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 353 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-709-709.100-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.100	$0$	✓	✓	$-0.383$	$0$	$0.892952$	Character $\chi_{709}(100, \cdot)$
1-709-709.102-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.102	$0$	✓	✓	$-0.396$	$0$	$0.468648$	Character $\chi_{709}(102, \cdot)$
1-709-709.103-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.103	$0$	✓	✓	$0.152$	$0$	$0.828258$	Character $\chi_{709}(103, \cdot)$
1-709-709.104-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.104	$0$	✓	✓	$-0.492$	$0$	$0.975798$	Character $\chi_{709}(104, \cdot)$
1-709-709.105-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.105	$0$	✓	✓	$0.392$	$0$	$0.173420$	Character $\chi_{709}(105, \cdot)$
1-709-709.106-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.106	$0$	✓	✓	$0.269$	$0$	$1.81594$	Character $\chi_{709}(106, \cdot)$
1-709-709.108-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.108	$0$	✓	✓	$-0.436$	$0$	$0.822693$	Character $\chi_{709}(108, \cdot)$
1-709-709.11-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.11	$0$	✓	✓	$-0.342$	$0$	$1.09172$	Character $\chi_{709}(11, \cdot)$
1-709-709.112-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.112	$0$	✓	✓	$0.340$	$0$	$1.58809$	Character $\chi_{709}(112, \cdot)$
1-709-709.113-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.113	$0$	✓	✓	$-0.182$	$0$	$0.581973$	Character $\chi_{709}(113, \cdot)$
1-709-709.116-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.116	$0$	✓	✓	$0.188$	$0$	$2.05674$	Character $\chi_{709}(116, \cdot)$
1-709-709.12-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.12	$0$	✓	✓	$0.139$	$0$	$0.615262$	Character $\chi_{709}(12, \cdot)$
1-709-709.121-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.121	$0$	✓	✓	$-0.376$	$0$	$0.470718$	Character $\chi_{709}(121, \cdot)$
1-709-709.122-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.122	$0$	✓	✓	$-0.0172$	$0$	$1.03401$	Character $\chi_{709}(122, \cdot)$
1-709-709.125-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.125	$0$	✓	✓	$-0.462$	$0$	$1.53697$	Character $\chi_{709}(125, \cdot)$
1-709-709.127-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.127	$0$	✓	✓	$0.0292$	$0$	$1.52835$	Character $\chi_{709}(127, \cdot)$
1-709-709.129-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.129	$0$	✓	✓	$0.342$	$0$	$1.77289$	Character $\chi_{709}(129, \cdot)$
1-709-709.130-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.130	$0$	✓	✓	$-0.431$	$0$	$0.998231$	Character $\chi_{709}(130, \cdot)$
1-709-709.132-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.132	$0$	✓	✓	$0.130$	$0$	$1.18591$	Character $\chi_{709}(132, \cdot)$
1-709-709.133-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.133	$0$	✓	✓	$0.0731$	$0$	$1.79913$	Character $\chi_{709}(133, \cdot)$
1-709-709.135-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.135	$0$	✓	✓	$0.0131$	$0$	$0.560657$	Character $\chi_{709}(135, \cdot)$
1-709-709.136-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.136	$0$	✓	✓	$-0.117$	$0$	$2.85520$	Character $\chi_{709}(136, \cdot)$
1-709-709.138-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.138	$0$	✓	✓	$0.161$	$0$	$1.91863$	Character $\chi_{709}(138, \cdot)$
1-709-709.140-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.140	$0$	✓	✓	$-0.0691$	$0$	$0.662064$	Character $\chi_{709}(140, \cdot)$
1-709-709.141-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.141	$0$	✓	✓	$-0.357$	$0$	$2.41640$	Character $\chi_{709}(141, \cdot)$
1-709-709.142-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.142	$0$	✓	✓	$-0.138$	$0$	$0.602915$	Character $\chi_{709}(142, \cdot)$
1-709-709.144-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.144	$0$	✓	✓	$-0.173$	$0$	$0.203899$	Character $\chi_{709}(144, \cdot)$
1-709-709.145-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.145	$0$	✓	✓	$0.0886$	$0$	$1.00846$	Character $\chi_{709}(145, \cdot)$
1-709-709.146-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.146	$0$	✓	✓	$0.378$	$0$	$1.85880$	Character $\chi_{709}(146, \cdot)$
1-709-709.147-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.147	$0$	✓	✓	$0.360$	$0$	$1.37834$	Character $\chi_{709}(147, \cdot)$
1-709-709.149-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.149	$0$	✓	✓	$-0.161$	$0$	$1.33009$	Character $\chi_{709}(149, \cdot)$
1-709-709.15-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.15	$0$	✓	✓	$0.479$	$0$	$0.282147$	Character $\chi_{709}(15, \cdot)$
1-709-709.151-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.151	$0$	✓	✓	$0.436$	$0$	$1.32816$	Character $\chi_{709}(151, \cdot)$
1-709-709.157-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.157	$0$	✓	✓	$0.0691$	$0$	$1.03241$	Character $\chi_{709}(157, \cdot)$
1-709-709.158-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.158	$0$	✓	✓	$-0.147$	$0$	$0.837298$	Character $\chi_{709}(158, \cdot)$
1-709-709.16-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.16	$0$	✓	✓	$-0.0731$	$0$	$1.43693$	Character $\chi_{709}(16, \cdot)$
1-709-709.163-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.163	$0$	✓	✓	$0.467$	$0$	$0.508616$	Character $\chi_{709}(163, \cdot)$
1-709-709.165-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.165	$0$	✓	✓	$-0.113$	$0$	$0.650415$	Character $\chi_{709}(165, \cdot)$
1-709-709.166-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.166	$0$	✓	✓	$-0.321$	$0$	$0.0560760$	Character $\chi_{709}(166, \cdot)$
1-709-709.169-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.169	$0$	✓	✓	$-0.234$	$0$	$0.907633$	Character $\chi_{709}(169, \cdot)$
1-709-709.170-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.170	$0$	✓	✓	$-0.0467$	$0$	$1.27421$	Character $\chi_{709}(170, \cdot)$
1-709-709.171-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.171	$0$	✓	✓	$0.0467$	$0$	$1.20330$	Character $\chi_{709}(171, \cdot)$
1-709-709.172-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.172	$0$	✓	✓	$-0.308$	$0$	$1.11383$	Character $\chi_{709}(172, \cdot)$
1-709-709.175-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.175	$0$	✓	✓	$0.0480$	$0$	$1.46939$	Character $\chi_{709}(175, \cdot)$
1-709-709.176-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.176	$0$	✓	✓	$0.357$	$0$	$0.218842$	Character $\chi_{709}(176, \cdot)$
1-709-709.177-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.177	$0$	✓	✓	$0.0487$	$0$	$1.15848$	Character $\chi_{709}(177, \cdot)$
1-709-709.178-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.178	$0$	✓	✓	$0.0363$	$0$	$0.124679$	Character $\chi_{709}(178, \cdot)$
1-709-709.179-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.179	$0$	✓	✓	$0.233$	$0$	$1.54841$	Character $\chi_{709}(179, \cdot)$
1-709-709.180-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.180	$0$	✓	✓	$0.0184$	$0$	$1.42450$	Character $\chi_{709}(180, \cdot)$
1-709-709.181-r0-0-0	$3.29$	$3.29$	$1$	$709$	709.181	$0$	✓	✓	$-0.122$	$0$	$0.982786$	Character $\chi_{709}(181, \cdot)$

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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.