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 324 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1305-1305.1003-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1003	$0$	✓	✓	$-0.00727$	$0$	$1.27858$	Character $\chi_{1305}(1003, \cdot)$
1-1305-1305.1004-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1004	$0$	✓	✓	$-0.182$	$0$	$0.616932$	Character $\chi_{1305}(1004, \cdot)$
1-1305-1305.1012-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1012	$0$	✓	✓	$0.398$	$0$	$0.987262$	Character $\chi_{1305}(1012, \cdot)$
1-1305-1305.1022-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1022	$0$	✓	✓	$0.377$	$0$	$1.17950$	Character $\chi_{1305}(1022, \cdot)$
1-1305-1305.1024-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1024	$0$	✓	✓	$0.283$	$0$	$1.05876$	Character $\chi_{1305}(1024, \cdot)$
1-1305-1305.1028-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1028	$0$	✓	✓	$0.156$	$0$	$1.19517$	Character $\chi_{1305}(1028, \cdot)$
1-1305-1305.1033-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1033	$0$	✓	✓	$-0.243$	$0$	$0.748706$	Character $\chi_{1305}(1033, \cdot)$
1-1305-1305.1037-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1037	$0$	✓	✓	$0.283$	$0$	$1.10210$	Character $\chi_{1305}(1037, \cdot)$
1-1305-1305.1039-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1039	$0$	✓	✓	$-0.339$	$0$	$2.22459$	Character $\chi_{1305}(1039, \cdot)$
1-1305-1305.104-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.104	$0$	✓	✓	$-0.169$	$0$	$0.489593$	Character $\chi_{1305}(104, \cdot)$
1-1305-1305.1042-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1042	$0$	✓	✓	$0.0780$	$0$	$0.737417$	Character $\chi_{1305}(1042, \cdot)$
1-1305-1305.1067-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1067	$0$	✓	✓	$-0.100$	$0$	$0.992424$	Character $\chi_{1305}(1067, \cdot)$
1-1305-1305.1069-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1069	$0$	✓	✓	$-0.0390$	$0$	$1.28457$	Character $\chi_{1305}(1069, \cdot)$
1-1305-1305.1082-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1082	$0$	✓	✓	$0.121$	$0$	$1.29435$	Character $\chi_{1305}(1082, \cdot)$
1-1305-1305.1087-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1087	$0$	✓	✓	$-0.124$	$0$	$0.280999$	Character $\chi_{1305}(1087, \cdot)$
1-1305-1305.1094-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1094	$0$	✓	✓	$-0.0949$	$0$	$1.20829$	Character $\chi_{1305}(1094, \cdot)$
1-1305-1305.1118-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1118	$0$	✓	✓	$0.208$	$0$	$1.42910$	Character $\chi_{1305}(1118, \cdot)$
1-1305-1305.1123-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1123	$0$	✓	✓	$-0.155$	$0$	$0.739669$	Character $\chi_{1305}(1123, \cdot)$
1-1305-1305.1127-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1127	$0$	✓	✓	$-0.200$	$0$	$0.749435$	Character $\chi_{1305}(1127, \cdot)$
1-1305-1305.1139-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1139	$0$	✓	✓	$0.151$	$0$	$0.970482$	Character $\chi_{1305}(1139, \cdot)$
1-1305-1305.1159-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1159	$0$	✓	✓	$-0.111$	$0$	$0.861365$	Character $\chi_{1305}(1159, \cdot)$
1-1305-1305.1168-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1168	$0$	✓	✓	$0.0915$	$0$	$0.817405$	Character $\chi_{1305}(1168, \cdot)$
1-1305-1305.1177-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1177	$0$	✓	✓	$-0.0532$	$0$	$0.952614$	Character $\chi_{1305}(1177, \cdot)$
1-1305-1305.119-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.119	$0$	✓	✓	$0.476$	$0$	$0.303971$	Character $\chi_{1305}(119, \cdot)$
1-1305-1305.1192-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1192	$0$	✓	✓	$-0.463$	$0$	$0.604703$	Character $\chi_{1305}(1192, \cdot)$
