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 758 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-3605-3605.1003-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1003	$1$	✓	✓	$0.0476$	$0$	$1.05160$	Character $\chi_{3605}(1003, \cdot)$
1-3605-3605.1007-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1007	$1$	✓	✓	$-0.0676$	$0$	$0.739879$	Character $\chi_{3605}(1007, \cdot)$
1-3605-3605.1013-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1013	$1$	✓	✓	$0.171$	$0$	$0.0125024$	Character $\chi_{3605}(1013, \cdot)$
1-3605-3605.1028-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1028	$1$	✓	✓	$0.0303$	$0$	$0.673072$	Character $\chi_{3605}(1028, \cdot)$
1-3605-3605.1034-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1034	$1$	✓	✓	$0.222$	$0$	$0.916041$	Character $\chi_{3605}(1034, \cdot)$
1-3605-3605.1038-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1038	$1$	✓	✓	$-0.327$	$0$	$1.09149$	Character $\chi_{3605}(1038, \cdot)$
1-3605-3605.1039-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1039	$1$	✓	✓	$0.315$	$0$	$0.829701$	Character $\chi_{3605}(1039, \cdot)$
1-3605-3605.1042-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1042	$1$	✓	✓	$-0.422$	$0$	$0.335415$	Character $\chi_{3605}(1042, \cdot)$
1-3605-3605.1047-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1047	$1$	✓	✓	$0.117$	$0$	$0.632693$	Character $\chi_{3605}(1047, \cdot)$
1-3605-3605.1049-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1049	$1$	✓	✓	$-0.312$	$0$	$0.278381$	Character $\chi_{3605}(1049, \cdot)$
1-3605-3605.1054-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1054	$1$	✓	✓	$0.277$	$0$	$0.823282$	Character $\chi_{3605}(1054, \cdot)$
1-3605-3605.1067-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1067	$1$	✓	✓	$-0.166$	$0$	$0.482548$	Character $\chi_{3605}(1067, \cdot)$
1-3605-3605.1068-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1068	$1$	✓	✓	$-0.0361$	$0$	$0.581639$	Character $\chi_{3605}(1068, \cdot)$
1-3605-3605.107-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.107	$1$	✓	✓	$0.424$	$0$	$0.418158$	Character $\chi_{3605}(107, \cdot)$
1-3605-3605.1077-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1077	$1$	✓	✓	$0.328$	$0$	$0.292032$	Character $\chi_{3605}(1077, \cdot)$
1-3605-3605.108-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.108	$1$	✓	✓	$0.263$	$0$	$0.768432$	Character $\chi_{3605}(108, \cdot)$
1-3605-3605.1082-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1082	$1$	✓	✓	$-0.168$	$0$	$0.262580$	Character $\chi_{3605}(1082, \cdot)$
1-3605-3605.1083-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1083	$1$	✓	✓	$0.0974$	$0$	$0.176114$	Character $\chi_{3605}(1083, \cdot)$
1-3605-3605.109-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.109	$1$	✓	✓	$0.126$	$0$	$0.974807$	Character $\chi_{3605}(109, \cdot)$
1-3605-3605.1097-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1097	$1$	✓	✓	$0.325$	$0$	$0.770435$	Character $\chi_{3605}(1097, \cdot)$
1-3605-3605.1109-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1109	$1$	✓	✓	$0.411$	$0$	$1.10106$	Character $\chi_{3605}(1109, \cdot)$
1-3605-3605.1118-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1118	$1$	✓	✓	$-0.390$	$0$	$0.564154$	Character $\chi_{3605}(1118, \cdot)$
1-3605-3605.1122-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1122	$1$	✓	✓	$-0.0809$	$0$	$0.429455$	Character $\chi_{3605}(1122, \cdot)$
1-3605-3605.1124-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1124	$1$	✓	✓	$0.395$	$0$	$0.148960$	Character $\chi_{3605}(1124, \cdot)$
1-3605-3605.1129-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1129	$1$	✓	✓	$0.289$	$0$	$0.799653$	Character $\chi_{3605}(1129, \cdot)$
