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 640 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4000-4000.1003-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1003	$0$	✓	✓	$-0.360$	$0$	$0.549778$	Character $\chi_{4000}(1003, \cdot)$
1-4000-4000.1021-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1021	$0$	✓	✓	$-0.273$	$0$	$0.483312$	Character $\chi_{4000}(1021, \cdot)$
1-4000-4000.1027-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1027	$0$	✓	✓	$0.262$	$0$	$1.22354$	Character $\chi_{4000}(1027, \cdot)$
1-4000-4000.1029-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1029	$0$	✓	✓	$-0.260$	$0$	$0.871262$	Character $\chi_{4000}(1029, \cdot)$
1-4000-4000.1061-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1061	$0$	✓	✓	$0.0752$	$0$	$0.703142$	Character $\chi_{4000}(1061, \cdot)$
1-4000-4000.1067-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1067	$0$	✓	✓	$-0.176$	$0$	$0.255804$	Character $\chi_{4000}(1067, \cdot)$
1-4000-4000.1069-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1069	$0$	✓	✓	$0.260$	$0$	$1.03298$	Character $\chi_{4000}(1069, \cdot)$
1-4000-4000.1083-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1083	$0$	✓	✓	$-0.326$	$0$	$0.479483$	Character $\chi_{4000}(1083, \cdot)$
1-4000-4000.109-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.109	$0$	✓	✓	$-0.0752$	$0$	$0.514034$	Character $\chi_{4000}(109, \cdot)$
1-4000-4000.1109-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1109	$0$	✓	✓	$0.237$	$0$	$1.12856$	Character $\chi_{4000}(1109, \cdot)$
1-4000-4000.1123-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1123	$0$	✓	✓	$0.0627$	$0$	$0.512058$	Character $\chi_{4000}(1123, \cdot)$
1-4000-4000.1141-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1141	$0$	✓	✓	$0.237$	$0$	$0.997196$	Character $\chi_{4000}(1141, \cdot)$
1-4000-4000.1147-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1147	$0$	✓	✓	$0.489$	$0$	$1.14568$	Character $\chi_{4000}(1147, \cdot)$
1-4000-4000.1163-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1163	$0$	✓	✓	$-0.262$	$0$	$0.574055$	Character $\chi_{4000}(1163, \cdot)$
1-4000-4000.1181-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1181	$0$	✓	✓	$-0.489$	$0$	$0.0197276$	Character $\chi_{4000}(1181, \cdot)$
1-4000-4000.1187-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1187	$0$	✓	✓	$-0.125$	$0$	$0.689648$	Character $\chi_{4000}(1187, \cdot)$
1-4000-4000.1189-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1189	$0$	✓	✓	$0.0752$	$0$	$0.950122$	Character $\chi_{4000}(1189, \cdot)$
1-4000-4000.1203-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1203	$0$	✓	✓	$0.226$	$0$	$0.721004$	Character $\chi_{4000}(1203, \cdot)$
1-4000-4000.1221-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1221	$0$	✓	✓	$0.239$	$0$	$0.685339$	Character $\chi_{4000}(1221, \cdot)$
1-4000-4000.1227-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1227	$0$	✓	✓	$0.325$	$0$	$1.28157$	Character $\chi_{4000}(1227, \cdot)$
1-4000-4000.1229-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1229	$0$	✓	✓	$0.476$	$0$	$1.09719$	Character $\chi_{4000}(1229, \cdot)$
1-4000-4000.123-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.123	$0$	✓	✓	$-0.124$	$0$	$0.595733$	Character $\chi_{4000}(123, \cdot)$
1-4000-4000.1261-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1261	$0$	✓	✓	$-0.187$	$0$	$0.622341$	Character $\chi_{4000}(1261, \cdot)$
1-4000-4000.1267-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1267	$0$	✓	✓	$0.0107$	$0$	$0.326425$	Character $\chi_{4000}(1267, \cdot)$
1-4000-4000.1269-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1269	$0$	✓	✓	$0.173$	$0$	$0.720672$	Character $\chi_{4000}(1269, \cdot)$
