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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
39.1.d.a	$39$	$1$	39.d	39.d	$2$	$1$	$1$	$0.019$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
208.1.c.a	$208$	$1$	208.c	52.b	$2$	$1$	$1$	$0.104$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-q^{13}-2q^{17}+q^{25}-2q^{29}+\cdots$
299.1.c.a	$299$	$1$	299.c	299.c	$2$	$1$	$1$	$0.149$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-299}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-2q^{3}+q^{4}+3q^{9}-2q^{12}+q^{13}+\cdots$
468.1.z.a	$468$	$1$	468.z	117.n	$6$	$2$	$1$	$0.234$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+(-\zeta_{6}+\cdots)q^{17}+\cdots$
507.1.c.a	$507$	$1$	507.c	3.b	$2$	$1$	$1$	$0.253$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}+q^{25}+\cdots$
507.1.h.a	$507$	$1$	507.h	39.h	$6$	$2$	$1$	$0.253$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$1$	$0$	$0$	$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}+q^{12}+\cdots$
507.1.i.a	$507$	$1$	507.i	39.i	$6$	$2$	$1$	$0.253$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{9}-q^{12}+\cdots$
559.1.d.a	$559$	$1$	559.d	559.d	$2$	$1$	$1$	$0.279$	$\Q$	$D_{2}$	$\Q(\sqrt{-43}) $, $\Q(\sqrt{-559}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+q^{9}+q^{13}+q^{16}+2q^{17}+\cdots$
624.1.l.a	$624$	$1$	624.l	39.d	$2$	$1$	$1$	$0.311$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}-q^{13}-q^{25}+q^{27}-q^{39}+\cdots$
663.1.g.a	$663$	$1$	663.g	663.g	$2$	$1$	$1$	$0.331$	$\Q$	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-663}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}-q^{4}+q^{9}+q^{12}+q^{13}+q^{16}+\cdots$
663.1.g.b	$663$	$1$	663.g	663.g	$2$	$1$	$1$	$0.331$	$\Q$	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-663}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots$
689.1.i.a	$689$	$1$	689.i	689.i	$4$	$2$	$1$	$0.344$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(1+i)q^{3}+iq^{4}+iq^{9}+(-1+i+\cdots)q^{12}+\cdots$
793.1.k.a	$793$	$1$	793.k	793.k	$4$	$2$	$1$	$0.396$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{3}+iq^{4}-3q^{9}-2q^{12}+q^{13}+\cdots$
832.1.c.a	$832$	$1$	832.c	52.b	$2$	$1$	$1$	$0.415$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}+q^{13}-2q^{17}+q^{25}+2q^{29}+\cdots$
975.1.e.a	$975$	$1$	975.e	195.e	$2$	$2$	$2$	$0.487$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}+q^{4}-q^{9}-iq^{12}-iq^{13}+\cdots$
975.1.g.a	$975$	$1$	975.g	39.d	$2$	$1$	$1$	$0.487$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots$
1027.1.b.a	$1027$	$1$	1027.b	1027.b	$2$	$1$	$1$	$0.513$	$\Q$	$D_{2}$	$\Q(\sqrt{-79}) $, $\Q(\sqrt{-1027}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-q^{13}+q^{16}-2q^{23}+\cdots$
1027.1.u.a	$1027$	$1$	1027.u	1027.u	$6$	$2$	$1$	$0.513$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+(1+\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{9}+\cdots$
1053.1.n.b	$1053$	$1$	1053.n	117.n	$6$	$2$	$1$	$0.526$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{6}q^{4}+\zeta_{6}q^{13}+\zeta_{6}^{2}q^{16}-\zeta_{6}^{2}q^{25}+\cdots$
1131.1.d.a	$1131$	$1$	1131.d	1131.d	$2$	$1$	$1$	$0.564$	$\Q$	$D_{2}$	$\Q(\sqrt{-87}) $, $\Q(\sqrt{-1131}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}-q^{13}+q^{16}+\cdots$
1131.1.d.b	$1131$	$1$	1131.d	1131.d	$2$	$1$	$1$	$0.564$	$\Q$	$D_{2}$	$\Q(\sqrt{-87}) $, $\Q(\sqrt{-1131}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
1313.1.h.a	$1313$	$1$	1313.h	1313.h	$4$	$2$	$1$	$0.655$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(-1-i)q^{3}+iq^{4}+iq^{9}+(1-i+\cdots)q^{12}+\cdots$
1339.1.b.a	$1339$	$1$	1339.b	1339.b	$2$	$1$	$1$	$0.668$	$\Q$	$D_{2}$	$\Q(\sqrt{-103}) $, $\Q(\sqrt{-1339}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}+q^{13}+q^{16}-2q^{17}+\cdots$
1391.1.d.a	$1391$	$1$	1391.d	1391.d	$2$	$1$	$1$	$0.694$	$\Q$	$D_{2}$	$\Q(\sqrt{-107}) $, $\Q(\sqrt{-1391}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+2q^{3}-q^{4}+3q^{9}-2q^{12}-q^{13}+\cdots$
1404.1.z.a	$1404$	$1$	1404.z	117.n	$6$	$2$	$1$	$0.701$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{6}q^{13}+(\zeta_{6}+\zeta_{6}^{2})q^{17}+(1-\zeta_{6}^{2}+\cdots)q^{23}+\cdots$
