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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
191.1.b.a	$191$	$1$	191.b	191.b	$2$	$6$	$6$	$0.095$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-191}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q-\beta _{3}q^{2}-\beta _{1}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
212.1.i.a	$212$	$1$	212.i	212.i	$26$	$12$	$1$	$0.106$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{26}^{6}q^{2}+\zeta_{26}^{12}q^{4}+(\zeta_{26}^{8}+\zeta_{26}^{10}+\cdots)q^{5}+\cdots$
237.1.k.a	$237$	$1$	237.k	237.k	$26$	$12$	$1$	$0.118$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{26}^{2}q^{3}-\zeta_{26}^{3}q^{4}+(\zeta_{26}^{8}-\zeta_{26}^{9}+\cdots)q^{7}+\cdots$
263.1.b.a	$263$	$1$	263.b	263.b	$2$	$6$	$6$	$0.131$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-263}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-\beta _{3}q^{2}+\beta _{2}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
371.1.n.a	$371$	$1$	371.n	371.n	$26$	$12$	$1$	$0.185$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{26}+\zeta_{26}^{6})q^{2}+(\zeta_{26}^{2}-\zeta_{26}^{7}+\cdots)q^{4}+\cdots$
471.1.o.a	$471$	$1$	471.o	471.o	$26$	$12$	$1$	$0.235$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{26}^{3}q^{3}+\zeta_{26}^{10}q^{4}+(-\zeta_{26}-\zeta_{26}^{5}+\cdots)q^{7}+\cdots$
507.1.o.a	$507$	$1$	507.o	507.o	$26$	$12$	$1$	$0.253$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{26}^{7}q^{3}+\zeta_{26}^{2}q^{4}+(-\zeta_{26}^{9}+\zeta_{26}^{10}+\cdots)q^{7}+\cdots$
551.1.d.a	$551$	$1$	551.d	551.d	$2$	$6$	$6$	$0.275$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-551}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q-\beta _{3}q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
551.1.d.b	$551$	$1$	551.d	551.d	$2$	$6$	$6$	$0.275$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-551}) $	None	✓	$2$	$0$	$1$	$1$	$-1$	$-1$	$1$		$q+\beta _{3}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$
553.1.x.a	$553$	$1$	553.x	553.x	$26$	$12$	$1$	$0.276$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(\zeta_{26}^{2}+\zeta_{26}^{12})q^{2}+(-\zeta_{26}+\zeta_{26}^{4}+\cdots)q^{4}+\cdots$
583.1.o.a	$583$	$1$	583.o	583.o	$26$	$12$	$1$	$0.291$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(-\zeta_{26}^{9}+\zeta_{26}^{10})q^{3}+\zeta_{26}^{8}q^{4}+\cdots$
607.1.b.a	$607$	$1$	607.b	607.b	$2$	$6$	$6$	$0.303$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-607}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
628.1.o.a	$628$	$1$	628.o	628.o	$26$	$12$	$1$	$0.313$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{26}^{5}q^{2}+\zeta_{26}^{10}q^{4}+(\zeta_{26}^{10}-\zeta_{26}^{11}+\cdots)q^{5}+\cdots$
631.1.b.a	$631$	$1$	631.b	631.b	$2$	$6$	$6$	$0.315$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-631}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
676.1.o.a	$676$	$1$	676.o	676.o	$26$	$12$	$1$	$0.337$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{26}^{8}q^{2}-\zeta_{26}^{3}q^{4}+(\zeta_{26}^{2}+\zeta_{26}^{12}+\cdots)q^{5}+\cdots$
727.1.b.a	$727$	$1$	727.b	727.b	$2$	$6$	$6$	$0.363$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-727}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
795.1.x.a	$795$	$1$	795.x	795.x	$26$	$12$	$1$	$0.397$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(-\zeta_{26}^{7}+\zeta_{26}^{10})q^{2}+\zeta_{26}^{8}q^{3}+\cdots$
795.1.x.b	$795$	$1$	795.x	795.x	$26$	$12$	$1$	$0.397$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(\zeta_{26}^{7}-\zeta_{26}^{10})q^{2}-\zeta_{26}^{8}q^{3}+(-\zeta_{26}+\cdots)q^{4}+\cdots$
