.300$	$\Q$	$_{}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$-5$	$-1$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-5q^{3}+4q^{4}-q^{5}+2^{4}q^{9}-11q^{11}+\cdots$
605.1.f.a	$605$	$1$	605.f	5.c	$4$	$2$	$1$	$0.302$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(1+i)q^{3}+iq^{4}-iq^{5}+iq^{9}+(-1+\cdots)q^{12}+\cdots$
605.1.h.a	$605$	$1$	605.h	55.h	$10$	$4$	$1$	$0.302$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $		$16$	$0$	$0$	$0$	$1$	$0$	$1$		$q+\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots$
605.1.l.a	$605$	$1$	605.l	55.k	$20$	$8$	$1$	$0.302$	$\Q(\zeta_{20})$	$D_{4}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(-\zeta_{20}-\zeta_{20}^{6})q^{3}-\zeta_{20}^{9}q^{4}-\zeta_{20}^{3}q^{5}+\cdots$
649.1.l.a	$649$	$1$	649.l	649.l	$58$	$28$	$1$	$0.324$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(\zeta_{58}^{8}-\zeta_{58}^{11})q^{3}-\zeta_{58}^{23}q^{4}+\cdots$

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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.