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

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Results (1-50 of 158 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-407-407.102-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.102	$0$	✓	✓	$-0.324$	$0$	$1.28697$	Character $\chi_{407}(102, \cdot)$
1-407-407.104-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.104	$0$	✓	✓	$-0.225$	$0$	$0.558468$	Character $\chi_{407}(104, \cdot)$
1-407-407.105-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.105	$0$	✓	✓	$-0.358$	$0$	$2.45044$	Character $\chi_{407}(105, \cdot)$
1-407-407.106-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.106	$0$	✓	✓	$0.0779$	$0$	$1.71772$	Character $\chi_{407}(106, \cdot)$
1-407-407.108-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.108	$0$	✓	✓	$-0.154$	$0$	$0.899981$	Character $\chi_{407}(108, \cdot)$
1-407-407.109-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.109	$0$	✓	✓	$0.0959$	$0$	$1.81168$	Character $\chi_{407}(109, \cdot)$
1-407-407.114-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.114	$0$	✓	✓	$-0.195$	$0$	$0.647410$	Character $\chi_{407}(114, \cdot)$
1-407-407.115-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.115	$0$	✓	✓	$-0.236$	$0$	$0.782374$	Character $\chi_{407}(115, \cdot)$
1-407-407.116-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.116	$0$	✓	✓	$-0.364$	$0$	$0.558852$	Character $\chi_{407}(116, \cdot)$
1-407-407.117-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.117	$0$	✓	✓	$0.150$	$0$	$1.51914$	Character $\chi_{407}(117, \cdot)$
1-407-407.128-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.128	$0$	✓	✓	$-0.262$	$0$	$0.999249$	Character $\chi_{407}(128, \cdot)$
1-407-407.129-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.129	$0$	✓	✓	$-0.134$	$0$	$1.30027$	Character $\chi_{407}(129, \cdot)$
1-407-407.13-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.13	$0$	✓	✓	$0.00159$	$0$	$0.707483$	Character $\chi_{407}(13, \cdot)$
1-407-407.131-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.131	$0$	✓	✓	$0.244$	$0$	$1.60034$	Character $\chi_{407}(131, \cdot)$
1-407-407.134-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.134	$0$	✓	✓	$-0.175$	$0$	$0.945785$	Character $\chi_{407}(134, \cdot)$
1-407-407.136-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.136	$0$	✓	✓	$0.203$	$0$	$1.58428$	Character $\chi_{407}(136, \cdot)$
1-407-407.137-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.137	$0$	✓	✓	$-0.247$	$0$	$0.974136$	Character $\chi_{407}(137, \cdot)$
1-407-407.140-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.140	$0$	✓	✓	$0.382$	$0$	$0.489404$	Character $\chi_{407}(140, \cdot)$
1-407-407.141-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.141	$0$	✓	✓	$-0.110$	$0$	$1.34716$	Character $\chi_{407}(141, \cdot)$
1-407-407.142-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.142	$0$	✓	✓	$-0.111$	$0$	$0.924724$	Character $\chi_{407}(142, \cdot)$
1-407-407.147-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.147	$0$	✓	✓	$0.496$	$0$	$0.150751$	Character $\chi_{407}(147, \cdot)$
1-407-407.150-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.150	$0$	✓	✓	$0.207$	$0$	$1.24169$	Character $\chi_{407}(150, \cdot)$
1-407-407.152-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.152	$0$	✓	✓	$-0.122$	$0$	$0.848084$	Character $\chi_{407}(152, \cdot)$
1-407-407.153-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.153	$0$	✓	✓	$-0.117$	$0$	$0.688852$	Character $\chi_{407}(153, \cdot)$
1-407-407.156-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.156	$0$	✓	✓	$0.444$	$0$	$2.14597$	Character $\chi_{407}(156, \cdot)$
1-407-407.157-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.157	$0$	✓	✓	$0.0296$	$0$	$0.864018$	Character $\chi_{407}(157, \cdot)$
1-407-407.158-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.158	$0$	✓	✓	$-0.306$	$0$	$1.18882$	Character $\chi_{407}(158, \cdot)$
1-407-407.159-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.159	$0$	✓	✓	$-0.343$	$0$	$0.258068$	Character $\chi_{407}(159, \cdot)$
1-407-407.16-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.16	$0$	✓	✓	$0.340$	$0$	$1.93121$	Character $\chi_{407}(16, \cdot)$
1-407-407.161-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.161	$0$	✓	✓	$-0.205$	$0$	$0.972826$	Character $\chi_{407}(161, \cdot)$
1-407-407.162-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.162	$0$	✓	✓	$-0.236$	$0$	$2.81425$	Character $\chi_{407}(162, \cdot)$
1-407-407.167-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.167	$0$	✓	✓	$0.0775$	$0$	$1.55412$	Character $\chi_{407}(167, \cdot)$
1-407-407.169-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.169	$0$	✓	✓	$-0.328$	$0$	$1.08320$	Character $\chi_{407}(169, \cdot)$
1-407-407.17-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.17	$0$	✓	✓	$0.451$	$0$	$2.34222$	Character $\chi_{407}(17, \cdot)$
1-407-407.171-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.171	$0$	✓	✓	$0.331$	$0$	$1.55887$	Character $\chi_{407}(171, \cdot)$
1-407-407.172-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.172	$0$	✓	✓	$0.340$	$0$	$1.17537$	Character $\chi_{407}(172, \cdot)$
1-407-407.174-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.174	$0$	✓	✓	$-0.132$	$0$	$1.21985$	Character $\chi_{407}(174, \cdot)$
1-407-407.18-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.18	$0$	✓	✓	$-0.0569$	$0$	$0.957987$	Character $\chi_{407}(18, \cdot)$
1-407-407.181-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.181	$0$	✓	✓	$0.409$	$0$	$0.124135$	Character $\chi_{407}(181, \cdot)$
1-407-407.183-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.183	$0$	✓	✓	$0.134$	$0$	$0.818037$	Character $\chi_{407}(183, \cdot)$
1-407-407.19-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.19	$0$	✓	✓	$-0.207$	$0$	$0.344668$	Character $\chi_{407}(19, \cdot)$
1-407-407.192-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.192	$0$	✓	✓	$-0.455$	$0$	$1.75328$	Character $\chi_{407}(192, \cdot)$
1-407-407.193-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.193	$0$	✓	✓	$-0.0484$	$0$	$0.999254$	Character $\chi_{407}(193, \cdot)$
1-407-407.196-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.196	$0$	✓	✓	$-0.229$	$0$	$0.465171$	Character $\chi_{407}(196, \cdot)$
1-407-407.2-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.2	$0$	✓	✓	$0.415$	$0$	$1.74790$	Character $\chi_{407}(2, \cdot)$
1-407-407.200-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.200	$0$	✓	✓	$0.364$	$0$	$1.52929$	Character $\chi_{407}(200, \cdot)$
1-407-407.201-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.201	$0$	✓	✓	$-0.105$	$0$	$1.17416$	Character $\chi_{407}(201, \cdot)$
1-407-407.204-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.204	$0$	✓	✓	$-0.415$	$0$	$0.568438$	Character $\chi_{407}(204, \cdot)$
1-407-407.205-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.205	$0$	✓	✓	$0.283$	$0$	$1.54852$	Character $\chi_{407}(205, \cdot)$
1-407-407.208-r0-0-0	$1.89$	$1.89$	$1$	$11 \cdot 37$	407.208	$0$	✓	✓	$-0.421$	$0$	$1.01605$	Character $\chi_{407}(208, \cdot)$

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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
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.