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 2223 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-3715-3715.1002-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1002	$0$	✓	✓	$-0.262$	$0$	$0.327584$	Character $\chi_{3715}(1002, \cdot)$
1-3715-3715.1008-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1008	$0$	✓	✓	$0.246$	$0$	$1.11226$	Character $\chi_{3715}(1008, \cdot)$
1-3715-3715.1013-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1013	$0$	✓	✓	$0.0190$	$0$	$0.477981$	Character $\chi_{3715}(1013, \cdot)$
1-3715-3715.1014-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1014	$0$	✓	✓	$0.179$	$0$	$0.835460$	Character $\chi_{3715}(1014, \cdot)$
1-3715-3715.1017-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1017	$0$	✓	✓	$-0.175$	$0$	$0.113401$	Character $\chi_{3715}(1017, \cdot)$
1-3715-3715.1019-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1019	$0$	✓	✓	$0.00418$	$0$	$0.838065$	Character $\chi_{3715}(1019, \cdot)$
1-3715-3715.102-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.102	$0$	✓	✓	$0.167$	$0$	$0.494446$	Character $\chi_{3715}(102, \cdot)$
1-3715-3715.1024-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1024	$0$	✓	✓	$0.392$	$0$	$1.22781$	Character $\chi_{3715}(1024, \cdot)$
1-3715-3715.1028-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1028	$0$	✓	✓	$0.300$	$0$	$1.17766$	Character $\chi_{3715}(1028, \cdot)$
1-3715-3715.1034-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1034	$0$	✓	✓	$-0.0991$	$0$	$0.912282$	Character $\chi_{3715}(1034, \cdot)$
1-3715-3715.1039-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1039	$0$	✓	✓	$-0.0373$	$0$	$0.542243$	Character $\chi_{3715}(1039, \cdot)$
1-3715-3715.1042-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1042	$0$	✓	✓	$-0.139$	$0$	$0.207577$	Character $\chi_{3715}(1042, \cdot)$
1-3715-3715.1053-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1053	$0$	✓	✓	$-0.438$	$0$	$0.344375$	Character $\chi_{3715}(1053, \cdot)$
1-3715-3715.1062-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1062	$0$	✓	✓	$0.287$	$0$	$1.38588$	Character $\chi_{3715}(1062, \cdot)$
1-3715-3715.1063-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1063	$0$	✓	✓	$0.0182$	$0$	$0.830822$	Character $\chi_{3715}(1063, \cdot)$
1-3715-3715.1068-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1068	$0$	✓	✓	$-0.184$	$0$	$0.0540201$	Character $\chi_{3715}(1068, \cdot)$
1-3715-3715.107-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.107	$0$	✓	✓	$0.0780$	$0$	$0.643065$	Character $\chi_{3715}(107, \cdot)$
1-3715-3715.1072-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1072	$0$	✓	✓	$0.0272$	$0$	$0.762273$	Character $\chi_{3715}(1072, \cdot)$
1-3715-3715.1073-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1073	$0$	✓	✓	$0.242$	$0$	$0.749389$	Character $\chi_{3715}(1073, \cdot)$
1-3715-3715.1077-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1077	$0$	✓	✓	$-0.111$	$0$	$0.695476$	Character $\chi_{3715}(1077, \cdot)$
1-3715-3715.1082-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1082	$0$	✓	✓	$-0.415$	$0$	$0.716663$	Character $\chi_{3715}(1082, \cdot)$
1-3715-3715.1084-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1084	$0$	✓	✓	$0.0215$	$0$	$0.693895$	Character $\chi_{3715}(1084, \cdot)$
1-3715-3715.1088-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1088	$0$	✓	✓	$-0.0256$	$0$	$1.07916$	Character $\chi_{3715}(1088, \cdot)$
1-3715-3715.1089-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1089	$0$	✓	✓	$-0.0382$	$0$	$0.837656$	Character $\chi_{3715}(1089, \cdot)$
1-3715-3715.109-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.109	$0$	✓	✓	$0.267$	$0$	$0.834235$	Character $\chi_{3715}(109, \cdot)$
