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 198 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1287-1287.1004-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1004	$1$	✓	✓	$0.0666$	$0$	$0.787778$	Character $\chi_{1287}(1004, \cdot)$
1-1287-1287.1006-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1006	$1$	✓	✓	$-0.121$	$0$	$0.883690$	Character $\chi_{1287}(1006, \cdot)$
1-1287-1287.1010-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1010	$1$	✓	✓	$0.486$	$0$	$1.16604$	Character $\chi_{1287}(1010, \cdot)$
1-1287-1287.1019-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1019	$1$	✓	✓	$-0.275$	$0$	$0.320169$	Character $\chi_{1287}(1019, \cdot)$
1-1287-1287.1021-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1021	$1$	✓	✓	$-0.244$	$0$	$0.399209$	Character $\chi_{1287}(1021, \cdot)$
1-1287-1287.1022-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1022	$1$	✓	✓	$0.314$	$0$	$0.0428234$	Character $\chi_{1287}(1022, \cdot)$
1-1287-1287.1030-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1030	$1$	✓	✓	$-0.140$	$0$	$0.435569$	Character $\chi_{1287}(1030, \cdot)$
1-1287-1287.1037-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1037	$1$	✓	✓	$-0.450$	$0$	$0.105107$	Character $\chi_{1287}(1037, \cdot)$
1-1287-1287.1048-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1048	$1$	✓	✓	$-0.439$	$0$	$0.00985774$	Character $\chi_{1287}(1048, \cdot)$
1-1287-1287.1049-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1049	$1$	✓	✓	$-0.344$	$0$	$0.556121$	Character $\chi_{1287}(1049, \cdot)$
1-1287-1287.1055-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1055	$1$	✓	✓	$0.0514$	$0$	$0.910310$	Character $\chi_{1287}(1055, \cdot)$
1-1287-1287.1058-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1058	$1$	✓	✓	$-0.345$	$0$	$0.140777$	Character $\chi_{1287}(1058, \cdot)$
1-1287-1287.1060-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1060	$1$	✓	✓	$-0.0198$	$0$	$0.643186$	Character $\chi_{1287}(1060, \cdot)$
1-1287-1287.1064-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1064	$1$	✓	✓	$-0.393$	$0$	$1.84750$	Character $\chi_{1287}(1064, \cdot)$
1-1287-1287.1069-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1069	$1$	✓	✓	$-0.155$	$0$	$0.391475$	Character $\chi_{1287}(1069, \cdot)$
1-1287-1287.1073-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1073	$1$	✓	✓	$-0.0201$	$0$	$1.00981$	Character $\chi_{1287}(1073, \cdot)$
1-1287-1287.1075-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1075	$1$	✓	✓	$0.362$	$0$	$1.08621$	Character $\chi_{1287}(1075, \cdot)$
1-1287-1287.1076-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1076	$1$	✓	✓	$-0.166$	$0$	$0.245283$	Character $\chi_{1287}(1076, \cdot)$
1-1287-1287.1082-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1082	$1$	✓	✓	$0.352$	$0$	$0.218676$	Character $\chi_{1287}(1082, \cdot)$
1-1287-1287.1085-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1085	$1$	✓	✓	$0.393$	$0$	$0.247146$	Character $\chi_{1287}(1085, \cdot)$
1-1287-1287.1087-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1087	$1$	✓	✓	$-0.100$	$0$	$0.712262$	Character $\chi_{1287}(1087, \cdot)$
1-1287-1287.1096-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1096	$1$	✓	✓	$0.0131$	$0$	$0.501489$	Character $\chi_{1287}(1096, \cdot)$
1-1287-1287.1102-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1102	$1$	✓	✓	$0.272$	$0$	$0.525926$	Character $\chi_{1287}(1102, \cdot)$
1-1287-1287.1109-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1109	$1$	✓	✓	$0.281$	$0$	$0.137526$	Character $\chi_{1287}(1109, \cdot)$
1-1287-1287.1120-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1120	$1$	✓	✓	$-0.419$	$0$	$0.166103$	Character $\chi_{1287}(1120, \cdot)$
