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 272 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-475-475.103-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.103	$0$	✓	✓	$0.188$	$0$	$1.10649$	Character $\chi_{475}(103, \cdot)$
1-475-475.104-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.104	$0$	✓	✓	$0.00918$	$0$	$0.943763$	Character $\chi_{475}(104, \cdot)$
1-475-475.106-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.106	$0$	✓	✓	$0.193$	$0$	$1.40447$	Character $\chi_{475}(106, \cdot)$
1-475-475.108-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.108	$0$	✓	✓	$-0.0901$	$0$	$0.648529$	Character $\chi_{475}(108, \cdot)$
1-475-475.11-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.11	$0$	✓	✓	$0.153$	$0$	$1.00510$	Character $\chi_{475}(11, \cdot)$
1-475-475.111-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.111	$0$	✓	✓	$0.344$	$0$	$1.85210$	Character $\chi_{475}(111, \cdot)$
1-475-475.113-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.113	$0$	✓	✓	$0.380$	$0$	$1.56212$	Character $\chi_{475}(113, \cdot)$
1-475-475.117-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.117	$0$	✓	✓	$-0.0898$	$0$	$0.839447$	Character $\chi_{475}(117, \cdot)$
1-475-475.119-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.119	$0$	✓	✓	$0.471$	$0$	$0.730401$	Character $\chi_{475}(119, \cdot)$
1-475-475.12-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.12	$0$	✓	✓	$0.281$	$0$	$1.48252$	Character $\chi_{475}(12, \cdot)$
1-475-475.121-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.121	$0$	✓	✓	$-0.193$	$0$	$1.09650$	Character $\chi_{475}(121, \cdot)$
1-475-475.122-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.122	$0$	✓	✓	$0.188$	$0$	$2.01785$	Character $\chi_{475}(122, \cdot)$
1-475-475.127-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.127	$0$	✓	✓	$0.119$	$0$	$1.31308$	Character $\chi_{475}(127, \cdot)$
1-475-475.128-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.128	$0$	✓	✓	$0.275$	$0$	$1.60334$	Character $\chi_{475}(128, \cdot)$
1-475-475.13-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.13	$0$	✓	✓	$-0.120$	$0$	$2.72321$	Character $\chi_{475}(13, \cdot)$
1-475-475.131-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.131	$0$	✓	✓	$-0.00918$	$0$	$1.77681$	Character $\chi_{475}(131, \cdot)$
1-475-475.139-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.139	$0$	✓	✓	$0.395$	$0$	$2.28705$	Character $\chi_{475}(139, \cdot)$
1-475-475.144-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.144	$0$	✓	✓	$0.193$	$0$	$1.52440$	Character $\chi_{475}(144, \cdot)$
1-475-475.147-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.147	$0$	✓	✓	$0.275$	$0$	$1.38919$	Character $\chi_{475}(147, \cdot)$
1-475-475.148-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.148	$0$	✓	✓	$0.434$	$0$	$1.88510$	Character $\chi_{475}(148, \cdot)$
1-475-475.156-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.156	$0$	✓	✓	$-0.151$	$0$	$0.444220$	Character $\chi_{475}(156, \cdot)$
1-475-475.159-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.159	$0$	✓	✓	$0.346$	$0$	$2.04542$	Character $\chi_{475}(159, \cdot)$
1-475-475.16-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.16	$0$	✓	✓	$0.104$	$0$	$0.728969$	Character $\chi_{475}(16, \cdot)$
1-475-475.161-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.161	$0$	✓	✓	$0.289$	$0$	$0.874365$	Character $\chi_{475}(161, \cdot)$
1-475-475.162-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.162	$0$	✓	✓	$0.133$	$0$	$0.840380$	Character $\chi_{475}(162, \cdot)$
1-475-475.167-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.167	$0$	✓	✓	$-0.275$	$0$	$0.134612$	Character $\chi_{475}(167, \cdot)$
1-475-475.169-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.169	$0$	✓	✓	$-0.00918$	$0$	$0.966094$	Character $\chi_{475}(169, \cdot)$
1-475-475.173-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.173	$0$	✓	✓	$-0.133$	$0$	$0.810477$	Character $\chi_{475}(173, \cdot)$
1-475-475.183-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.183	$0$	✓	✓	$-0.188$	$0$	$1.34745$	Character $\chi_{475}(183, \cdot)$
1-475-475.192-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.192	$0$	✓	✓	$0.156$	$0$	$1.20134$	Character $\chi_{475}(192, \cdot)$
1-475-475.194-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.194	$0$	✓	✓	$-0.151$	$0$	$1.16836$	Character $\chi_{475}(194, \cdot)$
1-475-475.196-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.196	$0$	✓	✓	$-0.384$	$0$	$1.50174$	Character $\chi_{475}(196, \cdot)$
1-475-475.198-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.198	$0$	✓	✓	$-0.281$	$0$	$0.960988$	Character $\chi_{475}(198, \cdot)$
1-475-475.2-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.2	$0$	✓	✓	$0.366$	$0$	$2.13704$	Character $\chi_{475}(2, \cdot)$
1-475-475.202-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.202	$0$	✓	✓	$0.0210$	$0$	$1.49344$	Character $\chi_{475}(202, \cdot)$
1-475-475.203-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.203	$0$	✓	✓	$0.0898$	$0$	$1.44430$	Character $\chi_{475}(203, \cdot)$
1-475-475.206-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.206	$0$	✓	✓	$0.384$	$0$	$0.109368$	Character $\chi_{475}(206, \cdot)$
1-475-475.208-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.208	$0$	✓	✓	$0.410$	$0$	$0.169601$	Character $\chi_{475}(208, \cdot)$
1-475-475.212-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.212	$0$	✓	✓	$0.380$	$0$	$1.27258$	Character $\chi_{475}(212, \cdot)$
1-475-475.214-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.214	$0$	✓	✓	$-0.0682$	$0$	$0.647855$	Character $\chi_{475}(214, \cdot)$
1-475-475.216-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.216	$0$	✓	✓	$-0.153$	$0$	$0.957009$	Character $\chi_{475}(216, \cdot)$
1-475-475.217-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.217	$0$	✓	✓	$0.00891$	$0$	$1.53168$	Character $\chi_{475}(217, \cdot)$
1-475-475.22-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.22	$0$	✓	✓	$0.0901$	$0$	$0.822814$	Character $\chi_{475}(22, \cdot)$
1-475-475.222-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.222	$0$	✓	✓	$0.0898$	$0$	$1.02139$	Character $\chi_{475}(222, \cdot)$
1-475-475.223-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.223	$0$	✓	✓	$-0.194$	$0$	$1.43679$	Character $\chi_{475}(223, \cdot)$
1-475-475.227-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.227	$0$	✓	✓	$-0.380$	$0$	$0.504691$	Character $\chi_{475}(227, \cdot)$
1-475-475.234-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.234	$0$	✓	✓	$0.155$	$0$	$1.47813$	Character $\chi_{475}(234, \cdot)$
1-475-475.238-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.238	$0$	✓	✓	$-0.366$	$0$	$0.881888$	Character $\chi_{475}(238, \cdot)$
1-475-475.239-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.239	$0$	✓	✓	$-0.346$	$0$	$0.859915$	Character $\chi_{475}(239, \cdot)$
1-475-475.242-r0-0-0	$2.20$	$2.20$	$1$	$5^{2} \cdot 19$	475.242	$0$	✓	✓	$0.0958$	$0$	$1.36962$	Character $\chi_{475}(242, \cdot)$

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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.