939.1.s.a	$939$	$1$	939.s	939.s	$26$	$12$	$1$	$0.469$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{26}^{7}q^{3}+\zeta_{26}^{10}q^{4}+(-\zeta_{26}^{9}+\cdots)q^{7}+\cdots$
951.1.d.a	$951$	$1$	951.d	951.d	$2$	$6$	$6$	$0.475$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-951}) $	None	✓	$2$	$0$	$-1$	$6$	$-1$	$-1$	$1$		$q-\beta _{3}q^{2}+q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
951.1.d.b	$951$	$1$	951.d	951.d	$2$	$6$	$6$	$0.475$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-951}) $	None	✓	$2$	$0$	$1$	$-6$	$1$	$-1$	$1$		$q+\beta _{3}q^{2}-q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
1019.1.b.a	$1019$	$1$	1019.b	1019.b	$2$	$6$	$6$	$0.509$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1019}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q-\beta _{3}q^{3}+q^{4}+\beta _{2}q^{5}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots$
1048.1.s.a	$1048$	$1$	1048.s	1048.s	$26$	$12$	$1$	$0.523$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-\zeta_{26}^{5}q^{2}+(\zeta_{26}^{2}-\zeta_{26}^{3})q^{3}+\zeta_{26}^{10}q^{4}+\cdots$
1185.1.bb.a	$1185$	$1$	1185.bb	1185.ab	$26$	$12$	$1$	$0.591$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(\zeta_{26}^{4}+\zeta_{26}^{6})q^{2}-\zeta_{26}^{11}q^{3}+(\zeta_{26}^{8}+\cdots)q^{4}+\cdots$
1185.1.bb.b	$1185$	$1$	1185.bb	1185.ab	$26$	$12$	$1$	$0.591$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(-\zeta_{26}^{4}-\zeta_{26}^{6})q^{2}+\zeta_{26}^{11}q^{3}+\cdots$
1247.1.d.a	$1247$	$1$	1247.d	1247.d	$2$	$6$	$6$	$0.622$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1247}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-\beta _{3}q^{2}-\beta _{5}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
1247.1.d.b	$1247$	$1$	1247.d	1247.d	$2$	$6$	$6$	$0.622$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1247}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$0$	$1$		$q+\beta _{3}q^{2}+\beta _{5}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
1252.1.t.a	$1252$	$1$	1252.t	1252.t	$26$	$12$	$1$	$0.625$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{26}^{8}q^{2}-\zeta_{26}^{3}q^{4}+(-\zeta_{26}^{3}+\zeta_{26}^{10}+\cdots)q^{5}+\cdots$
1256.1.h.a	$1256$	$1$	1256.h	1256.h	$2$	$6$	$6$	$0.627$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-314}) $	None	✓	$2$	$0$	$-6$	$-1$	$1$	$1$	$1$		$q-q^{2}-\beta _{3}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{3}q^{6}+\cdots$
1256.1.h.b	$1256$	$1$	1256.h	1256.h	$2$	$6$	$6$	$0.627$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-314}) $	None	✓	$2$	$0$	$6$	$-1$	$-1$	$-1$	$1$		$q+q^{2}-\beta _{3}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{3}q^{6}+\cdots$
1272.1.z.a	$1272$	$1$	1272.z	1272.z	$26$	$12$	$1$	$0.635$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$-2$	$-2$	$1$		$q+\zeta_{26}^{10}q^{2}-\zeta_{26}q^{3}-\zeta_{26}^{7}q^{4}+\cdots$
1272.1.z.b	$1272$	$1$	1272.z	1272.z	$26$	$12$	$1$	$0.635$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$2$	$-2$	$1$		$q-\zeta_{26}^{10}q^{2}+\zeta_{26}q^{3}-\zeta_{26}^{7}q^{4}+\cdots$
1439.1.b.b	$1439$	$1$	1439.b	1439.b	$2$	$6$	$6$	$0.718$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1439}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
1451.1.b.a	$1451$	$1$	1451.b	1451.b	$2$	$6$	$6$	$0.724$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1451}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q-\beta _{3}q^{3}+q^{4}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots$
1499.1.b.a	$1499$	$1$	1499.b	1499.b	$2$	$6$	$6$	$0.748$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1499}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q-\beta _{3}q^{3}+q^{4}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots$
