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 216 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2205-2205.1003-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1003	$1$	✓	✓	$0.369$	$0$	$0.961130$	Character $\chi_{2205}(1003, \cdot)$
1-2205-2205.1012-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1012	$1$	✓	✓	$-0.481$	$0$	$1.32898$	Character $\chi_{2205}(1012, \cdot)$
1-2205-2205.1013-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1013	$1$	✓	✓	$-0.402$	$0$	$0.351543$	Character $\chi_{2205}(1013, \cdot)$
1-2205-2205.1019-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1019	$1$	✓	✓	$0.380$	$0$	$1.01878$	Character $\chi_{2205}(1019, \cdot)$
1-2205-2205.1033-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1033	$1$	✓	✓	$0.147$	$0$	$0.664322$	Character $\chi_{2205}(1033, \cdot)$
1-2205-2205.1039-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1039	$1$	✓	✓	$0.269$	$0$	$0.0611607$	Character $\chi_{2205}(1039, \cdot)$
1-2205-2205.1067-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1067	$1$	✓	✓	$0.277$	$0$	$1.18941$	Character $\chi_{2205}(1067, \cdot)$
1-2205-2205.1069-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1069	$1$	✓	✓	$-0.439$	$0$	$1.00553$	Character $\chi_{2205}(1069, \cdot)$
1-2205-2205.1084-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1084	$1$	✓	✓	$-0.397$	$0$	$0.0848563$	Character $\chi_{2205}(1084, \cdot)$
1-2205-2205.1087-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1087	$1$	✓	✓	$0.398$	$0$	$0.706265$	Character $\chi_{2205}(1087, \cdot)$
1-2205-2205.1093-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1093	$1$	✓	✓	$0.111$	$0$	$0.624855$	Character $\chi_{2205}(1093, \cdot)$
1-2205-2205.1094-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1094	$1$	✓	✓	$0.435$	$0$	$0.338931$	Character $\chi_{2205}(1094, \cdot)$
1-2205-2205.1112-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1112	$1$	✓	✓	$0.287$	$0$	$1.02286$	Character $\chi_{2205}(1112, \cdot)$
1-2205-2205.1118-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1118	$1$	✓	✓	$-0.277$	$0$	$0.0265727$	Character $\chi_{2205}(1118, \cdot)$
1-2205-2205.1138-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1138	$1$	✓	✓	$-0.398$	$0$	$0.288232$	Character $\chi_{2205}(1138, \cdot)$
1-2205-2205.1172-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1172	$1$	✓	✓	$0.323$	$0$	$0.825639$	Character $\chi_{2205}(1172, \cdot)$
1-2205-2205.1174-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1174	$1$	✓	✓	$0.439$	$0$	$0.0725578$	Character $\chi_{2205}(1174, \cdot)$
1-2205-2205.1184-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1184	$1$	✓	✓	$0.286$	$0$	$0.964131$	Character $\chi_{2205}(1184, \cdot)$
1-2205-2205.1192-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1192	$1$	✓	✓	$0.274$	$0$	$1.29907$	Character $\chi_{2205}(1192, \cdot)$
1-2205-2205.1193-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1193	$1$	✓	✓	$0.342$	$0$	$1.02621$	Character $\chi_{2205}(1193, \cdot)$
1-2205-2205.1199-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1199	$1$	✓	✓	$0.319$	$0$	$0.455504$	Character $\chi_{2205}(1199, \cdot)$
1-2205-2205.1202-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1202	$1$	✓	✓	$0.0461$	$0$	$0.731331$	Character $\chi_{2205}(1202, \cdot)$
1-2205-2205.1213-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1213	$1$	✓	✓	$-0.212$	$0$	$0.133338$	Character $\chi_{2205}(1213, \cdot)$
1-2205-2205.1217-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1217	$1$	✓	✓	$-0.264$	$0$	$0.485292$	Character $\chi_{2205}(1217, \cdot)$
1-2205-2205.122-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.122	$1$	✓	✓	$0.287$	$0$	$1.22564$	Character $\chi_{2205}(122, \cdot)$
