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 500 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2032-2032.1003-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1003	$0$	✓	✓	$-0.362$	$0$	$0.190083$	Character $\chi_{2032}(1003, \cdot)$
1-2032-2032.1013-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1013	$0$	✓	✓	$-0.336$	$0$	$0.00842164$	Character $\chi_{2032}(1013, \cdot)$
1-2032-2032.1019-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1019	$0$	✓	✓	$0.140$	$0$	$0.981274$	Character $\chi_{2032}(1019, \cdot)$
1-2032-2032.1029-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1029	$0$	✓	✓	$0.332$	$0$	$1.21371$	Character $\chi_{2032}(1029, \cdot)$
1-2032-2032.1037-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1037	$0$	✓	✓	$0.288$	$0$	$1.16048$	Character $\chi_{2032}(1037, \cdot)$
1-2032-2032.1043-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1043	$0$	✓	✓	$0.482$	$0$	$0.688378$	Character $\chi_{2032}(1043, \cdot)$
1-2032-2032.1053-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1053	$0$	✓	✓	$-0.142$	$0$	$0.536458$	Character $\chi_{2032}(1053, \cdot)$
1-2032-2032.1059-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1059	$0$	✓	✓	$0.0662$	$0$	$0.777358$	Character $\chi_{2032}(1059, \cdot)$
1-2032-2032.1067-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1067	$0$	✓	✓	$-0.454$	$0$	$0.167880$	Character $\chi_{2032}(1067, \cdot)$
1-2032-2032.1075-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1075	$0$	✓	✓	$-0.200$	$0$	$0.837501$	Character $\chi_{2032}(1075, \cdot)$
1-2032-2032.1077-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1077	$0$	✓	✓	$0.109$	$0$	$0.714506$	Character $\chi_{2032}(1077, \cdot)$
1-2032-2032.1083-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1083	$0$	✓	✓	$-0.0734$	$0$	$0.958484$	Character $\chi_{2032}(1083, \cdot)$
1-2032-2032.1085-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1085	$0$	✓	✓	$-0.166$	$0$	$0.442903$	Character $\chi_{2032}(1085, \cdot)$
1-2032-2032.1091-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1091	$0$	✓	✓	$-0.385$	$0$	$0.226888$	Character $\chi_{2032}(1091, \cdot)$
1-2032-2032.1099-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1099	$0$	✓	✓	$0.142$	$0$	$1.05808$	Character $\chi_{2032}(1099, \cdot)$
1-2032-2032.1107-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1107	$0$	✓	✓	$0.0734$	$0$	$0.990008$	Character $\chi_{2032}(1107, \cdot)$
1-2032-2032.1133-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1133	$0$	✓	✓	$0.0645$	$0$	$1.28502$	Character $\chi_{2032}(1133, \cdot)$
1-2032-2032.1139-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1139	$0$	✓	✓	$-0.288$	$0$	$0.523291$	Character $\chi_{2032}(1139, \cdot)$
1-2032-2032.1155-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1155	$0$	✓	✓	$0.380$	$0$	$1.54070$	Character $\chi_{2032}(1155, \cdot)$
1-2032-2032.1163-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1163	$0$	✓	✓	$-0.0949$	$0$	$0.824036$	Character $\chi_{2032}(1163, \cdot)$
1-2032-2032.1165-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1165	$0$	✓	✓	$0.0694$	$0$	$0.399289$	Character $\chi_{2032}(1165, \cdot)$
1-2032-2032.117-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.117	$0$	✓	✓	$-0.0604$	$0$	$0.617529$	Character $\chi_{2032}(117, \cdot)$
1-2032-2032.1171-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1171	$0$	✓	✓	$-0.174$	$0$	$0.586864$	Character $\chi_{2032}(1171, \cdot)$
1-2032-2032.1173-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1173	$0$	✓	✓	$0.165$	$0$	$1.16948$	Character $\chi_{2032}(1173, \cdot)$
1-2032-2032.1181-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1181	$0$	✓	✓	$0.0604$	$0$	$0.843686$	Character $\chi_{2032}(1181, \cdot)$
