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 210 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2960-2960.1067-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1067	$1$	✓	✓	$0.163$	$0$	$0.553258$	Character $\chi_{2960}(1067, \cdot)$
1-2960-2960.1077-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1077	$1$	✓	✓	$0.429$	$0$	$0.00929390$	Character $\chi_{2960}(1077, \cdot)$
1-2960-2960.109-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.109	$1$	✓	✓	$0.0750$	$0$	$0.532151$	Character $\chi_{2960}(109, \cdot)$
1-2960-2960.1099-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1099	$1$	✓	✓	$0.00257$	$0$	$0.561795$	Character $\chi_{2960}(1099, \cdot)$
1-2960-2960.1117-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1117	$1$	✓	✓	$-0.164$	$0$	$0.159039$	Character $\chi_{2960}(1117, \cdot)$
1-2960-2960.1123-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1123	$1$	✓	✓	$-0.187$	$0$	$0.577893$	Character $\chi_{2960}(1123, \cdot)$
1-2960-2960.1149-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1149	$1$	✓	✓	$-0.351$	$0$	$0.203035$	Character $\chi_{2960}(1149, \cdot)$
1-2960-2960.1157-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1157	$1$	✓	✓	$-0.0343$	$0$	$0.814155$	Character $\chi_{2960}(1157, \cdot)$
1-2960-2960.1173-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1173	$1$	✓	✓	$-0.0906$	$0$	$0.692106$	Character $\chi_{2960}(1173, \cdot)$
1-2960-2960.1189-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1189	$1$	✓	✓	$0.403$	$0$	$1.03425$	Character $\chi_{2960}(1189, \cdot)$
1-2960-2960.1203-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1203	$1$	✓	✓	$-0.111$	$0$	$0.191540$	Character $\chi_{2960}(1203, \cdot)$
1-2960-2960.1227-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1227	$1$	✓	✓	$-0.112$	$0$	$0.339042$	Character $\chi_{2960}(1227, \cdot)$
1-2960-2960.1229-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1229	$1$	✓	✓	$-0.489$	$0$	$0.181978$	Character $\chi_{2960}(1229, \cdot)$
1-2960-2960.1237-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1237	$1$	✓	✓	$-0.159$	$0$	$0.261885$	Character $\chi_{2960}(1237, \cdot)$
1-2960-2960.1243-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1243	$1$	✓	✓	$-0.272$	$0$	$0.337632$	Character $\chi_{2960}(1243, \cdot)$
1-2960-2960.1299-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1299	$1$	✓	✓	$0.466$	$0$	$0.00198832$	Character $\chi_{2960}(1299, \cdot)$
1-2960-2960.1309-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1309	$1$	✓	✓	$-0.385$	$0$	$0.0414458$	Character $\chi_{2960}(1309, \cdot)$
1-2960-2960.1339-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1339	$1$	✓	✓	$0.122$	$0$	$0.937160$	Character $\chi_{2960}(1339, \cdot)$
1-2960-2960.1347-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1347	$1$	✓	✓	$-0.315$	$0$	$0.649819$	Character $\chi_{2960}(1347, \cdot)$
1-2960-2960.1349-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1349	$1$	✓	✓	$-0.447$	$0$	$0.969812$	Character $\chi_{2960}(1349, \cdot)$
1-2960-2960.1357-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1357	$1$	✓	✓	$-0.233$	$0$	$0.0535165$	Character $\chi_{2960}(1357, \cdot)$
1-2960-2960.1363-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1363	$1$	✓	✓	$0.112$	$0$	$0.760720$	Character $\chi_{2960}(1363, \cdot)$
1-2960-2960.1373-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1373	$1$	✓	✓	$-0.121$	$0$	$0.606504$	Character $\chi_{2960}(1373, \cdot)$
1-2960-2960.1379-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1379	$1$	✓	✓	$0.00257$	$0$	$0.643642$	Character $\chi_{2960}(1379, \cdot)$
1-2960-2960.1387-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1387	$1$	✓	✓	$-0.486$	$0$	$0.811573$	Character $\chi_{2960}(1387, \cdot)$
