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 144 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-26e2-676.11-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.11	$0$	✓	✓	$0.367$	$0$	$1.56077$	Character $\chi_{676}(11, \cdot)$
1-26e2-676.111-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.111	$0$	✓	✓	$0.111$	$0$	$1.66150$	Character $\chi_{676}(111, \cdot)$
1-26e2-676.115-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.115	$0$	✓	✓	$0.00147$	$0$	$1.56112$	Character $\chi_{676}(115, \cdot)$
1-26e2-676.119-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.119	$0$	✓	✓	$-0.396$	$0$	$0.388600$	Character $\chi_{676}(119, \cdot)$
1-26e2-676.123-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.123	$0$	✓	✓	$-0.367$	$0$	$0.443632$	Character $\chi_{676}(123, \cdot)$
1-26e2-676.135-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.135	$0$	✓	✓	$0.00147$	$0$	$0.939867$	Character $\chi_{676}(135, \cdot)$
1-26e2-676.15-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.15	$0$	✓	✓	$0.449$	$0$	$1.52324$	Character $\chi_{676}(15, \cdot)$
1-26e2-676.151-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.151	$0$	✓	✓	$-0.221$	$0$	$0.614127$	Character $\chi_{676}(151, \cdot)$
1-26e2-676.163-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.163	$0$	✓	✓	$-0.451$	$0$	$0.613254$	Character $\chi_{676}(163, \cdot)$
1-26e2-676.167-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.167	$0$	✓	✓	$0.299$	$0$	$1.00809$	Character $\chi_{676}(167, \cdot)$
1-26e2-676.171-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.171	$0$	✓	✓	$0.299$	$0$	$1.54756$	Character $\chi_{676}(171, \cdot)$
1-26e2-676.175-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.175	$0$	✓	✓	$0.0483$	$0$	$1.35745$	Character $\chi_{676}(175, \cdot)$
1-26e2-676.187-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.187	$0$	✓	✓	$0.278$	$0$	$1.11625$	Character $\chi_{676}(187, \cdot)$
1-26e2-676.203-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.203	$0$	✓	✓	$0.00147$	$0$	$0.432257$	Character $\chi_{676}(203, \cdot)$
1-26e2-676.215-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.215	$0$	✓	✓	$-0.367$	$0$	$0.307386$	Character $\chi_{676}(215, \cdot)$
1-26e2-676.219-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.219	$0$	✓	✓	$0.103$	$0$	$1.14237$	Character $\chi_{676}(219, \cdot)$
1-26e2-676.223-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.223	$0$	✓	✓	$0.00147$	$0$	$1.02737$	Character $\chi_{676}(223, \cdot)$
1-26e2-676.227-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.227	$0$	✓	✓	$-0.388$	$0$	$0.0116419$	Character $\chi_{676}(227, \cdot)$
1-26e2-676.255-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.255	$0$	✓	✓	$0.103$	$0$	$1.06806$	Character $\chi_{676}(255, \cdot)$
1-26e2-676.267-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.267	$0$	✓	✓	$0.396$	$0$	$1.32520$	Character $\chi_{676}(267, \cdot)$
1-26e2-676.271-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.271	$0$	✓	✓	$0.388$	$0$	$1.68568$	Character $\chi_{676}(271, \cdot)$
1-26e2-676.275-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.275	$0$	✓	✓	$0.00147$	$0$	$1.06037$	Character $\chi_{676}(275, \cdot)$
1-26e2-676.279-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.279	$0$	✓	✓	$0.00147$	$0$	$0.684749$	Character $\chi_{676}(279, \cdot)$
1-26e2-676.291-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.291	$0$	✓	✓	$0.221$	$0$	$1.36742$	Character $\chi_{676}(291, \cdot)$
1-26e2-676.307-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.307	$0$	✓	✓	$-0.118$	$0$	$0.572610$	Character $\chi_{676}(307, \cdot)$
