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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
1003.1.b.a	$1003$	$1$	1003.b	1003.b	$2$	$1$	$1$	$0.501$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-1003}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots$
1004.1.d.a	$1004$	$1$	1004.d	251.b	$2$	$1$	$1$	$0.501$	$\Q$	$D_{3}$	$\Q(\sqrt{-251}) $	None	✓	$2$	$0$	$0$	$2$	$-1$	$-1$	$1$		$q+2q^{3}-q^{5}-q^{7}+3q^{9}+2q^{13}+\cdots$
1007.1.d.a	$1007$	$1$	1007.d	1007.d	$2$	$1$	$1$	$0.503$	$\Q$	$D_{3}$	$\Q(\sqrt{-1007}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$2$	$1$		$q-q^{2}-q^{3}+q^{6}+2q^{7}+q^{8}-q^{11}+\cdots$
1007.1.d.b	$1007$	$1$	1007.d	1007.d	$2$	$1$	$1$	$0.503$	$\Q$	$D_{3}$	$\Q(\sqrt{-1007}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$2$	$1$		$q+q^{2}+q^{3}+q^{6}+2q^{7}-q^{8}-q^{11}+\cdots$
1008.1.f.a	$1008$	$1$	1008.f	7.b	$2$	$1$	$1$	$0.503$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+q^{7}+q^{25}-2q^{37}+2q^{43}+q^{49}+\cdots$
1011.1.c.a	$1011$	$1$	1011.c	1011.c	$2$	$1$	$1$	$0.505$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1011}) $	$\Q(\sqrt{337}) $	✓	$4$	$0$	$0$	$-1$	$0$	$2$	$1$		$q-q^{3}+q^{4}+2q^{7}+q^{9}-q^{12}-2q^{13}+\cdots$
1011.1.c.b	$1011$	$1$	1011.c	1011.c	$2$	$1$	$1$	$0.505$	$\Q$	$D_{3}$	$\Q(\sqrt{-1011}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$-1$	$1$		$q+q^{3}+q^{4}-q^{5}-q^{7}+q^{9}+2q^{11}+\cdots$
1011.1.c.c	$1011$	$1$	1011.c	1011.c	$2$	$1$	$1$	$0.505$	$\Q$	$D_{3}$	$\Q(\sqrt{-1011}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$-1$	$1$		$q+q^{3}+q^{4}+q^{5}-q^{7}+q^{9}-2q^{11}+\cdots$
1015.1.f.a	$1015$	$1$	1015.f	1015.f	$2$	$1$	$1$	$0.507$	$\Q$	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-1015}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q-q^{4}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{16}+\cdots$
1015.1.f.b	$1015$	$1$	1015.f	1015.f	$2$	$1$	$1$	$0.507$	$\Q$	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-1015}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$1$	$1$	$1$		$q-q^{4}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{16}+\cdots$
1016.1.h.a	$1016$	$1$	1016.h	1016.h	$2$	$1$	$1$	$0.507$	$\Q$	$D_{2}$	$\Q(\sqrt{-127}) $, $\Q(\sqrt{-254}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-q^{9}+q^{16}+2q^{17}+\cdots$
1023.1.g.a	$1023$	$1$	1023.g	1023.g	$2$	$1$	$1$	$0.511$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-1023}) $	$\Q(\sqrt{93}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}-q^{4}+q^{9}-q^{11}+q^{12}+q^{16}+\cdots$
1023.1.g.b	$1023$	$1$	1023.g	1023.g	$2$	$1$	$1$	$0.511$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-1023}) $	$\Q(\sqrt{93}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}-q^{4}+q^{9}+q^{11}-q^{12}+q^{16}+\cdots$
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}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-q^{13}+q^{16}-2q^{23}+\cdots$
1028.1.d.a	$1028$	$1$	1028.d	1028.d	$2$	$1$	$1$	$0.513$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-257}) $	$\Q(\sqrt{257}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-q^{9}+2q^{13}+q^{16}+\cdots$
