LMFDB - L-function search results

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Lowest zero	Conductor	Analytic conductor	Central character	Analytic rank

Degree	Bad $p$	Root analytic conductor	Motivic weight	Spectral label

Root angle	Primitive	Origin	Exclude origin	Self-dual

Arithmetic

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Results (1-50 of 501 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4024-4024.1003-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1003	$0$	✓	✓	$0.429$	$0$	$1.14601$	Character $\chi_{4024}(1003, \cdot)$
1-4024-4024.1011-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1011	$0$	✓	✓	$-0.183$	$0$	$0.212760$	Character $\chi_{4024}(1011, \cdot)$
1-4024-4024.1013-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1013	$0$	✓	✓	$-0.109$	$0$	$0.576276$	Character $\chi_{4024}(1013, \cdot)$
1-4024-4024.1029-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1029	$0$	✓	✓	$0.204$	$0$	$0.922786$	Character $\chi_{4024}(1029, \cdot)$
1-4024-4024.1035-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1035	$0$	✓	✓	$-0.136$	$0$	$1.06830$	Character $\chi_{4024}(1035, \cdot)$
1-4024-4024.1043-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1043	$0$	✓	✓	$-0.455$	$0$	$1.50010$	Character $\chi_{4024}(1043, \cdot)$
1-4024-4024.1045-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1045	$0$	✓	✓	$-0.104$	$0$	$0.782381$	Character $\chi_{4024}(1045, \cdot)$
1-4024-4024.1051-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1051	$0$	✓	✓	$0.135$	$0$	$0.730469$	Character $\chi_{4024}(1051, \cdot)$
1-4024-4024.1053-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1053	$0$	✓	✓	$0.0512$	$0$	$1.30232$	Character $\chi_{4024}(1053, \cdot)$
1-4024-4024.1059-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1059	$0$	✓	✓	$0.126$	$0$	$1.11383$	Character $\chi_{4024}(1059, \cdot)$
1-4024-4024.1069-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1069	$0$	✓	✓	$-0.208$	$0$	$0.0552314$	Character $\chi_{4024}(1069, \cdot)$
1-4024-4024.107-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.107	$0$	✓	✓	$0.193$	$0$	$0.532233$	Character $\chi_{4024}(107, \cdot)$
1-4024-4024.1085-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1085	$0$	✓	✓	$-0.400$	$0$	$1.50132$	Character $\chi_{4024}(1085, \cdot)$
1-4024-4024.1099-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1099	$0$	✓	✓	$0.478$	$0$	$1.28095$	Character $\chi_{4024}(1099, \cdot)$
1-4024-4024.1101-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1101	$0$	✓	✓	$-0.173$	$0$	$0.437760$	Character $\chi_{4024}(1101, \cdot)$
1-4024-4024.1107-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1107	$0$	✓	✓	$-0.152$	$0$	$0.796537$	Character $\chi_{4024}(1107, \cdot)$
1-4024-4024.1115-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1115	$0$	✓	✓	$0.000776$	$0$	$0.712247$	Character $\chi_{4024}(1115, \cdot)$
1-4024-4024.1131-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1131	$0$	✓	✓	$0.137$	$0$	$1.07240$	Character $\chi_{4024}(1131, \cdot)$
1-4024-4024.1139-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1139	$0$	✓	✓	$0.456$	$0$	$1.29303$	Character $\chi_{4024}(1139, \cdot)$
1-4024-4024.1149-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1149	$0$	✓	✓	$0.00388$	$0$	$0.678084$	Character $\chi_{4024}(1149, \cdot)$
1-4024-4024.115-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.115	$0$	✓	✓	$-0.170$	$0$	$0.548346$	Character $\chi_{4024}(115, \cdot)$
1-4024-4024.1155-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1155	$0$	✓	✓	$0.147$	$0$	$0.970997$	Character $\chi_{4024}(1155, \cdot)$
1-4024-4024.1163-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1163	$0$	✓	✓	$-0.478$	$0$	$0.213910$	Character $\chi_{4024}(1163, \cdot)$
1-4024-4024.117-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.117	$0$	✓	✓	$-0.0764$	$0$	$0.709149$	Character $\chi_{4024}(117, \cdot)$