1651.1.b.a	$1651$	$1$	1651.b	1651.b	$2$	$1$	$1$	$0.824$	$\Q$	$D_{2}$	$\Q(\sqrt{-127}) $, $\Q(\sqrt{-1651}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}+q^{13}+q^{16}-2q^{17}+\cdots$
1703.1.d.a	$1703$	$1$	1703.d	1703.d	$2$	$1$	$1$	$0.850$	$\Q$	$D_{2}$	$\Q(\sqrt{-131}) $, $\Q(\sqrt{-1703}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+2q^{3}-q^{4}+3q^{9}-2q^{12}-q^{13}+\cdots$
1703.1.u.a	$1703$	$1$	1703.u	1703.u	$26$	$12$	$1$	$0.850$	$\Q(\zeta_{26})$	$D_{26}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(\zeta_{26}^{6}-\zeta_{26}^{11})q^{3}-\zeta_{26}^{8}q^{4}+(\zeta_{26}^{4}+\cdots)q^{9}+\cdots$
1807.1.d.b	$1807$	$1$	1807.d	1807.d	$2$	$1$	$1$	$0.902$	$\Q$	$D_{2}$	$\Q(\sqrt{-139}) $, $\Q(\sqrt{-1807}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+q^{9}-q^{13}+q^{16}+q^{25}+2q^{29}+\cdots$
1872.1.i.b	$1872$	$1$	1872.i	52.b	$2$	$1$	$1$	$0.934$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{13}+2q^{17}+q^{25}+2q^{29}-q^{49}+\cdots$
1872.1.cm.a	$1872$	$1$	1872.cm	117.n	$6$	$2$	$1$	$0.934$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+(-\zeta_{6}+\cdots)q^{17}+\cdots$
1872.1.dc.a	$1872$	$1$	1872.dc	468.ag	$6$	$2$	$1$	$0.934$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+q^{17}+\cdots$
1872.1.dc.b	$1872$	$1$	1872.dc	468.ag	$6$	$2$	$1$	$0.934$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+q^{17}+\cdots$
1911.1.h.a	$1911$	$1$	1911.h	39.d	$2$	$1$	$1$	$0.954$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots$
1911.1.w.a	$1911$	$1$	1911.w	273.w	$6$	$2$	$1$	$0.954$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{12}+\cdots$
1911.1.w.b	$1911$	$1$	1911.w	273.w	$6$	$2$	$1$	$0.954$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$1$	$0$	$0$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{12}+\cdots$
2067.1.c.a	$2067$	$1$	2067.c	2067.c	$2$	$1$	$1$	$1.032$	$\Q$	$D_{2}$	$\Q(\sqrt{-159}) $, $\Q(\sqrt{-2067}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}-q^{13}+q^{16}+\cdots$
2067.1.c.b	$2067$	$1$	2067.c	2067.c	$2$	$1$	$1$	$1.032$	$\Q$	$D_{2}$	$\Q(\sqrt{-159}) $, $\Q(\sqrt{-2067}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
2236.1.bf.a	$2236$	$1$	2236.bf	559.v	$6$	$2$	$1$	$1.116$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+(-1+\zeta_{6}^{2})q^{3}+(1-\zeta_{6}-\zeta_{6}^{2})q^{9}+\cdots$
2249.1.h.a	$2249$	$1$	2249.h	2249.h	$4$	$2$	$1$	$1.122$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(1-i)q^{3}+iq^{4}-iq^{9}+(1+i)q^{12}+\cdots$
2327.1.d.b	$2327$	$1$	2327.d	2327.d	$2$	$1$	$1$	$1.161$	$\Q$	$D_{2}$	$\Q(\sqrt{-179}) $, $\Q(\sqrt{-2327}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+2q^{3}-q^{4}+3q^{9}-2q^{12}+q^{13}+\cdots$
2379.1.e.e	$2379$	$1$	2379.e	2379.e	$2$	$1$	$1$	$1.187$	$\Q$	$D_{2}$	$\Q(\sqrt{-183}) $, $\Q(\sqrt{-2379}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
2379.1.e.f	$2379$	$1$	2379.e	2379.e	$2$	$1$	$1$	$1.187$	$\Q$	$D_{2}$	$\Q(\sqrt{-183}) $, $\Q(\sqrt{-2379}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
2483.1.c.a	$2483$	$1$	2483.c	2483.c	$2$	$1$	$1$	$1.239$	$\Q$	$D_{2}$	$\Q(\sqrt{-191}) $, $\Q(\sqrt{-2483}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-2q^{3}+q^{4}+3q^{9}-2q^{12}-q^{13}+\cdots$
2496.1.l.a	$2496$	$1$	2496.l	39.d	$2$	$1$	$1$	$1.246$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{9}+q^{13}-q^{25}-q^{27}-q^{39}+\cdots$
2496.1.l.b	$2496$	$1$	2496.l	39.d	$2$	$1$	$1$	$1.246$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}+q^{13}-q^{25}+q^{27}+q^{39}+\cdots$
2587.1.b.a	$2587$	$1$	2587.b	2587.b	$2$	$1$	$1$	$1.291$	$\Q$	$D_{2}$	$\Q(\sqrt{-199}) $, $\Q(\sqrt{-2587}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}+q^{13}+q^{16}-2q^{23}+\cdots$
2691.1.e.a	$2691$	$1$	2691.e	299.c	$2$	$1$	$1$	$1.343$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-299}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{13}+q^{16}-q^{23}-q^{25}+\cdots$
2704.1.d.a	$2704$	$1$	2704.d	4.b	$2$	$1$	$1$	$1.349$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}+2q^{17}-q^{25}-2q^{29}+q^{49}+\cdots$
2704.1.y.b	$2704$	$1$	2704.y	52.i	$6$	$2$	$1$	$1.349$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{17}+q^{25}+\zeta_{6}q^{29}+\cdots$

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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.