1032.1.f.a	$1032$	$1$	1032.f	1032.f	$2$	$1$	$1$	$0.515$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-258}) $	$\Q(\sqrt{129}) $	✓	$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
1032.1.f.b	$1032$	$1$	1032.f	1032.f	$2$	$1$	$1$	$0.515$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-258}) $	$\Q(\sqrt{129}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
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}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{4}+q^{5}+q^{16}-2q^{17}+q^{20}+\cdots$
1036.1.e.a	$1036$	$1$	1036.e	259.b	$2$	$1$	$1$	$0.517$	$\Q$	$D_{3}$	$\Q(\sqrt{-259}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$1$	$1$		$q-q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+2q^{17}+\cdots$
1036.1.e.b	$1036$	$1$	1036.e	259.b	$2$	$1$	$1$	$0.517$	$\Q$	$D_{3}$	$\Q(\sqrt{-259}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$1$	$1$		$q+q^{5}+q^{7}+q^{9}-q^{11}+q^{13}-2q^{17}+\cdots$
1043.1.c.a	$1043$	$1$	1043.c	1043.c	$2$	$1$	$1$	$0.521$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-1043}) $	$\Q(\sqrt{149}) $	✓	$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+q^{4}+q^{7}-q^{9}+q^{16}+q^{25}+q^{28}+\cdots$
1044.1.g.a	$1044$	$1$	1044.g	116.d	$2$	$1$	$1$	$0.521$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{11}+\cdots$
1044.1.g.b	$1044$	$1$	1044.g	116.d	$2$	$1$	$1$	$0.521$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$	$1$		$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots$
1047.1.d.a	$1047$	$1$	1047.d	1047.d	$2$	$1$	$1$	$0.523$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1047}) $	$\Q(\sqrt{349}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}-q^{4}+q^{9}-q^{12}+q^{16}+2q^{19}+\cdots$
1048.1.b.a	$1048$	$1$	1048.b	1048.b	$2$	$1$	$1$	$0.523$	$\Q$	$D_{3}$	$\Q(\sqrt{-262}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{9}+q^{14}+\cdots$
1048.1.b.b	$1048$	$1$	1048.b	1048.b	$2$	$1$	$1$	$0.523$	$\Q$	$D_{3}$	$\Q(\sqrt{-262}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{9}-q^{14}+\cdots$
1055.1.d.a	$1055$	$1$	1055.d	1055.d	$2$	$1$	$1$	$0.527$	$\Q$	$D_{3}$	$\Q(\sqrt{-1055}) $	None	✓	$2$	$0$	$-2$	$1$	$1$	$1$	$1$		$q-2q^{2}+q^{3}+3q^{4}+q^{5}-2q^{6}+q^{7}+\cdots$
1055.1.d.b	$1055$	$1$	1055.d	1055.d	$2$	$1$	$1$	$0.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-211}) $, $\Q(\sqrt{-1055}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}-q^{5}-q^{9}+2q^{11}+q^{16}+2q^{19}+\cdots$
1055.1.d.c	$1055$	$1$	1055.d	1055.d	$2$	$1$	$1$	$0.527$	$\Q$	$D_{3}$	$\Q(\sqrt{-1055}) $	None	✓	$2$	$0$	$2$	$-1$	$1$	$-1$	$1$		$q+2q^{2}-q^{3}+3q^{4}+q^{5}-2q^{6}-q^{7}+\cdots$
1056.1.p.a	$1056$	$1$	1056.p	264.p	$2$	$1$	$1$	$0.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}-q^{11}+2q^{17}-q^{25}+\cdots$
1056.1.p.b	$1056$	$1$	1056.p	264.p	$2$	$1$	$1$	$0.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}+q^{11}-2q^{17}-q^{25}+\cdots$
1059.1.c.a	$1059$	$1$	1059.c	1059.c	$2$	$1$	$1$	$0.529$	$\Q$	$D_{3}$	$\Q(\sqrt{-1059}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$0$	$1$		$q-q^{3}+q^{4}+q^{5}+q^{9}-q^{12}-q^{15}+\cdots$