1-2205-2205.1222-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1222	$1$	✓	✓	$-0.0978$	$0$	$0.385614$	Character $\chi_{2205}(1222, \cdot)$
1-2205-2205.1229-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1229	$1$	✓	✓	$0.374$	$0$	$1.01492$	Character $\chi_{2205}(1229, \cdot)$
1-2205-2205.1238-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1238	$1$	✓	✓	$0.101$	$0$	$0.968875$	Character $\chi_{2205}(1238, \cdot)$
1-2205-2205.124-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.124	$1$	✓	✓	$0.319$	$0$	$1.14608$	Character $\chi_{2205}(124, \cdot)$
1-2205-2205.1249-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1249	$1$	✓	✓	$-0.439$	$0$	$1.34641$	Character $\chi_{2205}(1249, \cdot)$
1-2205-2205.1282-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1282	$1$	✓	✓	$0.124$	$0$	$0.0284804$	Character $\chi_{2205}(1282, \cdot)$
1-2205-2205.1289-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1289	$1$	✓	✓	$0.0606$	$0$	$0.377589$	Character $\chi_{2205}(1289, \cdot)$
1-2205-2205.1294-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1294	$1$	✓	✓	$0.458$	$0$	$0.727599$	Character $\chi_{2205}(1294, \cdot)$
1-2205-2205.1298-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1298	$1$	✓	✓	$-0.277$	$0$	$0.295937$	Character $\chi_{2205}(1298, \cdot)$
1-2205-2205.1303-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1303	$1$	✓	✓	$0.120$	$0$	$0.594462$	Character $\chi_{2205}(1303, \cdot)$
1-2205-2205.1307-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1307	$1$	✓	✓	$0.385$	$0$	$1.29941$	Character $\chi_{2205}(1307, \cdot)$
1-2205-2205.1318-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1318	$1$	✓	✓	$0.281$	$0$	$1.21058$	Character $\chi_{2205}(1318, \cdot)$
1-2205-2205.1327-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1327	$1$	✓	✓	$0.212$	$0$	$1.05724$	Character $\chi_{2205}(1327, \cdot)$
1-2205-2205.1328-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1328	$1$	✓	✓	$0.281$	$0$	$0.110704$	Character $\chi_{2205}(1328, \cdot)$
1-2205-2205.1334-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1334	$1$	✓	✓	$-0.449$	$0$	$1.10483$	Character $\chi_{2205}(1334, \cdot)$
1-2205-2205.1343-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1343	$1$	✓	✓	$-0.379$	$0$	$1.67213$	Character $\chi_{2205}(1343, \cdot)$
1-2205-2205.1348-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1348	$1$	✓	✓	$0.222$	$0$	$0.841757$	Character $\chi_{2205}(1348, \cdot)$
1-2205-2205.1382-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1382	$1$	✓	✓	$0.107$	$0$	$0.399211$	Character $\chi_{2205}(1382, \cdot)$
1-2205-2205.1384-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1384	$1$	✓	✓	$0.125$	$0$	$1.06516$	Character $\chi_{2205}(1384, \cdot)$
1-2205-2205.139-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.139	$1$	✓	✓	$0.286$	$0$	$0.703421$	Character $\chi_{2205}(139, \cdot)$
1-2205-2205.1399-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1399	$1$	✓	✓	$-0.458$	$0$	$0.0833860$	Character $\chi_{2205}(1399, \cdot)$
1-2205-2205.1408-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1408	$1$	✓	✓	$-0.398$	$0$	$0.231127$	Character $\chi_{2205}(1408, \cdot)$
1-2205-2205.1409-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1409	$1$	✓	✓	$0.0141$	$0$	$0.239678$	Character $\chi_{2205}(1409, \cdot)$
1-2205-2205.142-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.142	$1$	✓	✓	$-0.431$	$0$	$0.219487$	Character $\chi_{2205}(142, \cdot)$
1-2205-2205.1427-r1-0-0	$236.$	$236.$	$1$	$3^{2} \cdot 5 \cdot 7^{2}$	2205.1427	$1$	✓	✓	$0.440$	$0$	$0.294321$	Character $\chi_{2205}(1427, \cdot)$

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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.