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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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-5025-5025.1004-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1004	$0$	✓	✓	$0.0400$	$0$	$0.580179$	Character $\chi_{5025}(1004, \cdot)$
1-5025-5025.1016-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1016	$0$	✓	✓	$0.0672$	$0$	$0.512138$	Character $\chi_{5025}(1016, \cdot)$
1-5025-5025.1022-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1022	$0$	✓	✓	$0.0472$	$0$	$0.388016$	Character $\chi_{5025}(1022, \cdot)$
1-5025-5025.1028-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1028	$0$	✓	✓	$-0.353$	$0$	$1.05323$	Character $\chi_{5025}(1028, \cdot)$
1-5025-5025.1046-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1046	$0$	✓	✓	$0.215$	$0$	$0.0187422$	Character $\chi_{5025}(1046, \cdot)$
1-5025-5025.1052-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1052	$0$	✓	✓	$0.274$	$0$	$0.762096$	Character $\chi_{5025}(1052, \cdot)$
1-5025-5025.1067-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1067	$0$	✓	✓	$-0.347$	$0$	$0.679825$	Character $\chi_{5025}(1067, \cdot)$
1-5025-5025.1079-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1079	$0$	✓	✓	$0.145$	$0$	$0.998368$	Character $\chi_{5025}(1079, \cdot)$
1-5025-5025.1088-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1088	$0$	✓	✓	$-0.349$	$0$	$0.113593$	Character $\chi_{5025}(1088, \cdot)$
1-5025-5025.1097-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1097	$0$	✓	✓	$0.354$	$0$	$0.394301$	Character $\chi_{5025}(1097, \cdot)$
1-5025-5025.11-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.11	$0$	✓	✓	$-0.492$	$0$	$1.06700$	Character $\chi_{5025}(11, \cdot)$
1-5025-5025.1106-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1106	$0$	✓	✓	$0.245$	$0$	$0.0194456$	Character $\chi_{5025}(1106, \cdot)$
1-5025-5025.1112-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1112	$0$	✓	✓	$-0.162$	$0$	$0.342587$	Character $\chi_{5025}(1112, \cdot)$
1-5025-5025.1127-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1127	$0$	✓	✓	$0.0664$	$0$	$0.971156$	Character $\chi_{5025}(1127, \cdot)$
1-5025-5025.1148-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1148	$0$	✓	✓	$0.0102$	$0$	$0.583671$	Character $\chi_{5025}(1148, \cdot)$
1-5025-5025.1163-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1163	$0$	✓	✓	$-0.273$	$0$	$1.88064$	Character $\chi_{5025}(1163, \cdot)$
1-5025-5025.1166-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1166	$0$	✓	✓	$-0.387$	$0$	$0.102704$	Character $\chi_{5025}(1166, \cdot)$
1-5025-5025.1169-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1169	$0$	✓	✓	$0.0937$	$0$	$0.555400$	Character $\chi_{5025}(1169, \cdot)$
1-5025-5025.1172-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1172	$0$	✓	✓	$-0.216$	$0$	$0.433946$	Character $\chi_{5025}(1172, \cdot)$
1-5025-5025.1178-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1178	$0$	✓	✓	$-0.0564$	$0$	$1.00843$	Character $\chi_{5025}(1178, \cdot)$
1-5025-5025.1181-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1181	$0$	✓	✓	$0.475$	$0$	$0.404687$	Character $\chi_{5025}(1181, \cdot)$
1-5025-5025.1184-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1184	$0$	✓	✓	$-0.318$	$0$	$0.681277$	Character $\chi_{5025}(1184, \cdot)$
1-5025-5025.119-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.119	$0$	✓	✓	$-0.440$	$0$	$0.330580$	Character $\chi_{5025}(119, \cdot)$
1-5025-5025.1196-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1196	$0$	✓	✓	$-0.397$	$0$	$0.521409$	Character $\chi_{5025}(1196, \cdot)$
1-5025-5025.1211-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1211	$0$	✓	✓	$0.387$	$0$	$0.910429$	Character $\chi_{5025}(1211, \cdot)$