1-26e2-676.31-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.31	$0$	✓	✓	$0.381$	$0$	$1.79360$	Character $\chi_{676}(31, \cdot)$
1-26e2-676.323-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.323	$0$	✓	✓	$0.449$	$0$	$1.95450$	Character $\chi_{676}(323, \cdot)$
1-26e2-676.327-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.327	$0$	✓	✓	$0.367$	$0$	$1.12352$	Character $\chi_{676}(327, \cdot)$
1-26e2-676.331-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.331	$0$	✓	✓	$0.115$	$0$	$0.864600$	Character $\chi_{676}(331, \cdot)$
1-26e2-676.343-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.343	$0$	✓	✓	$0.00147$	$0$	$0.762780$	Character $\chi_{676}(343, \cdot)$
1-26e2-676.359-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.359	$0$	✓	✓	$0.217$	$0$	$1.50731$	Character $\chi_{676}(359, \cdot)$
1-26e2-676.371-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.371	$0$	✓	✓	$0.103$	$0$	$1.64906$	Character $\chi_{676}(371, \cdot)$
1-26e2-676.375-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.375	$0$	✓	✓	$0.214$	$0$	$1.35895$	Character $\chi_{676}(375, \cdot)$
1-26e2-676.379-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.379	$0$	✓	✓	$-0.103$	$0$	$1.04217$	Character $\chi_{676}(379, \cdot)$
1-26e2-676.383-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.383	$0$	✓	✓	$-0.449$	$0$	$0.595664$	Character $\chi_{676}(383, \cdot)$
1-26e2-676.395-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.395	$0$	✓	✓	$-0.103$	$0$	$1.16319$	Character $\chi_{676}(395, \cdot)$
1-26e2-676.411-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.411	$0$	✓	✓	$0.0340$	$0$	$1.29519$	Character $\chi_{676}(411, \cdot)$
1-26e2-676.423-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.423	$0$	✓	✓	$-0.299$	$0$	$0.938103$	Character $\chi_{676}(423, \cdot)$
1-26e2-676.431-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.431	$0$	✓	✓	$-0.0552$	$0$	$0.998157$	Character $\chi_{676}(431, \cdot)$
1-26e2-676.435-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.435	$0$	✓	✓	$0.00147$	$0$	$1.35890$	Character $\chi_{676}(435, \cdot)$
1-26e2-676.447-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.447	$0$	✓	✓	$0.118$	$0$	$1.26548$	Character $\chi_{676}(447, \cdot)$
1-26e2-676.463-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.463	$0$	✓	✓	$-0.0340$	$0$	$1.15144$	Character $\chi_{676}(463, \cdot)$
1-26e2-676.47-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.47	$0$	✓	✓	$-0.278$	$0$	$0.686109$	Character $\chi_{676}(47, \cdot)$
1-26e2-676.475-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.475	$0$	✓	✓	$0.285$	$0$	$1.16746$	Character $\chi_{676}(475, \cdot)$
1-26e2-676.479-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.479	$0$	✓	✓	$-0.0483$	$0$	$1.01707$	Character $\chi_{676}(479, \cdot)$
1-26e2-676.483-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.483	$0$	✓	✓	$-0.115$	$0$	$0.840076$	Character $\chi_{676}(483, \cdot)$
1-26e2-676.487-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.487	$0$	✓	✓	$-0.444$	$0$	$2.05269$	Character $\chi_{676}(487, \cdot)$
1-26e2-676.499-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.499	$0$	✓	✓	$-0.217$	$0$	$1.04746$	Character $\chi_{676}(499, \cdot)$
1-26e2-676.515-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.515	$0$	✓	✓	$-0.217$	$0$	$0.706646$	Character $\chi_{676}(515, \cdot)$
1-26e2-676.527-r0-0-0	$3.13$	$3.13$	$1$	$2^{2} \cdot 13^{2}$	676.527	$0$	✓	✓	$0.0552$	$0$	$0.896655$	Character $\chi_{676}(527, \cdot)$

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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
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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.