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 464 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-775-775.108-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.108	$0$	✓	✓	$0.463$	$0$	$0.340503$	Character $\chi_{775}(108, \cdot)$
1-775-775.109-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.109	$0$	✓	✓	$0.282$	$0$	$1.47997$	Character $\chi_{775}(109, \cdot)$
1-775-775.111-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.111	$0$	✓	✓	$-0.438$	$0$	$0.158146$	Character $\chi_{775}(111, \cdot)$
1-775-775.117-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.117	$0$	✓	✓	$0.217$	$0$	$1.98028$	Character $\chi_{775}(117, \cdot)$
1-775-775.12-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.12	$0$	✓	✓	$0.441$	$0$	$0.431515$	Character $\chi_{775}(12, \cdot)$
1-775-775.121-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.121	$0$	✓	✓	$-0.159$	$0$	$0.806461$	Character $\chi_{775}(121, \cdot)$
1-775-775.122-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.122	$0$	✓	✓	$-0.463$	$0$	$2.12137$	Character $\chi_{775}(122, \cdot)$
1-775-775.123-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.123	$0$	✓	✓	$-0.380$	$0$	$0.188879$	Character $\chi_{775}(123, \cdot)$
1-775-775.127-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.127	$0$	✓	✓	$0.186$	$0$	$1.32974$	Character $\chi_{775}(127, \cdot)$
1-775-775.129-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.129	$0$	✓	✓	$0.442$	$0$	$1.65900$	Character $\chi_{775}(129, \cdot)$
1-775-775.13-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.13	$0$	✓	✓	$-0.181$	$0$	$1.17111$	Character $\chi_{775}(13, \cdot)$
1-775-775.131-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.131	$0$	✓	✓	$0.493$	$0$	$0.694535$	Character $\chi_{775}(131, \cdot)$
1-775-775.134-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.134	$0$	✓	✓	$0.379$	$0$	$1.54639$	Character $\chi_{775}(134, \cdot)$
1-775-775.137-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.137	$0$	✓	✓	$0.318$	$0$	$0.699833$	Character $\chi_{775}(137, \cdot)$
1-775-775.14-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.14	$0$	✓	✓	$-0.399$	$0$	$1.00614$	Character $\chi_{775}(14, \cdot)$
1-775-775.144-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.144	$0$	✓	✓	$0.179$	$0$	$0.922131$	Character $\chi_{775}(144, \cdot)$
1-775-775.147-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.147	$0$	✓	✓	$-0.0683$	$0$	$0.807924$	Character $\chi_{775}(147, \cdot)$
1-775-775.148-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.148	$0$	✓	✓	$-0.0721$	$0$	$1.02312$	Character $\chi_{775}(148, \cdot)$
1-775-775.153-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.153	$0$	✓	✓	$-0.463$	$0$	$0.317857$	Character $\chi_{775}(153, \cdot)$
1-775-775.158-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.158	$0$	✓	✓	$-0.0238$	$0$	$1.46562$	Character $\chi_{775}(158, \cdot)$
1-775-775.159-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.159	$0$	✓	✓	$0.323$	$0$	$1.36397$	Character $\chi_{775}(159, \cdot)$
1-775-775.16-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.16	$0$	✓	✓	$-0.217$	$0$	$0.817391$	Character $\chi_{775}(16, \cdot)$
1-775-775.164-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.164	$0$	✓	✓	$0.286$	$0$	$1.97617$	Character $\chi_{775}(164, \cdot)$
1-775-775.167-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.167	$0$	✓	✓	$-0.0285$	$0$	$1.33319$	Character $\chi_{775}(167, \cdot)$
1-775-775.169-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.169	$0$	✓	✓	$0.140$	$0$	$1.48453$	Character $\chi_{775}(169, \cdot)$
1-775-775.17-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.17	$0$	✓	✓	$-0.270$	$0$	$0.509910$	Character $\chi_{775}(17, \cdot)$
1-775-775.171-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.171	$0$	✓	✓	$-0.257$	$0$	$0.123352$	Character $\chi_{775}(171, \cdot)$
1-775-775.172-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.172	$0$	✓	✓	$-0.0901$	$0$	$0.561024$	Character $\chi_{775}(172, \cdot)$
1-775-775.177-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.177	$0$	✓	✓	$-0.187$	$0$	$1.11099$	Character $\chi_{775}(177, \cdot)$
1-775-775.178-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.178	$0$	✓	✓	$-0.0683$	$0$	$0.990097$	Character $\chi_{775}(178, \cdot)$
1-775-775.19-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.19	$0$	✓	✓	$-0.281$	$0$	$2.25797$	Character $\chi_{775}(19, \cdot)$
1-775-775.191-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.191	$0$	✓	✓	$0.482$	$0$	$1.66934$	Character $\chi_{775}(191, \cdot)$
1-775-775.192-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.192	$0$	✓	✓	$0.115$	$0$	$0.750859$	Character $\chi_{775}(192, \cdot)$
1-775-775.194-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.194	$0$	✓	✓	$0.216$	$0$	$0.940659$	Character $\chi_{775}(194, \cdot)$
1-775-775.196-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.196	$0$	✓	✓	$-0.160$	$0$	$1.04342$	Character $\chi_{775}(196, \cdot)$
1-775-775.197-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.197	$0$	✓	✓	$0.270$	$0$	$1.02041$	Character $\chi_{775}(197, \cdot)$
1-775-775.198-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.198	$0$	✓	✓	$-0.318$	$0$	$0.313696$	Character $\chi_{775}(198, \cdot)$
1-775-775.203-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.203	$0$	✓	✓	$-0.0901$	$0$	$1.35913$	Character $\chi_{775}(203, \cdot)$
1-775-775.204-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.204	$0$	✓	✓	$0.281$	$0$	$0.0910088$	Character $\chi_{775}(204, \cdot)$
1-775-775.206-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.206	$0$	✓	✓	$0.179$	$0$	$1.57824$	Character $\chi_{775}(206, \cdot)$
1-775-775.208-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.208	$0$	✓	✓	$-0.397$	$0$	$0.595770$	Character $\chi_{775}(208, \cdot)$
1-775-775.211-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.211	$0$	✓	✓	$-0.482$	$0$	$0.549041$	Character $\chi_{775}(211, \cdot)$
1-775-775.212-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.212	$0$	✓	✓	$0.174$	$0$	$0.932309$	Character $\chi_{775}(212, \cdot)$
1-775-775.213-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.213	$0$	✓	✓	$0.0383$	$0$	$0.772002$	Character $\chi_{775}(213, \cdot)$
1-775-775.214-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.214	$0$	✓	✓	$-0.379$	$0$	$0.0160768$	Character $\chi_{775}(214, \cdot)$
1-775-775.219-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.219	$0$	✓	✓	$0.257$	$0$	$1.63791$	Character $\chi_{775}(219, \cdot)$
1-775-775.22-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.22	$0$	✓	✓	$-0.217$	$0$	$0.336314$	Character $\chi_{775}(22, \cdot)$
1-775-775.221-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.221	$0$	✓	✓	$-0.216$	$0$	$1.13592$	Character $\chi_{775}(221, \cdot)$
1-775-775.223-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.223	$0$	✓	✓	$-0.174$	$0$	$0.827958$	Character $\chi_{775}(223, \cdot)$
1-775-775.228-r0-0-0	$3.59$	$3.59$	$1$	$5^{2} \cdot 31$	775.228	$0$	✓	✓	$0.270$	$0$	$1.68445$	Character $\chi_{775}(228, \cdot)$

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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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Results (1-50 of 464 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.