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 325 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1407-1407.1010-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1010	$0$	✓	✓	$-0.330$	$0$	$0.0423459$	Character $\chi_{1407}(1010, \cdot)$
1-1407-1407.1028-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1028	$0$	✓	✓	$0.386$	$0$	$1.60222$	Character $\chi_{1407}(1028, \cdot)$
1-1407-1407.1034-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1034	$0$	✓	✓	$-0.286$	$0$	$0.858267$	Character $\chi_{1407}(1034, \cdot)$
1-1407-1407.104-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.104	$0$	✓	✓	$-0.233$	$0$	$0.986940$	Character $\chi_{1407}(104, \cdot)$
1-1407-1407.1067-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1067	$0$	✓	✓	$0.371$	$0$	$1.58255$	Character $\chi_{1407}(1067, \cdot)$
1-1407-1407.1070-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1070	$0$	✓	✓	$-0.0994$	$0$	$0.994505$	Character $\chi_{1407}(1070, \cdot)$
1-1407-1407.1076-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1076	$0$	✓	✓	$-0.489$	$0$	$1.45446$	Character $\chi_{1407}(1076, \cdot)$
1-1407-1407.1088-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1088	$0$	✓	✓	$0.466$	$0$	$0.201654$	Character $\chi_{1407}(1088, \cdot)$
1-1407-1407.1091-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1091	$0$	✓	✓	$-0.426$	$0$	$0.0916081$	Character $\chi_{1407}(1091, \cdot)$
1-1407-1407.1097-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1097	$0$	✓	✓	$0.362$	$0$	$1.13442$	Character $\chi_{1407}(1097, \cdot)$
1-1407-1407.11-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.11	$0$	✓	✓	$-0.0637$	$0$	$0.935519$	Character $\chi_{1407}(11, \cdot)$
1-1407-1407.1103-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1103	$0$	✓	✓	$0.314$	$0$	$1.01534$	Character $\chi_{1407}(1103, \cdot)$
1-1407-1407.1109-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1109	$0$	✓	✓	$0.286$	$0$	$0.952320$	Character $\chi_{1407}(1109, \cdot)$
1-1407-1407.1112-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1112	$0$	✓	✓	$0.148$	$0$	$1.30930$	Character $\chi_{1407}(1112, \cdot)$
1-1407-1407.1115-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1115	$0$	✓	✓	$-0.0224$	$0$	$0.438861$	Character $\chi_{1407}(1115, \cdot)$
1-1407-1407.1124-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1124	$0$	✓	✓	$-0.220$	$0$	$0.192262$	Character $\chi_{1407}(1124, \cdot)$
1-1407-1407.1154-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1154	$0$	✓	✓	$0.482$	$0$	$1.18067$	Character $\chi_{1407}(1154, \cdot)$
1-1407-1407.1157-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1157	$0$	✓	✓	$0.0386$	$0$	$0.571611$	Character $\chi_{1407}(1157, \cdot)$
1-1407-1407.1160-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1160	$0$	✓	✓	$-0.466$	$0$	$1.80916$	Character $\chi_{1407}(1160, \cdot)$
1-1407-1407.1166-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1166	$0$	✓	✓	$0.330$	$0$	$1.02977$	Character $\chi_{1407}(1166, \cdot)$
1-1407-1407.1172-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1172	$0$	✓	✓	$-0.380$	$0$	$0.243868$	Character $\chi_{1407}(1172, \cdot)$
1-1407-1407.1175-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1175	$0$	✓	✓	$-0.446$	$0$	$0.229642$	Character $\chi_{1407}(1175, \cdot)$
1-1407-1407.1187-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1187	$0$	✓	✓	$-0.259$	$0$	$0.404997$	Character $\chi_{1407}(1187, \cdot)$
1-1407-1407.1193-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1193	$0$	✓	✓	$-0.0337$	$0$	$0.806161$	Character $\chi_{1407}(1193, \cdot)$
1-1407-1407.1208-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1208	$0$	✓	✓	$0.00639$	$0$	$1.54740$	Character $\chi_{1407}(1208, \cdot)$