1641.1.p.a	$1641$	$1$	1641.p	1641.p	$26$	$12$	$1$	$0.819$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$12$	$0$	$-2$	$1$		$q+q^{3}+\zeta_{26}^{4}q^{4}+(-\zeta_{26}+\zeta_{26}^{8}+\cdots)q^{7}+\cdots$
1667.1.b.a	$1667$	$1$	1667.b	1667.b	$2$	$6$	$6$	$0.832$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1667}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-\beta _{3}q^{3}+q^{4}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{9}+\cdots$
1679.1.d.c	$1679$	$1$	1679.d	1679.d	$2$	$6$	$6$	$0.838$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1679}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q+\beta _{4}q^{2}-\beta _{1}q^{3}+(1-\beta _{5})q^{4}-\beta _{3}q^{5}+\cdots$
1679.1.d.d	$1679$	$1$	1679.d	1679.d	$2$	$6$	$6$	$0.838$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1679}) $	None	✓	$2$	$0$	$-1$	$-1$	$1$	$1$	$1$		$q+\beta _{4}q^{2}-\beta _{1}q^{3}+(1-\beta _{5})q^{4}+\beta _{3}q^{5}+\cdots$
1719.1.d.a	$1719$	$1$	1719.d	191.b	$2$	$6$	$6$	$0.858$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-191}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$	$1$		$q+\beta _{3}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
1727.1.v.a	$1727$	$1$	1727.v	1727.v	$26$	$12$	$1$	$0.862$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$11$	$0$	$1$		$q+(\zeta_{26}^{8}+\zeta_{26}^{10})q^{3}+\zeta_{26}^{4}q^{4}+(1+\cdots)q^{5}+\cdots$
1735.1.d.a	$1735$	$1$	1735.d	1735.d	$2$	$6$	$6$	$0.866$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1735}) $	None	✓	$2$	$0$	$-1$	$0$	$6$	$-1$	$1$		$q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
1735.1.d.b	$1735$	$1$	1735.d	1735.d	$2$	$6$	$6$	$0.866$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1735}) $	None	✓	$2$	$0$	$1$	$0$	$-6$	$1$	$1$		$q+\beta _{3}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
1832.1.g.a	$1832$	$1$	1832.g	1832.g	$2$	$6$	$6$	$0.914$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-458}) $	None	✓	$2$	$0$	$-6$	$-1$	$0$	$1$	$1$		$q-q^{2}-\beta _{3}q^{3}+q^{4}+\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots$
1832.1.g.b	$1832$	$1$	1832.g	1832.g	$2$	$6$	$6$	$0.914$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-458}) $	None	✓	$2$	$0$	$6$	$-1$	$0$	$-1$	$1$		$q+q^{2}-\beta _{3}q^{3}+q^{4}-\beta _{3}q^{6}-\beta _{1}q^{7}+\cdots$
1896.1.bh.a	$1896$	$1$	1896.bh	1896.ah	$26$	$12$	$1$	$0.946$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$11$	$-2$	$1$		$q+\zeta_{26}^{4}q^{2}-\zeta_{26}q^{3}+\zeta_{26}^{8}q^{4}+(1+\cdots)q^{5}+\cdots$
1896.1.bh.b	$1896$	$1$	1896.bh	1896.ah	$26$	$12$	$1$	$0.946$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$-11$	$-2$	$1$		$q-\zeta_{26}^{4}q^{2}+\zeta_{26}q^{3}+\zeta_{26}^{8}q^{4}+(-1+\cdots)q^{5}+\cdots$
1907.1.b.a	$1907$	$1$	1907.b	1907.b	$2$	$6$	$6$	$0.952$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1907}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-\beta _{3}q^{3}+q^{4}-\beta _{1}q^{7}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots$
1908.1.bb.a	$1908$	$1$	1908.bb	212.i	$26$	$12$	$1$	$0.952$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q+\zeta_{26}^{5}q^{2}+\zeta_{26}^{10}q^{4}+(-\zeta_{26}^{4}+\cdots)q^{5}+\cdots$
2015.1.h.b	$2015$	$1$	2015.h	2015.h	$2$	$6$	$6$	$1.006$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2015}) $	None	✓	$2$	$0$	$-1$	$-1$	$6$	$-1$	$1$		$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$

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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.