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 161 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-163-163.10-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.10	$0$	✓	✓	$0.198$	$0$	$2.38742$	Character $\chi_{163}(10, \cdot)$
1-163-163.100-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.100	$0$	✓	✓	$0.201$	$0$	$2.01745$	Character $\chi_{163}(100, \cdot)$
1-163-163.104-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.104	$0$	✓	✓	$0.0108$	$0$	$1.07698$	Character $\chi_{163}(104, \cdot)$
1-163-163.111-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.111	$0$	✓	✓	$0.112$	$0$	$1.61968$	Character $\chi_{163}(111, \cdot)$
1-163-163.113-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.113	$0$	✓	✓	$0.221$	$0$	$2.05551$	Character $\chi_{163}(113, \cdot)$
1-163-163.115-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.115	$0$	✓	✓	$0.202$	$0$	$2.21303$	Character $\chi_{163}(115, \cdot)$
1-163-163.118-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.118	$0$	✓	✓	$0.461$	$0$	$0.687096$	Character $\chi_{163}(118, \cdot)$
1-163-163.119-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.119	$0$	✓	✓	$-0.201$	$0$	$1.50810$	Character $\chi_{163}(119, \cdot)$
1-163-163.121-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.121	$0$	✓	✓	$0.0849$	$0$	$1.29149$	Character $\chi_{163}(121, \cdot)$
1-163-163.126-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.126	$0$	✓	✓	$0.00291$	$0$	$1.59088$	Character $\chi_{163}(126, \cdot)$
1-163-163.131-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.131	$0$	✓	✓	$-0.209$	$0$	$1.06820$	Character $\chi_{163}(131, \cdot)$
1-163-163.132-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.132	$0$	✓	✓	$-0.312$	$0$	$0.979707$	Character $\chi_{163}(132, \cdot)$
1-163-163.133-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.133	$0$	✓	✓	$-0.309$	$0$	$2.84886$	Character $\chi_{163}(133, \cdot)$
1-163-163.134-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.134	$0$	✓	✓	$-0.461$	$0$	$3.18338$	Character $\chi_{163}(134, \cdot)$
1-163-163.135-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.135	$0$	✓	✓	$0.210$	$0$	$2.39906$	Character $\chi_{163}(135, \cdot)$
1-163-163.136-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.136	$0$	✓	✓	$0.339$	$0$	$1.34044$	Character $\chi_{163}(136, \cdot)$
1-163-163.14-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.14	$0$	✓	✓	$0.238$	$0$	$1.83077$	Character $\chi_{163}(14, \cdot)$
1-163-163.140-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.140	$0$	✓	✓	$0.314$	$0$	$2.16227$	Character $\chi_{163}(140, \cdot)$
1-163-163.143-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.143	$0$	✓	✓	$0.107$	$0$	$2.18119$	Character $\chi_{163}(143, \cdot)$
1-163-163.144-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.144	$0$	✓	✓	$0.120$	$0$	$1.01361$	Character $\chi_{163}(144, \cdot)$
1-163-163.145-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.145	$0$	✓	✓	$-0.00836$	$0$	$1.95613$	Character $\chi_{163}(145, \cdot)$
1-163-163.146-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.146	$0$	✓	✓	$-0.202$	$0$	$1.71498$	Character $\chi_{163}(146, \cdot)$
1-163-163.15-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.15	$0$	✓	✓	$0.484$	$0$	$0.175696$	Character $\chi_{163}(15, \cdot)$
1-163-163.150-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.150	$0$	✓	✓	$0.297$	$0$	$2.46845$	Character $\chi_{163}(150, \cdot)$
1-163-163.151-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.151	$0$	✓	✓	$0.0775$	$0$	$1.69420$	Character $\chi_{163}(151, \cdot)$
1-163-163.152-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.152	$0$	✓	✓	$-0.484$	$0$	$1.06364$	Character $\chi_{163}(152, \cdot)$
1-163-163.155-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.155	$0$	✓	✓	$-0.297$	$0$	$0.451248$	Character $\chi_{163}(155, \cdot)$
1-163-163.156-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.156	$0$	✓	✓	$0.00440$	$0$	$2.29907$	Character $\chi_{163}(156, \cdot)$
1-163-163.158-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.158	$0$	✓	✓	$-0.234$	$0$	$1.29395$	Character $\chi_{163}(158, \cdot)$
1-163-163.16-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.16	$0$	✓	✓	$0.155$	$0$	$1.81329$	Character $\chi_{163}(16, \cdot)$
1-163-163.160-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.160	$0$	✓	✓	$0.178$	$0$	$1.61359$	Character $\chi_{163}(160, \cdot)$
1-163-163.161-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.161	$0$	✓	✓	$-0.0172$	$0$	$1.15996$	Character $\chi_{163}(161, \cdot)$
1-163-163.21-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.21	$0$	✓	✓	$0.312$	$0$	$2.32934$	Character $\chi_{163}(21, \cdot)$
1-163-163.22-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.22	$0$	✓	✓	$0.00291$	$0$	$1.02333$	Character $\chi_{163}(22, \cdot)$
1-163-163.24-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.24	$0$	✓	✓	$-0.453$	$0$	$0.823142$	Character $\chi_{163}(24, \cdot)$
1-163-163.25-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.25	$0$	✓	✓	$-0.297$	$0$	$0.400858$	Character $\chi_{163}(25, \cdot)$
1-163-163.26-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.26	$0$	✓	✓	$0.337$	$0$	$1.38353$	Character $\chi_{163}(26, \cdot)$
1-163-163.33-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.33	$0$	✓	✓	$-0.208$	$0$	$1.08267$	Character $\chi_{163}(33, \cdot)$
1-163-163.34-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.34	$0$	✓	✓	$0.453$	$0$	$2.17833$	Character $\chi_{163}(34, \cdot)$
1-163-163.35-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.35	$0$	✓	✓	$-0.238$	$0$	$0.972366$	Character $\chi_{163}(35, \cdot)$
1-163-163.36-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.36	$0$	✓	✓	$0.300$	$0$	$1.81871$	Character $\chi_{163}(36, \cdot)$
1-163-163.38-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.38	$0$	✓	✓	$0.309$	$0$	$0.323316$	Character $\chi_{163}(38, \cdot)$
1-163-163.39-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.39	$0$	✓	✓	$-0.226$	$0$	$1.56819$	Character $\chi_{163}(39, \cdot)$
1-163-163.4-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.4	$0$	✓	✓	$0.182$	$0$	$2.44451$	Character $\chi_{163}(4, \cdot)$
1-163-163.40-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.40	$0$	✓	✓	$0.348$	$0$	$2.49278$	Character $\chi_{163}(40, \cdot)$
1-163-163.41-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.41	$0$	✓	✓	$-0.182$	$0$	$1.72674$	Character $\chi_{163}(41, \cdot)$
1-163-163.43-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.43	$0$	✓	✓	$0.206$	$0$	$1.38490$	Character $\chi_{163}(43, \cdot)$
1-163-163.46-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.46	$0$	✓	✓	$0.226$	$0$	$2.35342$	Character $\chi_{163}(46, \cdot)$
1-163-163.47-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.47	$0$	✓	✓	$-0.112$	$0$	$0.421922$	Character $\chi_{163}(47, \cdot)$
1-163-163.49-r0-0-0	$0.756$	$0.756$	$1$	$163$	163.49	$0$	✓	✓	$-0.198$	$0$	$1.48447$	Character $\chi_{163}(49, \cdot)$

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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.