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 52 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-644-644.107-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.107	$0$	✓	✓	$-0.0527$	$0$	$0.593247$	Character $\chi_{644}(107, \cdot)$
1-644-644.11-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.11	$0$	✓	✓	$0.492$	$0$	$0.472319$	Character $\chi_{644}(11, \cdot)$
1-644-644.131-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.131	$0$	✓	✓	$0.424$	$0$	$1.70097$	Character $\chi_{644}(131, \cdot)$
1-644-644.135-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.135	$0$	✓	✓	$-0.0937$	$0$	$0.884994$	Character $\chi_{644}(135, \cdot)$
1-644-644.167-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.167	$0$	✓	✓	$0.231$	$0$	$1.51859$	Character $\chi_{644}(167, \cdot)$
1-644-644.187-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.187	$0$	✓	✓	$-0.147$	$0$	$1.04199$	Character $\chi_{644}(187, \cdot)$
1-644-644.191-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.191	$0$	✓	✓	$-0.0999$	$0$	$0.732962$	Character $\chi_{644}(191, \cdot)$
1-644-644.215-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.215	$0$	✓	✓	$-0.226$	$0$	$0.513079$	Character $\chi_{644}(215, \cdot)$
1-644-644.223-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.223	$0$	✓	✓	$-0.388$	$0$	$0.689648$	Character $\chi_{644}(223, \cdot)$
1-644-644.235-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.235	$0$	✓	✓	$-0.355$	$0$	$0.405880$	Character $\chi_{644}(235, \cdot)$
1-644-644.243-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.243	$0$	✓	✓	$0.201$	$0$	$1.17987$	Character $\chi_{644}(243, \cdot)$
1-644-644.247-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.247	$0$	✓	✓	$-0.188$	$0$	$0.966161$	Character $\chi_{644}(247, \cdot)$
1-644-644.255-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.255	$0$	✓	✓	$0.0114$	$0$	$1.18346$	Character $\chi_{644}(255, \cdot)$
1-644-644.263-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.263	$0$	✓	✓	$0.0999$	$0$	$0.712951$	Character $\chi_{644}(263, \cdot)$
1-644-644.27-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.27	$0$	✓	✓	$-0.231$	$0$	$0.933156$	Character $\chi_{644}(27, \cdot)$
1-644-644.271-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.271	$0$	✓	✓	$-0.114$	$0$	$0.920356$	Character $\chi_{644}(271, \cdot)$
1-644-644.275-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.275	$0$	✓	✓	$-0.0732$	$0$	$1.09827$	Character $\chi_{644}(275, \cdot)$
1-644-644.279-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.279	$0$	✓	✓	$0.0396$	$0$	$1.02605$	Character $\chi_{644}(279, \cdot)$
1-644-644.291-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.291	$0$	✓	✓	$0.0937$	$0$	$1.16762$	Character $\chi_{644}(291, \cdot)$
1-644-644.3-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.3	$0$	✓	✓	$0.226$	$0$	$0.958793$	Character $\chi_{644}(3, \cdot)$
1-644-644.307-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.307	$0$	✓	✓	$-0.0396$	$0$	$0.776385$	Character $\chi_{644}(307, \cdot)$
1-644-644.31-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.31	$0$	✓	✓	$0.147$	$0$	$1.60919$	Character $\chi_{644}(31, \cdot)$
1-644-644.311-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.311	$0$	✓	✓	$0.362$	$0$	$1.56686$	Character $\chi_{644}(311, \cdot)$
1-644-644.319-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.319	$0$	✓	✓	$0.0527$	$0$	$1.23904$	Character $\chi_{644}(319, \cdot)$
1-644-644.335-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.335	$0$	✓	✓	$0.388$	$0$	$1.95672$	Character $\chi_{644}(335, \cdot)$
1-644-644.359-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.359	$0$	✓	✓	$0.355$	$0$	$1.66020$	Character $\chi_{644}(359, \cdot)$
1-644-644.363-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.363	$0$	✓	✓	$0.0718$	$0$	$1.42946$	Character $\chi_{644}(363, \cdot)$
1-644-644.375-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.375	$0$	✓	✓	$0.0465$	$0$	$1.38127$	Character $\chi_{644}(375, \cdot)$
1-644-644.387-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.387	$0$	✓	✓	$0.0425$	$0$	$1.07145$	Character $\chi_{644}(387, \cdot)$
1-644-644.395-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.395	$0$	✓	✓	$-0.0444$	$0$	$1.05869$	Character $\chi_{644}(395, \cdot)$
1-644-644.423-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.423	$0$	✓	✓	$0.114$	$0$	$1.46010$	Character $\chi_{644}(423, \cdot)$
1-644-644.431-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.431	$0$	✓	✓	$-0.0425$	$0$	$0.662186$	Character $\chi_{644}(431, \cdot)$
1-644-644.439-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.439	$0$	✓	✓	$-0.362$	$0$	$0.436002$	Character $\chi_{644}(439, \cdot)$
1-644-644.459-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.459	$0$	✓	✓	$0.0732$	$0$	$1.17294$	Character $\chi_{644}(459, \cdot)$
1-644-644.471-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.471	$0$	✓	✓	$0.346$	$0$	$1.41546$	Character $\chi_{644}(471, \cdot)$
1-644-644.495-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.495	$0$	✓	✓	$-0.0114$	$0$	$1.53472$	Character $\chi_{644}(495, \cdot)$
1-644-644.51-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.51	$0$	✓	✓	$0.497$	$0$	$0.227867$	Character $\chi_{644}(51, \cdot)$
1-644-644.527-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.527	$0$	✓	✓	$-0.492$	$0$	$1.85599$	Character $\chi_{644}(527, \cdot)$
1-644-644.531-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.531	$0$	✓	✓	$-0.175$	$0$	$0.451107$	Character $\chi_{644}(531, \cdot)$
1-644-644.535-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.535	$0$	✓	✓	$0.418$	$0$	$0.283065$	Character $\chi_{644}(535, \cdot)$
1-644-644.543-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.543	$0$	✓	✓	$0.497$	$0$	$1.56099$	Character $\chi_{644}(543, \cdot)$
1-644-644.55-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.55	$0$	✓	✓	$-0.0718$	$0$	$0.709527$	Character $\chi_{644}(55, \cdot)$
1-644-644.571-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.571	$0$	✓	✓	$0.188$	$0$	$1.72629$	Character $\chi_{644}(571, \cdot)$
1-644-644.579-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.579	$0$	✓	✓	$-0.418$	$0$	$1.97953$	Character $\chi_{644}(579, \cdot)$
1-644-644.587-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.587	$0$	✓	✓	$0.175$	$0$	$0.956797$	Character $\chi_{644}(587, \cdot)$
1-644-644.59-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.59	$0$	✓	✓	$-0.424$	$0$	$0.380388$	Character $\chi_{644}(59, \cdot)$
1-644-644.591-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.591	$0$	✓	✓	$-0.201$	$0$	$0.356368$	Character $\chi_{644}(591, \cdot)$
1-644-644.607-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.607	$0$	✓	✓	$-0.258$	$0$	$0.692754$	Character $\chi_{644}(607, \cdot)$
1-644-644.67-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.67	$0$	✓	✓	$-0.346$	$0$	$0.492167$	Character $\chi_{644}(67, \cdot)$
1-644-644.75-r0-0-0	$2.99$	$2.99$	$1$	$2^{2} \cdot 7 \cdot 23$	644.75	$0$	✓	✓	$0.0444$	$0$	$1.01443$	Character $\chi_{644}(75, \cdot)$

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Classical	Maass
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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.