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 1560 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-6304-6304.1003-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1003	$0$	✓	✓	$0.404$	$0$	$0.968600$	Character $\chi_{6304}(1003, \cdot)$
1-6304-6304.101-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.101	$0$	✓	✓	$-0.207$	$0$	$0.631644$	Character $\chi_{6304}(101, \cdot)$
1-6304-6304.1013-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1013	$0$	✓	✓	$0.171$	$0$	$0.741198$	Character $\chi_{6304}(1013, \cdot)$
1-6304-6304.1021-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1021	$0$	✓	✓	$-0.201$	$0$	$0.562834$	Character $\chi_{6304}(1021, \cdot)$
1-6304-6304.1035-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1035	$0$	✓	✓	$-0.114$	$0$	$0.808961$	Character $\chi_{6304}(1035, \cdot)$
1-6304-6304.1043-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1043	$0$	✓	✓	$0.279$	$0$	$0.710666$	Character $\chi_{6304}(1043, \cdot)$
1-6304-6304.1045-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1045	$0$	✓	✓	$0.244$	$0$	$1.40520$	Character $\chi_{6304}(1045, \cdot)$
1-6304-6304.1051-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1051	$0$	✓	✓	$-0.0771$	$0$	$1.03883$	Character $\chi_{6304}(1051, \cdot)$
1-6304-6304.1059-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1059	$0$	✓	✓	$-0.155$	$0$	$0.949806$	Character $\chi_{6304}(1059, \cdot)$
1-6304-6304.1061-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1061	$0$	✓	✓	$0.0854$	$0$	$0.734682$	Character $\chi_{6304}(1061, \cdot)$
1-6304-6304.1067-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1067	$0$	✓	✓	$0.145$	$0$	$1.10604$	Character $\chi_{6304}(1067, \cdot)$
1-6304-6304.1077-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1077	$0$	✓	✓	$0.283$	$0$	$1.18370$	Character $\chi_{6304}(1077, \cdot)$
1-6304-6304.1083-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1083	$0$	✓	✓	$-0.487$	$0$	$1.25085$	Character $\chi_{6304}(1083, \cdot)$
1-6304-6304.1085-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1085	$0$	✓	✓	$-0.0297$	$0$	$0.384737$	Character $\chi_{6304}(1085, \cdot)$
1-6304-6304.109-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.109	$0$	✓	✓	$-0.0430$	$0$	$0.839592$	Character $\chi_{6304}(109, \cdot)$
1-6304-6304.1091-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1091	$0$	✓	✓	$-0.132$	$0$	$0.483729$	Character $\chi_{6304}(1091, \cdot)$
1-6304-6304.11-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.11	$0$	✓	✓	$0.158$	$0$	$0.933472$	Character $\chi_{6304}(11, \cdot)$
1-6304-6304.1101-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1101	$0$	✓	✓	$0.140$	$0$	$1.22979$	Character $\chi_{6304}(1101, \cdot)$
1-6304-6304.1107-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1107	$0$	✓	✓	$0.0834$	$0$	$0.309472$	Character $\chi_{6304}(1107, \cdot)$
1-6304-6304.1115-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1115	$0$	✓	✓	$0.0352$	$0$	$0.445043$	Character $\chi_{6304}(1115, \cdot)$
1-6304-6304.1117-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1117	$0$	✓	✓	$-0.0327$	$0$	$0.839306$	Character $\chi_{6304}(1117, \cdot)$
1-6304-6304.1133-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1133	$0$	✓	✓	$-0.218$	$0$	$0.689347$	Character $\chi_{6304}(1133, \cdot)$
1-6304-6304.1141-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1141	$0$	✓	✓	$0.0269$	$0$	$1.14014$	Character $\chi_{6304}(1141, \cdot)$
1-6304-6304.1147-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1147	$0$	✓	✓	$0.312$	$0$	$0.687043$	Character $\chi_{6304}(1147, \cdot)$
1-6304-6304.1149-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1149	$0$	✓	✓	$-0.0192$	$0$	$0.413641$	Character $\chi_{6304}(1149, \cdot)$