1-4024-4024.1171-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1171	$0$	✓	✓	$0.412$	$0$	$0.510838$	Character $\chi_{4024}(1171, \cdot)$
1-4024-4024.1181-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1181	$0$	✓	✓	$-0.204$	$0$	$0.823281$	Character $\chi_{4024}(1181, \cdot)$
1-4024-4024.1187-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1187	$0$	✓	✓	$-0.386$	$0$	$0.100566$	Character $\chi_{4024}(1187, \cdot)$
1-4024-4024.1189-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1189	$0$	✓	✓	$0.321$	$0$	$0.915175$	Character $\chi_{4024}(1189, \cdot)$
1-4024-4024.1205-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1205	$0$	✓	✓	$0.300$	$0$	$1.14487$	Character $\chi_{4024}(1205, \cdot)$
1-4024-4024.1213-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1213	$0$	✓	✓	$0.184$	$0$	$1.06185$	Character $\chi_{4024}(1213, \cdot)$
1-4024-4024.1219-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1219	$0$	✓	✓	$-0.283$	$0$	$0.673589$	Character $\chi_{4024}(1219, \cdot)$
1-4024-4024.1227-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1227	$0$	✓	✓	$0.238$	$0$	$1.00952$	Character $\chi_{4024}(1227, \cdot)$
1-4024-4024.1229-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1229	$0$	✓	✓	$0.189$	$0$	$0.778212$	Character $\chi_{4024}(1229, \cdot)$
1-4024-4024.123-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.123	$0$	✓	✓	$0.324$	$0$	$0.752636$	Character $\chi_{4024}(123, \cdot)$
1-4024-4024.1237-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1237	$0$	✓	✓	$0.149$	$0$	$0.922320$	Character $\chi_{4024}(1237, \cdot)$
1-4024-4024.1251-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1251	$0$	✓	✓	$-0.0336$	$0$	$0.976011$	Character $\chi_{4024}(1251, \cdot)$
1-4024-4024.1261-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1261	$0$	✓	✓	$0.117$	$0$	$0.704857$	Character $\chi_{4024}(1261, \cdot)$
1-4024-4024.1267-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1267	$0$	✓	✓	$0.279$	$0$	$1.11024$	Character $\chi_{4024}(1267, \cdot)$
1-4024-4024.1269-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1269	$0$	✓	✓	$-0.0838$	$0$	$0.463741$	Character $\chi_{4024}(1269, \cdot)$
1-4024-4024.1275-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1275	$0$	✓	✓	$0.0475$	$0$	$0.418775$	Character $\chi_{4024}(1275, \cdot)$
1-4024-4024.1277-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1277	$0$	✓	✓	$-0.125$	$0$	$0.571657$	Character $\chi_{4024}(1277, \cdot)$
1-4024-4024.1283-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1283	$0$	✓	✓	$0.436$	$0$	$0.294655$	Character $\chi_{4024}(1283, \cdot)$
1-4024-4024.13-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.13	$0$	✓	✓	$0.0508$	$0$	$1.04949$	Character $\chi_{4024}(13, \cdot)$
1-4024-4024.1315-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1315	$0$	✓	✓	$0.0742$	$0$	$0.963243$	Character $\chi_{4024}(1315, \cdot)$
1-4024-4024.1339-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1339	$0$	✓	✓	$0.0907$	$0$	$0.598845$	Character $\chi_{4024}(1339, \cdot)$
1-4024-4024.1347-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1347	$0$	✓	✓	$-0.336$	$0$	$0.366978$	Character $\chi_{4024}(1347, \cdot)$
1-4024-4024.1349-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1349	$0$	✓	✓	$0.0683$	$0$	$1.01653$	Character $\chi_{4024}(1349, \cdot)$
1-4024-4024.1355-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1355	$0$	✓	✓	$0.00378$	$0$	$0.845196$	Character $\chi_{4024}(1355, \cdot)$
1-4024-4024.1357-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1357	$0$	✓	✓	$0.103$	$0$	$0.854759$	Character $\chi_{4024}(1357, \cdot)$
1-4024-4024.1363-r0-0-0	$18.6$	$18.6$	$1$	$2^{3} \cdot 503$	4024.1363	$0$	✓	✓	$0.362$	$0$	$0.759163$	Character $\chi_{4024}(1363, \cdot)$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.