1-4000-4000.1283-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1283	$0$	✓	✓	$0.460$	$0$	$1.15424$	Character $\chi_{4000}(1283, \cdot)$
1-4000-4000.1309-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1309	$0$	✓	✓	$0.0747$	$0$	$0.773379$	Character $\chi_{4000}(1309, \cdot)$
1-4000-4000.1323-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1323	$0$	✓	✓	$-0.0747$	$0$	$0.966429$	Character $\chi_{4000}(1323, \cdot)$
1-4000-4000.1341-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1341	$0$	✓	✓	$-0.125$	$0$	$0.868421$	Character $\chi_{4000}(1341, \cdot)$
1-4000-4000.1347-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1347	$0$	✓	✓	$-0.323$	$0$	$0.0742521$	Character $\chi_{4000}(1347, \cdot)$
1-4000-4000.1363-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1363	$0$	✓	✓	$0.324$	$0$	$0.846758$	Character $\chi_{4000}(1363, \cdot)$
1-4000-4000.1381-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1381	$0$	✓	✓	$0.0232$	$0$	$1.13044$	Character $\chi_{4000}(1381, \cdot)$
1-4000-4000.1387-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1387	$0$	✓	✓	$0.137$	$0$	$0.951315$	Character $\chi_{4000}(1387, \cdot)$
1-4000-4000.1389-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1389	$0$	✓	✓	$-0.387$	$0$	$0.529873$	Character $\chi_{4000}(1389, \cdot)$
1-4000-4000.1403-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1403	$0$	✓	✓	$-0.0107$	$0$	$1.08317$	Character $\chi_{4000}(1403, \cdot)$
1-4000-4000.141-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.141	$0$	✓	✓	$-0.0752$	$0$	$0.765061$	Character $\chi_{4000}(141, \cdot)$
1-4000-4000.1421-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1421	$0$	✓	✓	$-0.423$	$0$	$0.499942$	Character $\chi_{4000}(1421, \cdot)$
1-4000-4000.1427-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1427	$0$	✓	✓	$0.112$	$0$	$1.29630$	Character $\chi_{4000}(1427, \cdot)$
1-4000-4000.1429-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1429	$0$	✓	✓	$-0.210$	$0$	$0.425364$	Character $\chi_{4000}(1429, \cdot)$
1-4000-4000.1461-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1461	$0$	✓	✓	$0.325$	$0$	$1.09659$	Character $\chi_{4000}(1461, \cdot)$
1-4000-4000.1467-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1467	$0$	✓	✓	$-0.226$	$0$	$0.229662$	Character $\chi_{4000}(1467, \cdot)$
1-4000-4000.1469-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1469	$0$	✓	✓	$0.0107$	$0$	$1.00342$	Character $\chi_{4000}(1469, \cdot)$
1-4000-4000.147-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.147	$0$	✓	✓	$-0.0732$	$0$	$0.441341$	Character $\chi_{4000}(147, \cdot)$
1-4000-4000.1483-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1483	$0$	✓	✓	$0.323$	$0$	$1.57213$	Character $\chi_{4000}(1483, \cdot)$
1-4000-4000.1509-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1509	$0$	✓	✓	$0.387$	$0$	$1.02869$	Character $\chi_{4000}(1509, \cdot)$
1-4000-4000.1523-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1523	$0$	✓	✓	$-0.487$	$0$	$1.09958$	Character $\chi_{4000}(1523, \cdot)$
1-4000-4000.1541-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1541	$0$	✓	✓	$-0.0127$	$0$	$0.682380$	Character $\chi_{4000}(1541, \cdot)$
1-4000-4000.1547-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1547	$0$	✓	✓	$-0.460$	$0$	$1.66257$	Character $\chi_{4000}(1547, \cdot)$
1-4000-4000.1563-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1563	$0$	✓	✓	$-0.312$	$0$	$0.563661$	Character $\chi_{4000}(1563, \cdot)$
1-4000-4000.1581-r0-0-0	$18.5$	$18.5$	$1$	$2^{5} \cdot 5^{3}$	4000.1581	$0$	✓	✓	$-0.0392$	$0$	$0.746720$	Character $\chi_{4000}(1581, \cdot)$

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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.