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 108 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-3e5-243.103-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.103	$0$	✓	✓	$0.161$	$0$	$1.99618$	Character $\chi_{243}(103, \cdot)$
1-3e5-243.106-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.106	$0$	✓	✓	$0.134$	$0$	$1.63229$	Character $\chi_{243}(106, \cdot)$
1-3e5-243.112-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.112	$0$	✓	✓	$0.0874$	$0$	$1.11285$	Character $\chi_{243}(112, \cdot)$
1-3e5-243.115-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.115	$0$	✓	✓	$-0.0874$	$0$	$0.898710$	Character $\chi_{243}(115, \cdot)$
1-3e5-243.121-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.121	$0$	✓	✓	$0.0874$	$0$	$1.03887$	Character $\chi_{243}(121, \cdot)$
1-3e5-243.124-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.124	$0$	✓	✓	$0.394$	$0$	$2.36277$	Character $\chi_{243}(124, \cdot)$
1-3e5-243.13-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.13	$0$	✓	✓	$0.198$	$0$	$2.18640$	Character $\chi_{243}(13, \cdot)$
1-3e5-243.130-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.130	$0$	✓	✓	$-0.0606$	$0$	$0.633685$	Character $\chi_{243}(130, \cdot)$
1-3e5-243.133-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.133	$0$	✓	✓	$0.0236$	$0$	$1.02319$	Character $\chi_{243}(133, \cdot)$
1-3e5-243.139-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.139	$0$	✓	✓	$-0.245$	$0$	$0.769712$	Character $\chi_{243}(139, \cdot)$
1-3e5-243.142-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.142	$0$	✓	✓	$-0.0874$	$0$	$0.414614$	Character $\chi_{243}(142, \cdot)$
1-3e5-243.148-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.148	$0$	✓	✓	$-0.0236$	$0$	$1.34040$	Character $\chi_{243}(148, \cdot)$
1-3e5-243.151-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.151	$0$	✓	✓	$-0.161$	$0$	$1.59804$	Character $\chi_{243}(151, \cdot)$
1-3e5-243.157-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.157	$0$	✓	✓	$0.383$	$0$	$1.66522$	Character $\chi_{243}(157, \cdot)$
1-3e5-243.16-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.16	$0$	✓	✓	$-0.0504$	$0$	$1.28820$	Character $\chi_{243}(16, \cdot)$
1-3e5-243.160-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.160	$0$	✓	✓	$0.245$	$0$	$1.77402$	Character $\chi_{243}(160, \cdot)$
1-3e5-243.166-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.166	$0$	✓	✓	$0.0874$	$0$	$1.31482$	Character $\chi_{243}(166, \cdot)$
1-3e5-243.169-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.169	$0$	✓	✓	$0.245$	$0$	$1.98666$	Character $\chi_{243}(169, \cdot)$
1-3e5-243.175-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.175	$0$	✓	✓	$-0.468$	$0$	$0.363289$	Character $\chi_{243}(175, \cdot)$
1-3e5-243.178-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.178	$0$	✓	✓	$-0.383$	$0$	$0.643575$	Character $\chi_{243}(178, \cdot)$
1-3e5-243.184-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.184	$0$	✓	✓	$0.494$	$0$	$1.67681$	Character $\chi_{243}(184, \cdot)$
1-3e5-243.187-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.187	$0$	✓	✓	$-0.198$	$0$	$1.28066$	Character $\chi_{243}(187, \cdot)$
1-3e5-243.193-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.193	$0$	✓	✓	$0.0874$	$0$	$1.85721$	Character $\chi_{243}(193, \cdot)$
1-3e5-243.196-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.196	$0$	✓	✓	$-0.0874$	$0$	$1.56085$	Character $\chi_{243}(196, \cdot)$
1-3e5-243.202-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.202	$0$	✓	✓	$-0.245$	$0$	$1.34697$	Character $\chi_{243}(202, \cdot)$
