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

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-65e2-4225.1002-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1002	$1$	✓	✓	$-0.205$	$0$	$0.0300342$	Character $\chi_{4225}(1002, \cdot)$
1-65e2-4225.1006-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1006	$1$	✓	✓	$-0.249$	$0$	$0.475076$	Character $\chi_{4225}(1006, \cdot)$
1-65e2-4225.1009-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1009	$1$	✓	✓	$-0.195$	$0$	$1.26051$	Character $\chi_{4225}(1009, \cdot)$
1-65e2-4225.1016-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1016	$1$	✓	✓	$-0.218$	$0$	$0.0791682$	Character $\chi_{4225}(1016, \cdot)$
1-65e2-4225.1017-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1017	$1$	✓	✓	$0.0243$	$0$	$0.187616$	Character $\chi_{4225}(1017, \cdot)$
1-65e2-4225.1019-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1019	$1$	✓	✓	$-0.415$	$0$	$0.186241$	Character $\chi_{4225}(1019, \cdot)$
1-65e2-4225.1021-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1021	$1$	✓	✓	$0.430$	$0$	$0.402155$	Character $\chi_{4225}(1021, \cdot)$
1-65e2-4225.1023-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1023	$1$	✓	✓	$0.438$	$0$	$1.02777$	Character $\chi_{4225}(1023, \cdot)$
1-65e2-4225.1028-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1028	$1$	✓	✓	$0.415$	$0$	$0.949699$	Character $\chi_{4225}(1028, \cdot)$
1-65e2-4225.1029-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1029	$1$	✓	✓	$0.430$	$0$	$0.126178$	Character $\chi_{4225}(1029, \cdot)$
1-65e2-4225.103-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.103	$1$	✓	✓	$0.371$	$0$	$0.0316243$	Character $\chi_{4225}(103, \cdot)$
1-65e2-4225.1034-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1034	$1$	✓	✓	$0.0634$	$0$	$0.883617$	Character $\chi_{4225}(1034, \cdot)$
1-65e2-4225.1046-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1046	$1$	✓	✓	$-0.362$	$0$	$0.0385152$	Character $\chi_{4225}(1046, \cdot)$
1-65e2-4225.1052-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1052	$1$	✓	✓	$-0.394$	$0$	$1.09129$	Character $\chi_{4225}(1052, \cdot)$
1-65e2-4225.1059-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1059	$1$	✓	✓	$-0.210$	$0$	$0.206757$	Character $\chi_{4225}(1059, \cdot)$
1-65e2-4225.106-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.106	$1$	✓	✓	$0.0687$	$0$	$0.444552$	Character $\chi_{4225}(106, \cdot)$
1-65e2-4225.1061-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1061	$1$	✓	✓	$-0.196$	$0$	$1.17769$	Character $\chi_{4225}(1061, \cdot)$
1-65e2-4225.1062-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1062	$1$	✓	✓	$-0.436$	$0$	$0.168658$	Character $\chi_{4225}(1062, \cdot)$
1-65e2-4225.1063-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1063	$1$	✓	✓	$-0.0677$	$0$	$0.0910407$	Character $\chi_{4225}(1063, \cdot)$
1-65e2-4225.1064-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1064	$1$	✓	✓	$0.172$	$0$	$0.206344$	Character $\chi_{4225}(1064, \cdot)$
1-65e2-4225.1067-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1067	$1$	✓	✓	$-0.249$	$0$	$0.480511$	Character $\chi_{4225}(1067, \cdot)$
1-65e2-4225.1071-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1071	$1$	✓	✓	$-0.378$	$0$	$0.138911$	Character $\chi_{4225}(1071, \cdot)$
1-65e2-4225.1078-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1078	$1$	✓	✓	$-0.191$	$0$	$0.184177$	Character $\chi_{4225}(1078, \cdot)$
1-65e2-4225.108-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.108	$1$	✓	✓	$0.0697$	$0$	$0.201885$	Character $\chi_{4225}(108, \cdot)$
1-65e2-4225.1081-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1081	$1$	✓	✓	$0.343$	$0$	$0.691961$	Character $\chi_{4225}(1081, \cdot)$