1-1407-1407.122-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.122	$0$	✓	✓	$0.0181$	$0$	$1.27850$	Character $\chi_{1407}(122, \cdot)$
1-1407-1407.1223-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1223	$0$	✓	✓	$0.449$	$0$	$1.54769$	Character $\chi_{1407}(1223, \cdot)$
1-1407-1407.1235-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1235	$0$	✓	✓	$-0.246$	$0$	$0.124829$	Character $\chi_{1407}(1235, \cdot)$
1-1407-1407.1250-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1250	$0$	✓	✓	$0.0981$	$0$	$0.983669$	Character $\chi_{1407}(1250, \cdot)$
1-1407-1407.1265-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1265	$0$	✓	✓	$-0.402$	$0$	$0.600196$	Character $\chi_{1407}(1265, \cdot)$
1-1407-1407.1277-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1277	$0$	✓	✓	$-0.449$	$0$	$0.696822$	Character $\chi_{1407}(1277, \cdot)$
1-1407-1407.128-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.128	$0$	✓	✓	$0.0637$	$0$	$0.799866$	Character $\chi_{1407}(128, \cdot)$
1-1407-1407.1298-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1298	$0$	✓	✓	$0.402$	$0$	$1.23418$	Character $\chi_{1407}(1298, \cdot)$
1-1407-1407.1304-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1304	$0$	✓	✓	$0.498$	$0$	$0.576182$	Character $\chi_{1407}(1304, \cdot)$
1-1407-1407.131-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.131	$0$	✓	✓	$0.353$	$0$	$1.26731$	Character $\chi_{1407}(131, \cdot)$
1-1407-1407.1322-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1322	$0$	✓	✓	$0.289$	$0$	$0.715640$	Character $\chi_{1407}(1322, \cdot)$
1-1407-1407.1325-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1325	$0$	✓	✓	$-0.0339$	$0$	$0.885807$	Character $\chi_{1407}(1325, \cdot)$
1-1407-1407.1328-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1328	$0$	✓	✓	$-0.0222$	$0$	$0.456017$	Character $\chi_{1407}(1328, \cdot)$
1-1407-1407.1334-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1334	$0$	✓	✓	$-0.123$	$0$	$0.841849$	Character $\chi_{1407}(1334, \cdot)$
1-1407-1407.1349-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1349	$0$	✓	✓	$0.00266$	$0$	$0.467083$	Character $\chi_{1407}(1349, \cdot)$
1-1407-1407.1361-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1361	$0$	✓	✓	$-0.426$	$0$	$0.280982$	Character $\chi_{1407}(1361, \cdot)$
1-1407-1407.1364-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1364	$0$	✓	✓	$-0.00853$	$0$	$0.487732$	Character $\chi_{1407}(1364, \cdot)$
1-1407-1407.1367-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1367	$0$	✓	✓	$-0.482$	$0$	$0.407393$	Character $\chi_{1407}(1367, \cdot)$
1-1407-1407.137-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.137	$0$	✓	✓	$0.368$	$0$	$1.42638$	Character $\chi_{1407}(137, \cdot)$
1-1407-1407.1388-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1388	$0$	✓	✓	$-0.0724$	$0$	$1.13890$	Character $\chi_{1407}(1388, \cdot)$
1-1407-1407.1397-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.1397	$0$	✓	✓	$-0.227$	$0$	$0.694731$	Character $\chi_{1407}(1397, \cdot)$
1-1407-1407.143-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.143	$0$	✓	✓	$0.0376$	$0$	$1.32763$	Character $\chi_{1407}(143, \cdot)$
1-1407-1407.167-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.167	$0$	✓	✓	$0.0994$	$0$	$1.32103$	Character $\chi_{1407}(167, \cdot)$
1-1407-1407.17-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.17	$0$	✓	✓	$0.489$	$0$	$0.482500$	Character $\chi_{1407}(17, \cdot)$
1-1407-1407.173-r0-0-0	$6.53$	$6.53$	$1$	$3 \cdot 7 \cdot 67$	1407.173	$0$	✓	✓	$-0.0181$	$0$	$1.03470$	Character $\chi_{1407}(173, \cdot)$

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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.