1-3605-3605.1132-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1132	$1$	✓	✓	$0.234$	$0$	$1.23473$	Character $\chi_{3605}(1132, \cdot)$
1-3605-3605.114-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.114	$1$	✓	✓	$0.317$	$0$	$0.521072$	Character $\chi_{3605}(114, \cdot)$
1-3605-3605.1152-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1152	$1$	✓	✓	$-0.484$	$0$	$1.29830$	Character $\chi_{3605}(1152, \cdot)$
1-3605-3605.1153-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1153	$1$	✓	✓	$-0.0320$	$0$	$0.453084$	Character $\chi_{3605}(1153, \cdot)$
1-3605-3605.1164-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1164	$1$	✓	✓	$0.0297$	$0$	$0.673599$	Character $\chi_{3605}(1164, \cdot)$
1-3605-3605.1168-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1168	$1$	✓	✓	$-0.127$	$0$	$0.756465$	Character $\chi_{3605}(1168, \cdot)$
1-3605-3605.1172-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1172	$1$	✓	✓	$0.0501$	$0$	$0.347976$	Character $\chi_{3605}(1172, \cdot)$
1-3605-3605.1174-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1174	$1$	✓	✓	$-0.306$	$0$	$0.195775$	Character $\chi_{3605}(1174, \cdot)$
1-3605-3605.1179-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1179	$1$	✓	✓	$0.140$	$0$	$0.494157$	Character $\chi_{3605}(1179, \cdot)$
1-3605-3605.1189-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1189	$1$	✓	✓	$-0.286$	$0$	$1.47282$	Character $\chi_{3605}(1189, \cdot)$
1-3605-3605.1192-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1192	$1$	✓	✓	$0.263$	$0$	$0.761312$	Character $\chi_{3605}(1192, \cdot)$
1-3605-3605.12-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.12	$1$	✓	✓	$-0.275$	$0$	$0.160224$	Character $\chi_{3605}(12, \cdot)$
1-3605-3605.1202-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1202	$1$	✓	✓	$0.451$	$0$	$1.13332$	Character $\chi_{3605}(1202, \cdot)$
1-3605-3605.1203-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1203	$1$	✓	✓	$0.366$	$0$	$0.0541919$	Character $\chi_{3605}(1203, \cdot)$
1-3605-3605.1207-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1207	$1$	✓	✓	$-0.219$	$0$	$0.252758$	Character $\chi_{3605}(1207, \cdot)$
1-3605-3605.1209-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1209	$1$	✓	✓	$0.0221$	$0$	$0.441985$	Character $\chi_{3605}(1209, \cdot)$
1-3605-3605.1214-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1214	$1$	✓	✓	$-0.234$	$0$	$1.18162$	Character $\chi_{3605}(1214, \cdot)$
1-3605-3605.1217-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1217	$1$	✓	✓	$0.383$	$0$	$0.301084$	Character $\chi_{3605}(1217, \cdot)$
1-3605-3605.1223-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1223	$1$	✓	✓	$-0.243$	$0$	$0.183945$	Character $\chi_{3605}(1223, \cdot)$
1-3605-3605.1224-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1224	$1$	✓	✓	$0.489$	$0$	$0.891010$	Character $\chi_{3605}(1224, \cdot)$
1-3605-3605.1228-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1228	$1$	✓	✓	$0.0672$	$0$	$0.605725$	Character $\chi_{3605}(1228, \cdot)$
1-3605-3605.1229-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1229	$1$	✓	✓	$0.260$	$0$	$0.541998$	Character $\chi_{3605}(1229, \cdot)$
1-3605-3605.1234-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1234	$1$	✓	✓	$-0.121$	$0$	$1.59184$	Character $\chi_{3605}(1234, \cdot)$
1-3605-3605.1242-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1242	$1$	✓	✓	$-0.171$	$0$	$1.31007$	Character $\chi_{3605}(1242, \cdot)$
1-3605-3605.1243-r1-0-0	$387.$	$387.$	$1$	$5 \cdot 7 \cdot 103$	3605.1243	$1$	✓	✓	$-0.263$	$0$	$0.503749$	Character $\chi_{3605}(1243, \cdot)$

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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.