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 576 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2816-2816.1003-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1003	$0$	✓	✓	$0.0847$	$0$	$1.20354$	Character $\chi_{2816}(1003, \cdot)$
1-2816-2816.1005-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1005	$0$	✓	✓	$0.246$	$0$	$1.19718$	Character $\chi_{2816}(1005, \cdot)$
1-2816-2816.1011-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1011	$0$	✓	✓	$0.0429$	$0$	$0.681990$	Character $\chi_{2816}(1011, \cdot)$
1-2816-2816.1019-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1019	$0$	✓	✓	$0.445$	$0$	$0.368915$	Character $\chi_{2816}(1019, \cdot)$
1-2816-2816.1021-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1021	$0$	✓	✓	$-0.330$	$0$	$0.551515$	Character $\chi_{2816}(1021, \cdot)$
1-2816-2816.1037-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1037	$0$	✓	✓	$0.0891$	$0$	$1.13815$	Character $\chi_{2816}(1037, \cdot)$
1-2816-2816.1051-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1051	$0$	✓	✓	$0.360$	$0$	$1.40889$	Character $\chi_{2816}(1051, \cdot)$
1-2816-2816.1061-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1061	$0$	✓	✓	$-0.450$	$0$	$0.449649$	Character $\chi_{2816}(1061, \cdot)$
1-2816-2816.107-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.107	$0$	✓	✓	$0.000652$	$0$	$0.748127$	Character $\chi_{2816}(107, \cdot)$
1-2816-2816.1075-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1075	$0$	✓	✓	$-0.445$	$0$	$1.25272$	Character $\chi_{2816}(1075, \cdot)$
1-2816-2816.1091-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1091	$0$	✓	✓	$-0.391$	$0$	$1.81486$	Character $\chi_{2816}(1091, \cdot)$
1-2816-2816.1093-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1093	$0$	✓	✓	$0.410$	$0$	$1.13846$	Character $\chi_{2816}(1093, \cdot)$
1-2816-2816.1099-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1099	$0$	✓	✓	$0.113$	$0$	$0.802125$	Character $\chi_{2816}(1099, \cdot)$
1-2816-2816.1107-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1107	$0$	✓	✓	$0.281$	$0$	$0.611255$	Character $\chi_{2816}(1107, \cdot)$
1-2816-2816.1109-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1109	$0$	✓	✓	$-0.354$	$0$	$0.630397$	Character $\chi_{2816}(1109, \cdot)$
1-2816-2816.1125-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1125	$0$	✓	✓	$0.246$	$0$	$0.806691$	Character $\chi_{2816}(1125, \cdot)$
1-2816-2816.1139-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1139	$0$	✓	✓	$-0.303$	$0$	$0.706826$	Character $\chi_{2816}(1139, \cdot)$
1-2816-2816.1149-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1149	$0$	✓	✓	$0.354$	$0$	$0.0844720$	Character $\chi_{2816}(1149, \cdot)$
1-2816-2816.1163-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1163	$0$	✓	✓	$-0.125$	$0$	$1.10827$	Character $\chi_{2816}(1163, \cdot)$
1-2816-2816.1179-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1179	$0$	✓	✓	$-0.446$	$0$	$0.0218181$	Character $\chi_{2816}(1179, \cdot)$
1-2816-2816.1181-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1181	$0$	✓	✓	$0.340$	$0$	$0.877668$	Character $\chi_{2816}(1181, \cdot)$
1-2816-2816.1187-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1187	$0$	✓	✓	$-0.113$	$0$	$0.848865$	Character $\chi_{2816}(1187, \cdot)$
1-2816-2816.1195-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1195	$0$	✓	✓	$-0.0227$	$0$	$1.04682$	Character $\chi_{2816}(1195, \cdot)$
1-2816-2816.1197-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1197	$0$	✓	✓	$0.450$	$0$	$1.71583$	Character $\chi_{2816}(1197, \cdot)$
1-2816-2816.1213-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1213	$0$	✓	✓	$-0.192$	$0$	$0.238472$	Character $\chi_{2816}(1213, \cdot)$