1-3e5-243.205-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.205	$0$	✓	✓	$-0.272$	$0$	$0.716671$	Character $\chi_{243}(205, \cdot)$
1-3e5-243.211-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.211	$0$	✓	✓	$0.272$	$0$	$1.95937$	Character $\chi_{243}(211, \cdot)$
1-3e5-243.214-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.214	$0$	✓	✓	$-0.309$	$0$	$1.05520$	Character $\chi_{243}(214, \cdot)$
1-3e5-243.22-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.22	$0$	✓	✓	$-0.171$	$0$	$1.06222$	Character $\chi_{243}(22, \cdot)$
1-3e5-243.220-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.220	$0$	✓	✓	$-0.245$	$0$	$1.30093$	Character $\chi_{243}(220, \cdot)$
1-3e5-243.223-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.223	$0$	✓	✓	$-0.0874$	$0$	$1.37632$	Character $\chi_{243}(223, \cdot)$
1-3e5-243.229-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.229	$0$	✓	✓	$-0.356$	$0$	$0.738798$	Character $\chi_{243}(229, \cdot)$
1-3e5-243.232-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.232	$0$	✓	✓	$0.171$	$0$	$1.12922$	Character $\chi_{243}(232, \cdot)$
1-3e5-243.238-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.238	$0$	✓	✓	$-0.282$	$0$	$0.966890$	Character $\chi_{243}(238, \cdot)$
1-3e5-243.241-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.241	$0$	✓	✓	$-0.0874$	$0$	$0.816092$	Character $\chi_{243}(241, \cdot)$
1-3e5-243.25-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.25	$0$	✓	✓	$0.468$	$0$	$1.65856$	Character $\chi_{243}(25, \cdot)$
1-3e5-243.31-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.31	$0$	✓	✓	$0.0874$	$0$	$1.38160$	Character $\chi_{243}(31, \cdot)$
1-3e5-243.34-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.34	$0$	✓	✓	$-0.0874$	$0$	$0.676563$	Character $\chi_{243}(34, \cdot)$
1-3e5-243.4-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.4	$0$	✓	✓	$0.0874$	$0$	$1.84882$	Character $\chi_{243}(4, \cdot)$
1-3e5-243.40-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.40	$0$	✓	✓	$0.420$	$0$	$2.08171$	Character $\chi_{243}(40, \cdot)$
1-3e5-243.43-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.43	$0$	✓	✓	$0.0606$	$0$	$1.64484$	Character $\chi_{243}(43, \cdot)$
1-3e5-243.49-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.49	$0$	✓	✓	$-0.394$	$0$	$0.847260$	Character $\chi_{243}(49, \cdot)$
1-3e5-243.52-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.52	$0$	✓	✓	$0.356$	$0$	$2.51397$	Character $\chi_{243}(52, \cdot)$
1-3e5-243.58-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.58	$0$	✓	✓	$-0.245$	$0$	$2.80378$	Character $\chi_{243}(58, \cdot)$
1-3e5-243.61-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.61	$0$	✓	✓	$-0.0874$	$0$	$1.46335$	Character $\chi_{243}(61, \cdot)$
1-3e5-243.67-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.67	$0$	✓	✓	$0.309$	$0$	$1.55460$	Character $\chi_{243}(67, \cdot)$
1-3e5-243.7-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.7	$0$	✓	✓	$0.245$	$0$	$1.71283$	Character $\chi_{243}(7, \cdot)$
1-3e5-243.70-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.70	$0$	✓	✓	$-0.494$	$0$	$0.0491925$	Character $\chi_{243}(70, \cdot)$
1-3e5-243.76-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.76	$0$	✓	✓	$0.0504$	$0$	$1.71419$	Character $\chi_{243}(76, \cdot)$
1-3e5-243.79-r0-0-0	$1.12$	$1.12$	$1$	$3^{5}$	243.79	$0$	✓	✓	$-0.420$	$0$	$0.621103$	Character $\chi_{243}(79, \cdot)$

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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.