1-3715-3715.1093-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1093	$0$	✓	✓	$0.495$	$0$	$0.0808734$	Character $\chi_{3715}(1093, \cdot)$
1-3715-3715.1097-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1097	$0$	✓	✓	$0.0460$	$0$	$0.951120$	Character $\chi_{3715}(1097, \cdot)$
1-3715-3715.1098-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1098	$0$	✓	✓	$0.268$	$0$	$1.02591$	Character $\chi_{3715}(1098, \cdot)$
1-3715-3715.1102-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1102	$0$	✓	✓	$-0.0201$	$0$	$0.945757$	Character $\chi_{3715}(1102, \cdot)$
1-3715-3715.1103-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1103	$0$	✓	✓	$0.190$	$0$	$1.14398$	Character $\chi_{3715}(1103, \cdot)$
1-3715-3715.1104-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1104	$0$	✓	✓	$-0.0975$	$0$	$0.587823$	Character $\chi_{3715}(1104, \cdot)$
1-3715-3715.1113-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1113	$0$	✓	✓	$0.475$	$0$	$1.35308$	Character $\chi_{3715}(1113, \cdot)$
1-3715-3715.1117-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1117	$0$	✓	✓	$-0.169$	$0$	$0.296997$	Character $\chi_{3715}(1117, \cdot)$
1-3715-3715.1118-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1118	$0$	✓	✓	$-0.438$	$0$	$1.37459$	Character $\chi_{3715}(1118, \cdot)$
1-3715-3715.1119-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1119	$0$	✓	✓	$-0.402$	$0$	$0.424128$	Character $\chi_{3715}(1119, \cdot)$
1-3715-3715.112-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.112	$0$	✓	✓	$-0.441$	$0$	$1.73379$	Character $\chi_{3715}(112, \cdot)$
1-3715-3715.1122-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1122	$0$	✓	✓	$-0.170$	$0$	$0.570931$	Character $\chi_{3715}(1122, \cdot)$
1-3715-3715.1123-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1123	$0$	✓	✓	$0.0480$	$0$	$1.23355$	Character $\chi_{3715}(1123, \cdot)$
1-3715-3715.1124-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1124	$0$	✓	✓	$0.377$	$0$	$0.432313$	Character $\chi_{3715}(1124, \cdot)$
1-3715-3715.113-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.113	$0$	✓	✓	$0.316$	$0$	$0.435755$	Character $\chi_{3715}(113, \cdot)$
1-3715-3715.1137-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1137	$0$	✓	✓	$-0.288$	$0$	$0.798419$	Character $\chi_{3715}(1137, \cdot)$
1-3715-3715.1139-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1139	$0$	✓	✓	$-0.441$	$0$	$0.136194$	Character $\chi_{3715}(1139, \cdot)$
1-3715-3715.114-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.114	$0$	✓	✓	$0.230$	$0$	$1.26167$	Character $\chi_{3715}(114, \cdot)$
1-3715-3715.1142-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1142	$0$	✓	✓	$-0.395$	$0$	$1.83413$	Character $\chi_{3715}(1142, \cdot)$
1-3715-3715.1148-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1148	$0$	✓	✓	$0.325$	$0$	$0.987003$	Character $\chi_{3715}(1148, \cdot)$
1-3715-3715.1149-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1149	$0$	✓	✓	$0.482$	$0$	$0.190898$	Character $\chi_{3715}(1149, \cdot)$
1-3715-3715.1153-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1153	$0$	✓	✓	$0.211$	$0$	$0.803401$	Character $\chi_{3715}(1153, \cdot)$
1-3715-3715.1158-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1158	$0$	✓	✓	$-0.447$	$0$	$0.385977$	Character $\chi_{3715}(1158, \cdot)$
1-3715-3715.1162-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1162	$0$	✓	✓	$0.498$	$0$	$0.0623447$	Character $\chi_{3715}(1162, \cdot)$
1-3715-3715.1164-r0-0-0	$17.2$	$17.2$	$1$	$5 \cdot 743$	3715.1164	$0$	✓	✓	$-0.219$	$0$	$0.688677$	Character $\chi_{3715}(1164, \cdot)$

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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.