1-2816-2816.1227-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1227	$0$	✓	✓	$0.266$	$0$	$0.680256$	Character $\chi_{2816}(1227, \cdot)$
1-2816-2816.123-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.123	$0$	✓	✓	$-0.446$	$0$	$1.32213$	Character $\chi_{2816}(123, \cdot)$
1-2816-2816.1237-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1237	$0$	✓	✓	$0.330$	$0$	$1.06270$	Character $\chi_{2816}(1237, \cdot)$
1-2816-2816.125-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.125	$0$	✓	✓	$-0.284$	$0$	$0.289075$	Character $\chi_{2816}(125, \cdot)$
1-2816-2816.1251-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1251	$0$	✓	✓	$-0.352$	$0$	$0.0231531$	Character $\chi_{2816}(1251, \cdot)$
1-2816-2816.1267-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1267	$0$	✓	✓	$-0.110$	$0$	$0.610817$	Character $\chi_{2816}(1267, \cdot)$
1-2816-2816.1269-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1269	$0$	✓	✓	$0.0670$	$0$	$0.891592$	Character $\chi_{2816}(1269, \cdot)$
1-2816-2816.1275-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1275	$0$	✓	✓	$0.207$	$0$	$1.50706$	Character $\chi_{2816}(1275, \cdot)$
1-2816-2816.1283-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1283	$0$	✓	✓	$0.499$	$0$	$1.23399$	Character $\chi_{2816}(1283, \cdot)$
1-2816-2816.1285-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1285	$0$	✓	✓	$0.114$	$0$	$0.435242$	Character $\chi_{2816}(1285, \cdot)$
1-2816-2816.1301-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1301	$0$	✓	✓	$-0.215$	$0$	$0.790553$	Character $\chi_{2816}(1301, \cdot)$
1-2816-2816.131-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.131	$0$	✓	✓	$0.261$	$0$	$1.12742$	Character $\chi_{2816}(131, \cdot)$
1-2816-2816.1315-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1315	$0$	✓	✓	$0.0402$	$0$	$1.13178$	Character $\chi_{2816}(1315, \cdot)$
1-2816-2816.1325-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1325	$0$	✓	✓	$-0.364$	$0$	$0.422580$	Character $\chi_{2816}(1325, \cdot)$
1-2816-2816.1339-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1339	$0$	✓	✓	$-0.281$	$0$	$1.62113$	Character $\chi_{2816}(1339, \cdot)$
1-2816-2816.1355-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1355	$0$	✓	✓	$-0.0402$	$0$	$0.857981$	Character $\chi_{2816}(1355, \cdot)$
1-2816-2816.1357-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1357	$0$	✓	✓	$-0.246$	$0$	$0.194802$	Character $\chi_{2816}(1357, \cdot)$
1-2816-2816.1363-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1363	$0$	✓	✓	$0.0429$	$0$	$1.14078$	Character $\chi_{2816}(1363, \cdot)$
1-2816-2816.1371-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1371	$0$	✓	✓	$-0.304$	$0$	$0.0367303$	Character $\chi_{2816}(1371, \cdot)$
1-2816-2816.1373-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1373	$0$	✓	✓	$0.294$	$0$	$1.21323$	Character $\chi_{2816}(1373, \cdot)$
1-2816-2816.1389-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1389	$0$	✓	✓	$0.339$	$0$	$1.41102$	Character $\chi_{2816}(1389, \cdot)$
1-2816-2816.139-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.139	$0$	✓	✓	$0.352$	$0$	$1.08212$	Character $\chi_{2816}(139, \cdot)$
1-2816-2816.1403-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1403	$0$	✓	✓	$-0.139$	$0$	$0.809932$	Character $\chi_{2816}(1403, \cdot)$
1-2816-2816.141-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.141	$0$	✓	✓	$-0.0497$	$0$	$0.785111$	Character $\chi_{2816}(141, \cdot)$
1-2816-2816.1413-r0-0-0	$13.0$	$13.0$	$1$	$2^{8} \cdot 11$	2816.1413	$0$	✓	✓	$0.299$	$0$	$1.17621$	Character $\chi_{2816}(1413, \cdot)$

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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.