1-1287-1287.1127-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1127	$1$	✓	✓	$0.372$	$0$	$0.544299$	Character $\chi_{1287}(1127, \cdot)$
1-1287-1287.113-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.113	$1$	✓	✓	$-0.352$	$0$	$1.05504$	Character $\chi_{1287}(113, \cdot)$
1-1287-1287.1138-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1138	$1$	✓	✓	$-0.358$	$0$	$0.173422$	Character $\chi_{1287}(1138, \cdot)$
1-1287-1287.1139-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1139	$1$	✓	✓	$0.0678$	$0$	$1.08651$	Character $\chi_{1287}(1139, \cdot)$
1-1287-1287.1141-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1141	$1$	✓	✓	$-0.235$	$0$	$0.756804$	Character $\chi_{1287}(1141, \cdot)$
1-1287-1287.1148-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1148	$1$	✓	✓	$0.450$	$0$	$0.557417$	Character $\chi_{1287}(1148, \cdot)$
1-1287-1287.115-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.115	$1$	✓	✓	$-0.162$	$0$	$0.633576$	Character $\chi_{1287}(115, \cdot)$
1-1287-1287.1159-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1159	$1$	✓	✓	$-0.194$	$0$	$1.05657$	Character $\chi_{1287}(1159, \cdot)$
1-1287-1287.1163-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1163	$1$	✓	✓	$-0.406$	$0$	$0.557966$	Character $\chi_{1287}(1163, \cdot)$
1-1287-1287.1172-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1172	$1$	✓	✓	$-0.195$	$0$	$0.0828612$	Character $\chi_{1287}(1172, \cdot)$
1-1287-1287.1174-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1174	$1$	✓	✓	$0.157$	$0$	$0.905128$	Character $\chi_{1287}(1174, \cdot)$
1-1287-1287.1190-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1190	$1$	✓	✓	$0.472$	$0$	$0.757081$	Character $\chi_{1287}(1190, \cdot)$
1-1287-1287.1193-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1193	$1$	✓	✓	$-0.281$	$0$	$1.99189$	Character $\chi_{1287}(1193, \cdot)$
1-1287-1287.1195-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1195	$1$	✓	✓	$-0.0721$	$0$	$0.840118$	Character $\chi_{1287}(1195, \cdot)$
1-1287-1287.1204-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1204	$1$	✓	✓	$-0.215$	$0$	$1.50875$	Character $\chi_{1287}(1204, \cdot)$
1-1287-1287.1208-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1208	$1$	✓	✓	$0.196$	$0$	$0.544424$	Character $\chi_{1287}(1208, \cdot)$
1-1287-1287.1217-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1217	$1$	✓	✓	$-0.368$	$0$	$1.64132$	Character $\chi_{1287}(1217, \cdot)$
1-1287-1287.1220-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1220	$1$	✓	✓	$0.367$	$0$	$1.30974$	Character $\chi_{1287}(1220, \cdot)$
1-1287-1287.1226-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1226	$1$	✓	✓	$0.166$	$0$	$1.06493$	Character $\chi_{1287}(1226, \cdot)$
1-1287-1287.1229-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1229	$1$	✓	✓	$-0.0903$	$0$	$0.428822$	Character $\chi_{1287}(1229, \cdot)$
1-1287-1287.1231-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1231	$1$	✓	✓	$0.179$	$0$	$0.809959$	Character $\chi_{1287}(1231, \cdot)$
1-1287-1287.1237-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1237	$1$	✓	✓	$0.466$	$0$	$0.289656$	Character $\chi_{1287}(1237, \cdot)$
1-1287-1287.124-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.124	$1$	✓	✓	$-0.0274$	$0$	$0.491466$	Character $\chi_{1287}(124, \cdot)$
1-1287-1287.1246-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1246	$1$	✓	✓	$-0.386$	$0$	$0.0728151$	Character $\chi_{1287}(1246, \cdot)$
1-1287-1287.1247-r1-0-0	$138.$	$138.$	$1$	$3^{2} \cdot 11 \cdot 13$	1287.1247	$1$	✓	✓	$0.364$	$0$	$0.991214$	Character $\chi_{1287}(1247, \cdot)$

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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.