1-2032-2032.1205-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1205	$0$	✓	✓	$0.469$	$0$	$0.278476$	Character $\chi_{2032}(1205, \cdot)$
1-2032-2032.1213-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1213	$0$	✓	✓	$-0.456$	$0$	$0.258836$	Character $\chi_{2032}(1213, \cdot)$
1-2032-2032.123-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.123	$0$	✓	✓	$0.0866$	$0$	$1.26320$	Character $\chi_{2032}(123, \cdot)$
1-2032-2032.1235-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1235	$0$	✓	✓	$-0.419$	$0$	$0.599929$	Character $\chi_{2032}(1235, \cdot)$
1-2032-2032.1237-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1237	$0$	✓	✓	$-0.112$	$0$	$0.725384$	Character $\chi_{2032}(1237, \cdot)$
1-2032-2032.1251-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1251	$0$	✓	✓	$0.0949$	$0$	$1.13977$	Character $\chi_{2032}(1251, \cdot)$
1-2032-2032.1259-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1259	$0$	✓	✓	$0.128$	$0$	$0.462938$	Character $\chi_{2032}(1259, \cdot)$
1-2032-2032.1275-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1275	$0$	✓	✓	$-0.170$	$0$	$0.477966$	Character $\chi_{2032}(1275, \cdot)$
1-2032-2032.1285-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1285	$0$	✓	✓	$-0.266$	$0$	$0.416760$	Character $\chi_{2032}(1285, \cdot)$
1-2032-2032.1299-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1299	$0$	✓	✓	$0.0443$	$0$	$0.974547$	Character $\chi_{2032}(1299, \cdot)$
1-2032-2032.13-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.13	$0$	✓	✓	$0.457$	$0$	$1.56411$	Character $\chi_{2032}(13, \cdot)$
1-2032-2032.1301-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1301	$0$	✓	✓	$0.180$	$0$	$1.20778$	Character $\chi_{2032}(1301, \cdot)$
1-2032-2032.1315-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1315	$0$	✓	✓	$0.390$	$0$	$1.17651$	Character $\chi_{2032}(1315, \cdot)$
1-2032-2032.1317-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1317	$0$	✓	✓	$0.0861$	$0$	$0.619893$	Character $\chi_{2032}(1317, \cdot)$
1-2032-2032.1323-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1323	$0$	✓	✓	$-0.380$	$0$	$0.00909137$	Character $\chi_{2032}(1323, \cdot)$
1-2032-2032.1341-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1341	$0$	✓	✓	$-0.0733$	$0$	$0.621156$	Character $\chi_{2032}(1341, \cdot)$
1-2032-2032.1347-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1347	$0$	✓	✓	$0.256$	$0$	$1.28956$	Character $\chi_{2032}(1347, \cdot)$
1-2032-2032.1349-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1349	$0$	✓	✓	$-0.360$	$0$	$0.0253352$	Character $\chi_{2032}(1349, \cdot)$
1-2032-2032.1355-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1355	$0$	✓	✓	$0.234$	$0$	$0.942617$	Character $\chi_{2032}(1355, \cdot)$
1-2032-2032.1357-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1357	$0$	✓	✓	$-0.300$	$0$	$1.79575$	Character $\chi_{2032}(1357, \cdot)$
1-2032-2032.1363-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1363	$0$	✓	✓	$0.357$	$0$	$1.54460$	Character $\chi_{2032}(1363, \cdot)$
1-2032-2032.1371-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1371	$0$	✓	✓	$0.232$	$0$	$1.21876$	Character $\chi_{2032}(1371, \cdot)$
1-2032-2032.1373-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1373	$0$	✓	✓	$0.267$	$0$	$1.39723$	Character $\chi_{2032}(1373, \cdot)$
1-2032-2032.1379-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.1379	$0$	✓	✓	$0.312$	$0$	$1.53233$	Character $\chi_{2032}(1379, \cdot)$
1-2032-2032.139-r0-0-0	$9.43$	$9.43$	$1$	$2^{4} \cdot 127$	2032.139	$0$	✓	✓	$-0.244$	$0$	$0.136309$	Character $\chi_{2032}(139, \cdot)$

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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.