1-5025-5025.1214-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1214	$0$	✓	✓	$-0.295$	$0$	$0.600824$	Character $\chi_{5025}(1214, \cdot)$
1-5025-5025.122-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.122	$0$	✓	✓	$-0.363$	$0$	$1.56942$	Character $\chi_{5025}(122, \cdot)$
1-5025-5025.1223-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1223	$0$	✓	✓	$-0.0227$	$0$	$0.813392$	Character $\chi_{5025}(1223, \cdot)$
1-5025-5025.1244-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1244	$0$	✓	✓	$-0.173$	$0$	$0.493013$	Character $\chi_{5025}(1244, \cdot)$
1-5025-5025.1253-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1253	$0$	✓	✓	$-0.155$	$0$	$0.560956$	Character $\chi_{5025}(1253, \cdot)$
1-5025-5025.1256-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1256	$0$	✓	✓	$-0.107$	$0$	$0.619955$	Character $\chi_{5025}(1256, \cdot)$
1-5025-5025.1259-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1259	$0$	✓	✓	$0.441$	$0$	$1.22636$	Character $\chi_{5025}(1259, \cdot)$
1-5025-5025.1262-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1262	$0$	✓	✓	$0.166$	$0$	$0.682676$	Character $\chi_{5025}(1262, \cdot)$
1-5025-5025.1277-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1277	$0$	✓	✓	$-0.0372$	$0$	$0.869419$	Character $\chi_{5025}(1277, \cdot)$
1-5025-5025.1283-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1283	$0$	✓	✓	$0.155$	$0$	$1.12930$	Character $\chi_{5025}(1283, \cdot)$
1-5025-5025.1286-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1286	$0$	✓	✓	$-0.173$	$0$	$0.348341$	Character $\chi_{5025}(1286, \cdot)$
1-5025-5025.1292-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1292	$0$	✓	✓	$0.344$	$0$	$0.953782$	Character $\chi_{5025}(1292, \cdot)$
1-5025-5025.1298-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1298	$0$	✓	✓	$0.284$	$0$	$0.990838$	Character $\chi_{5025}(1298, \cdot)$
1-5025-5025.1304-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1304	$0$	✓	✓	$-0.0668$	$0$	$0.382491$	Character $\chi_{5025}(1304, \cdot)$
1-5025-5025.1313-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1313	$0$	✓	✓	$0.337$	$0$	$0.0109829$	Character $\chi_{5025}(1313, \cdot)$
1-5025-5025.1316-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1316	$0$	✓	✓	$-0.381$	$0$	$0.507144$	Character $\chi_{5025}(1316, \cdot)$
1-5025-5025.1319-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1319	$0$	✓	✓	$0.105$	$0$	$0.00667716$	Character $\chi_{5025}(1319, \cdot)$
1-5025-5025.1322-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1322	$0$	✓	✓	$0.458$	$0$	$1.61517$	Character $\chi_{5025}(1322, \cdot)$
1-5025-5025.1328-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1328	$0$	✓	✓	$-0.363$	$0$	$0.348799$	Character $\chi_{5025}(1328, \cdot)$
1-5025-5025.1331-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1331	$0$	✓	✓	$0.360$	$0$	$1.17420$	Character $\chi_{5025}(1331, \cdot)$
1-5025-5025.1334-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1334	$0$	✓	✓	$-0.00720$	$0$	$0.462510$	Character $\chi_{5025}(1334, \cdot)$
1-5025-5025.1337-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1337	$0$	✓	✓	$0.290$	$0$	$1.30393$	Character $\chi_{5025}(1337, \cdot)$
1-5025-5025.1373-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1373	$0$	✓	✓	$-0.286$	$0$	$0.576700$	Character $\chi_{5025}(1373, \cdot)$
1-5025-5025.1391-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1391	$0$	✓	✓	$0.134$	$0$	$0.715865$	Character $\chi_{5025}(1391, \cdot)$
1-5025-5025.1406-r0-0-0	$23.3$	$23.3$	$1$	$3 \cdot 5^{2} \cdot 67$	5025.1406	$0$	✓	✓	$-0.0400$	$0$	$0.339631$	Character $\chi_{5025}(1406, \cdot)$

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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.