1-1305-1305.1193-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1193	$0$	✓	✓	$-0.283$	$0$	$0.637368$	Character $\chi_{1305}(1193, \cdot)$
1-1305-1305.1199-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1199	$0$	✓	✓	$-0.198$	$0$	$0.497668$	Character $\chi_{1305}(1199, \cdot)$
1-1305-1305.1202-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1202	$0$	✓	✓	$0.0550$	$0$	$1.18673$	Character $\chi_{1305}(1202, \cdot)$
1-1305-1305.1217-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1217	$0$	✓	✓	$-0.273$	$0$	$0.914585$	Character $\chi_{1305}(1217, \cdot)$
1-1305-1305.122-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.122	$0$	✓	✓	$0.498$	$0$	$1.48516$	Character $\chi_{1305}(122, \cdot)$
1-1305-1305.1228-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1228	$0$	✓	✓	$-0.314$	$0$	$0.920961$	Character $\chi_{1305}(1228, \cdot)$
1-1305-1305.1229-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1229	$0$	✓	✓	$-0.429$	$0$	$1.33596$	Character $\chi_{1305}(1229, \cdot)$
1-1305-1305.1237-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1237	$0$	✓	✓	$0.000477$	$0$	$1.12295$	Character $\chi_{1305}(1237, \cdot)$
1-1305-1305.1238-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1238	$0$	✓	✓	$-0.385$	$0$	$1.71806$	Character $\chi_{1305}(1238, \cdot)$
1-1305-1305.1244-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1244	$0$	✓	✓	$0.338$	$0$	$1.18460$	Character $\chi_{1305}(1244, \cdot)$
1-1305-1305.1253-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1253	$0$	✓	✓	$-0.400$	$0$	$1.85727$	Character $\chi_{1305}(1253, \cdot)$
1-1305-1305.1258-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1258	$0$	✓	✓	$-0.489$	$0$	$1.34724$	Character $\chi_{1305}(1258, \cdot)$
1-1305-1305.1273-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1273	$0$	✓	✓	$0.222$	$0$	$1.52724$	Character $\chi_{1305}(1273, \cdot)$
1-1305-1305.1274-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1274	$0$	✓	✓	$-0.0378$	$0$	$1.14707$	Character $\chi_{1305}(1274, \cdot)$
1-1305-1305.1283-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1283	$0$	✓	✓	$0.200$	$0$	$1.45395$	Character $\chi_{1305}(1283, \cdot)$
1-1305-1305.1292-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1292	$0$	✓	✓	$0.107$	$0$	$0.573173$	Character $\chi_{1305}(1292, \cdot)$
1-1305-1305.1298-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1298	$0$	✓	✓	$0.107$	$0$	$1.12564$	Character $\chi_{1305}(1298, \cdot)$
1-1305-1305.1303-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.1303	$0$	✓	✓	$-0.0981$	$0$	$1.30446$	Character $\chi_{1305}(1303, \cdot)$
1-1305-1305.133-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.133	$0$	✓	✓	$-0.229$	$0$	$2.00707$	Character $\chi_{1305}(133, \cdot)$
1-1305-1305.139-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.139	$0$	✓	✓	$-0.438$	$0$	$1.66857$	Character $\chi_{1305}(139, \cdot)$
1-1305-1305.14-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.14	$0$	✓	✓	$-0.239$	$0$	$0.573814$	Character $\chi_{1305}(14, \cdot)$
1-1305-1305.142-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.142	$0$	✓	✓	$0.176$	$0$	$1.10489$	Character $\chi_{1305}(142, \cdot)$
1-1305-1305.148-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.148	$0$	✓	✓	$0.360$	$0$	$1.08188$	Character $\chi_{1305}(148, \cdot)$
1-1305-1305.157-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.157	$0$	✓	✓	$0.229$	$0$	$0.0600773$	Character $\chi_{1305}(157, \cdot)$
1-1305-1305.158-r0-0-0	$6.06$	$6.06$	$1$	$3^{2} \cdot 5 \cdot 29$	1305.158	$0$	✓	✓	$-0.121$	$0$	$0.392832$	Character $\chi_{1305}(158, \cdot)$

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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.