1-6304-6304.115-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.115	$0$	✓	✓	$-0.180$	$0$	$0.719160$	Character $\chi_{6304}(115, \cdot)$
1-6304-6304.1155-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1155	$0$	✓	✓	$-0.412$	$0$	$0.0726980$	Character $\chi_{6304}(1155, \cdot)$
1-6304-6304.1157-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1157	$0$	✓	✓	$0.214$	$0$	$0.549806$	Character $\chi_{6304}(1157, \cdot)$
1-6304-6304.1171-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1171	$0$	✓	✓	$-0.0329$	$0$	$0.374711$	Character $\chi_{6304}(1171, \cdot)$
1-6304-6304.1173-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1173	$0$	✓	✓	$0.0331$	$0$	$0.841848$	Character $\chi_{6304}(1173, \cdot)$
1-6304-6304.1179-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1179	$0$	✓	✓	$-0.216$	$0$	$0.373511$	Character $\chi_{6304}(1179, \cdot)$
1-6304-6304.1181-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1181	$0$	✓	✓	$-0.0312$	$0$	$0.802858$	Character $\chi_{6304}(1181, \cdot)$
1-6304-6304.1187-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1187	$0$	✓	✓	$0.152$	$0$	$0.883267$	Character $\chi_{6304}(1187, \cdot)$
1-6304-6304.1189-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1189	$0$	✓	✓	$0.453$	$0$	$1.05525$	Character $\chi_{6304}(1189, \cdot)$
1-6304-6304.1195-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1195	$0$	✓	✓	$0.00299$	$0$	$0.369422$	Character $\chi_{6304}(1195, \cdot)$
1-6304-6304.1197-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1197	$0$	✓	✓	$-0.0339$	$0$	$0.626842$	Character $\chi_{6304}(1197, \cdot)$
1-6304-6304.1203-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1203	$0$	✓	✓	$-0.145$	$0$	$0.382100$	Character $\chi_{6304}(1203, \cdot)$
1-6304-6304.1205-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1205	$0$	✓	✓	$-0.182$	$0$	$0.730373$	Character $\chi_{6304}(1205, \cdot)$
1-6304-6304.1221-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1221	$0$	✓	✓	$-0.0715$	$0$	$0.734619$	Character $\chi_{6304}(1221, \cdot)$
1-6304-6304.1227-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1227	$0$	✓	✓	$0.000355$	$0$	$0.679104$	Character $\chi_{6304}(1227, \cdot)$
1-6304-6304.1229-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1229	$0$	✓	✓	$0.480$	$0$	$0.219682$	Character $\chi_{6304}(1229, \cdot)$
1-6304-6304.123-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.123	$0$	✓	✓	$-0.0712$	$0$	$0.451894$	Character $\chi_{6304}(123, \cdot)$
1-6304-6304.1237-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1237	$0$	✓	✓	$0.285$	$0$	$1.21988$	Character $\chi_{6304}(1237, \cdot)$
1-6304-6304.1245-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1245	$0$	✓	✓	$-0.464$	$0$	$1.38007$	Character $\chi_{6304}(1245, \cdot)$
1-6304-6304.1251-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1251	$0$	✓	✓	$0.178$	$0$	$1.00560$	Character $\chi_{6304}(1251, \cdot)$
1-6304-6304.1259-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1259	$0$	✓	✓	$0.241$	$0$	$1.24782$	Character $\chi_{6304}(1259, \cdot)$
1-6304-6304.1299-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1299	$0$	✓	✓	$0.471$	$0$	$0.114451$	Character $\chi_{6304}(1299, \cdot)$
1-6304-6304.1307-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1307	$0$	✓	✓	$0.410$	$0$	$0.712417$	Character $\chi_{6304}(1307, \cdot)$
1-6304-6304.1309-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.1309	$0$	✓	✓	$0.297$	$0$	$0.935933$	Character $\chi_{6304}(1309, \cdot)$
1-6304-6304.131-r0-0-0	$29.2$	$29.2$	$1$	$2^{5} \cdot 197$	6304.131	$0$	✓	✓	$-0.0339$	$0$	$0.954231$	Character $\chi_{6304}(131, \cdot)$

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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.