1-65e2-4225.1083-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1083	$1$	✓	✓	$-0.142$	$0$	$0.825293$	Character $\chi_{4225}(1083, \cdot)$
1-65e2-4225.1086-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1086	$1$	✓	✓	$0.362$	$0$	$0.813395$	Character $\chi_{4225}(1086, \cdot)$
1-65e2-4225.1088-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1088	$1$	✓	✓	$0.221$	$0$	$0.836980$	Character $\chi_{4225}(1088, \cdot)$
1-65e2-4225.109-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.109	$1$	✓	✓	$-0.155$	$0$	$0.0148538$	Character $\chi_{4225}(109, \cdot)$
1-65e2-4225.11-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.11	$1$	✓	✓	$-0.448$	$0$	$0.128032$	Character $\chi_{4225}(11, \cdot)$
1-65e2-4225.1102-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1102	$1$	✓	✓	$0.436$	$0$	$0.421529$	Character $\chi_{4225}(1102, \cdot)$
1-65e2-4225.1108-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1108	$1$	✓	✓	$0.0914$	$0$	$0.737980$	Character $\chi_{4225}(1108, \cdot)$
1-65e2-4225.111-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.111	$1$	✓	✓	$-0.0634$	$0$	$0.317895$	Character $\chi_{4225}(111, \cdot)$
1-65e2-4225.1111-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1111	$1$	✓	✓	$0.362$	$0$	$1.20609$	Character $\chi_{4225}(1111, \cdot)$
1-65e2-4225.1116-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1116	$1$	✓	✓	$-0.436$	$0$	$0.593002$	Character $\chi_{4225}(1116, \cdot)$
1-65e2-4225.1117-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1117	$1$	✓	✓	$0.191$	$0$	$0.917507$	Character $\chi_{4225}(1117, \cdot)$
1-65e2-4225.1122-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1122	$1$	✓	✓	$0.249$	$0$	$0.410777$	Character $\chi_{4225}(1122, \cdot)$
1-65e2-4225.1127-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1127	$1$	✓	✓	$0.00560$	$0$	$0.399371$	Character $\chi_{4225}(1127, \cdot)$
1-65e2-4225.1128-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1128	$1$	✓	✓	$0.292$	$0$	$0.789233$	Character $\chi_{4225}(1128, \cdot)$
1-65e2-4225.1129-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1129	$1$	✓	✓	$-0.402$	$0$	$0.00312997$	Character $\chi_{4225}(1129, \cdot)$
1-65e2-4225.113-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.113	$1$	✓	✓	$-0.234$	$0$	$1.37089$	Character $\chi_{4225}(113, \cdot)$
1-65e2-4225.1136-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1136	$1$	✓	✓	$0.303$	$0$	$0.102480$	Character $\chi_{4225}(1136, \cdot)$
1-65e2-4225.1139-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1139	$1$	✓	✓	$-0.144$	$0$	$0.481335$	Character $\chi_{4225}(1139, \cdot)$
1-65e2-4225.1146-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1146	$1$	✓	✓	$-0.457$	$0$	$1.22510$	Character $\chi_{4225}(1146, \cdot)$
1-65e2-4225.1147-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1147	$1$	✓	✓	$-0.0697$	$0$	$0.876281$	Character $\chi_{4225}(1147, \cdot)$
1-65e2-4225.1148-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1148	$1$	✓	✓	$0.468$	$0$	$0.459493$	Character $\chi_{4225}(1148, \cdot)$
1-65e2-4225.1153-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1153	$1$	✓	✓	$0.0821$	$0$	$0.868386$	Character $\chi_{4225}(1153, \cdot)$
1-65e2-4225.1158-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1158	$1$	✓	✓	$-0.125$	$0$	$0.603517$	Character $\chi_{4225}(1158, \cdot)$
1-65e2-4225.1159-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1159	$1$	✓	✓	$-0.210$	$0$	$0.611373$	Character $\chi_{4225}(1159, \cdot)$
1-65e2-4225.1167-r1-0-0	$454.$	$454.$	$1$	$5^{2} \cdot 13^{2}$	4225.1167	$1$	✓	✓	$-0.431$	$0$	$0.813969$	Character $\chi_{4225}(1167, \cdot)$

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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
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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.