1-2960-2960.1389-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1389	$1$	✓	✓	$-0.275$	$0$	$0.189281$	Character $\chi_{2960}(1389, \cdot)$
1-2960-2960.139-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.139	$1$	✓	✓	$-0.466$	$0$	$0.882925$	Character $\chi_{2960}(139, \cdot)$
1-2960-2960.1397-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1397	$1$	✓	✓	$0.121$	$0$	$0.877251$	Character $\chi_{2960}(1397, \cdot)$
1-2960-2960.1413-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1413	$1$	✓	✓	$0.0346$	$0$	$0.739761$	Character $\chi_{2960}(1413, \cdot)$
1-2960-2960.1429-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1429	$1$	✓	✓	$-0.234$	$0$	$0.123723$	Character $\chi_{2960}(1429, \cdot)$
1-2960-2960.1453-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1453	$1$	✓	✓	$0.414$	$0$	$0.418011$	Character $\chi_{2960}(1453, \cdot)$
1-2960-2960.1459-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1459	$1$	✓	✓	$-0.122$	$0$	$0.289866$	Character $\chi_{2960}(1459, \cdot)$
1-2960-2960.1467-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1467	$1$	✓	✓	$-0.0892$	$0$	$0.891721$	Character $\chi_{2960}(1467, \cdot)$
1-2960-2960.1477-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1477	$1$	✓	✓	$-0.102$	$0$	$0.609914$	Character $\chi_{2960}(1477, \cdot)$
1-2960-2960.1509-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1509	$1$	✓	✓	$0.109$	$0$	$0.490611$	Character $\chi_{2960}(1509, \cdot)$
1-2960-2960.1523-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1523	$1$	✓	✓	$-0.163$	$0$	$0.557584$	Character $\chi_{2960}(1523, \cdot)$
1-2960-2960.1533-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1533	$1$	✓	✓	$0.289$	$0$	$0.688597$	Character $\chi_{2960}(1533, \cdot)$
1-2960-2960.1549-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1549	$1$	✓	✓	$0.184$	$0$	$0.555792$	Character $\chi_{2960}(1549, \cdot)$
1-2960-2960.1557-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1557	$1$	✓	✓	$-0.0903$	$0$	$0.282442$	Character $\chi_{2960}(1557, \cdot)$
1-2960-2960.157-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.157	$1$	✓	✓	$0.100$	$0$	$0.887627$	Character $\chi_{2960}(157, \cdot)$
1-2960-2960.1579-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1579	$1$	✓	✓	$0.0534$	$0$	$0.683419$	Character $\chi_{2960}(1579, \cdot)$
1-2960-2960.1589-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1589	$1$	✓	✓	$-0.0499$	$0$	$0.919681$	Character $\chi_{2960}(1589, \cdot)$
1-2960-2960.1619-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1619	$1$	✓	✓	$0.158$	$0$	$0.872091$	Character $\chi_{2960}(1619, \cdot)$
1-2960-2960.163-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.163	$1$	✓	✓	$0.00859$	$0$	$0.283888$	Character $\chi_{2960}(163, \cdot)$
1-2960-2960.1637-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1637	$1$	✓	✓	$-0.0242$	$0$	$0.582274$	Character $\chi_{2960}(1637, \cdot)$
1-2960-2960.1643-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1643	$1$	✓	✓	$0.383$	$0$	$1.02215$	Character $\chi_{2960}(1643, \cdot)$
1-2960-2960.1653-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1653	$1$	✓	✓	$-0.0346$	$0$	$0.359050$	Character $\chi_{2960}(1653, \cdot)$
1-2960-2960.1667-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1667	$1$	✓	✓	$-0.263$	$0$	$1.63271$	Character $\chi_{2960}(1667, \cdot)$
1-2960-2960.1677-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1677	$1$	✓	✓	$-0.221$	$0$	$0.224980$	Character $\chi_{2960}(1677, \cdot)$
1-2960-2960.1683-r1-0-0	$318.$	$318.$	$1$	$2^{4} \cdot 5 \cdot 37$	2960.1683	$1$	✓	✓	$0.461$	$0$	$0.793921$	Character $\chi_{2960}(1683, \cdot)$

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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.