1059.1.c.b	$1059$	$1$	1059.c	1059.c	$2$	$1$	$1$	$0.529$	$\Q$	$D_{3}$	$\Q(\sqrt{-1059}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$0$	$1$		$q+q^{3}+q^{4}-q^{5}+q^{9}+q^{12}-q^{15}+\cdots$
1060.1.d.a	$1060$	$1$	1060.d	1060.d	$2$	$1$	$1$	$0.529$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-265}) $	$\Q(\sqrt{265}) $	✓	$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}+q^{9}-q^{10}+\cdots$
1060.1.d.b	$1060$	$1$	1060.d	1060.d	$2$	$1$	$1$	$0.529$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-265}) $	$\Q(\sqrt{265}) $	✓	$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots$
1067.1.b.a	$1067$	$1$	1067.b	1067.b	$2$	$1$	$1$	$0.533$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-1067}) $	$\Q(\sqrt{97}) $	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-2q^{3}+q^{4}+3q^{9}-q^{11}-2q^{12}+\cdots$
1067.1.b.b	$1067$	$1$	1067.b	1067.b	$2$	$1$	$1$	$0.533$	$\Q$	$D_{3}$	$\Q(\sqrt{-1067}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-q^{3}+q^{4}-2q^{7}+q^{11}-q^{12}+q^{13}+\cdots$
1067.1.b.c	$1067$	$1$	1067.b	1067.b	$2$	$1$	$1$	$0.533$	$\Q$	$D_{3}$	$\Q(\sqrt{-1067}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$2$	$1$		$q-q^{3}+q^{4}+2q^{7}+q^{11}-q^{12}-q^{13}+\cdots$
1068.1.b.a	$1068$	$1$	1068.b	267.b	$2$	$1$	$1$	$0.533$	$\Q$	$D_{3}$	$\Q(\sqrt{-267}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{9}+q^{23}+q^{25}-q^{27}+q^{29}+\cdots$
1068.1.b.b	$1068$	$1$	1068.b	267.b	$2$	$1$	$1$	$0.533$	$\Q$	$D_{3}$	$\Q(\sqrt{-267}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}-q^{23}+q^{25}+q^{27}-q^{29}+\cdots$
1072.1.b.a	$1072$	$1$	1072.b	67.b	$2$	$1$	$1$	$0.535$	$\Q$	$D_{3}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-q^{17}+q^{19}+q^{23}+q^{25}+\cdots$
1075.1.c.a	$1075$	$1$	1075.c	43.b	$2$	$1$	$1$	$0.536$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-q^{11}-q^{13}+q^{16}+2q^{17}+\cdots$
1075.1.c.b	$1075$	$1$	1075.c	43.b	$2$	$1$	$1$	$0.536$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-q^{11}+q^{13}+q^{16}-2q^{17}+\cdots$
1080.1.i.a	$1080$	$1$	1080.i	120.i	$2$	$1$	$1$	$0.539$	$\Q$	$D_{3}$	$\Q(\sqrt{-30}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots$
1080.1.i.b	$1080$	$1$	1080.i	120.i	$2$	$1$	$1$	$0.539$	$\Q$	$D_{3}$	$\Q(\sqrt{-30}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{11}+\cdots$
1080.1.i.c	$1080$	$1$	1080.i	120.i	$2$	$1$	$1$	$0.539$	$\Q$	$D_{3}$	$\Q(\sqrt{-30}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{11}+\cdots$
1080.1.i.d	$1080$	$1$	1080.i	120.i	$2$	$1$	$1$	$0.539$	$\Q$	$D_{3}$	$\Q(\sqrt{-30}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$	$1$		$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots$
1083.1.b.a	$1083$	$1$	1083.b	3.b	$2$	$1$	$1$	$0.540$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-q^{3}+q^{4}-q^{7}+q^{9}-q^{12}+q^{13}+\cdots$
1083.1.b.b	$1083$	$1$	1083.b	3.b	$2$	$1$	$1$	$0.540$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$-1$	$1$		$q+q^{3}+q^{4}-q^{7}+q^{9}+q^{12}-q^{13}+\cdots$

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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.