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 (32 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1380-1380.107-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.107	$0$	✓	✓	$0.0631$	$0$	$0.841842$	Character $\chi_{1380}(107, \cdot)$
1-1380-1380.1103-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.1103	$0$	✓	✓	$0.411$	$0$	$1.33601$	Character $\chi_{1380}(1103, \cdot)$
1-1380-1380.1139-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.1139	$0$	✓	✓	$0.357$	$0$	$1.56014$	Character $\chi_{1380}(1139, \cdot)$
1-1380-1380.1187-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.1187	$0$	✓	✓	$0.108$	$0$	$1.09715$	Character $\chi_{1380}(1187, \cdot)$
1-1380-1380.119-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.119	$0$	✓	✓	$0.405$	$0$	$1.34251$	Character $\chi_{1380}(119, \cdot)$
1-1380-1380.1199-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.1199	$0$	✓	✓	$-0.414$	$0$	$0.266197$	Character $\chi_{1380}(1199, \cdot)$
1-1380-1380.1247-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.1247	$0$	✓	✓	$0.0681$	$0$	$0.805077$	Character $\chi_{1380}(1247, \cdot)$
1-1380-1380.1307-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.1307	$0$	✓	✓	$0.340$	$0$	$1.38357$	Character $\chi_{1380}(1307, \cdot)$
1-1380-1380.1319-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.1319	$0$	✓	✓	$0.414$	$0$	$1.53638$	Character $\chi_{1380}(1319, \cdot)$
1-1380-1380.1367-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.1367	$0$	✓	✓	$0.342$	$0$	$1.30032$	Character $\chi_{1380}(1367, \cdot)$
1-1380-1380.143-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.143	$0$	✓	✓	$-0.108$	$0$	$0.644449$	Character $\chi_{1380}(143, \cdot)$
1-1380-1380.179-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.179	$0$	✓	✓	$-0.0190$	$0$	$0.781185$	Character $\chi_{1380}(179, \cdot)$
1-1380-1380.203-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.203	$0$	✓	✓	$0.164$	$0$	$1.20935$	Character $\chi_{1380}(203, \cdot)$
1-1380-1380.227-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.227	$0$	✓	✓	$0.113$	$0$	$1.22995$	Character $\chi_{1380}(227, \cdot)$
1-1380-1380.239-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.239	$0$	✓	✓	$0.0190$	$0$	$0.924941$	Character $\chi_{1380}(239, \cdot)$
1-1380-1380.263-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.263	$0$	✓	✓	$0.165$	$0$	$1.33120$	Character $\chi_{1380}(263, \cdot)$
1-1380-1380.287-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.287	$0$	✓	✓	$0.189$	$0$	$0.918889$	Character $\chi_{1380}(287, \cdot)$
1-1380-1380.383-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.383	$0$	✓	✓	$-0.113$	$0$	$0.841940$	Character $\chi_{1380}(383, \cdot)$
1-1380-1380.467-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.467	$0$	✓	✓	$-0.165$	$0$	$0.644355$	Character $\chi_{1380}(467, \cdot)$
1-1380-1380.503-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.503	$0$	✓	✓	$-0.0631$	$0$	$0.682953$	Character $\chi_{1380}(503, \cdot)$
1-1380-1380.527-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.527	$0$	✓	✓	$-0.0132$	$0$	$0.961465$	Character $\chi_{1380}(527, \cdot)$
1-1380-1380.563-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.563	$0$	✓	✓	$0.0132$	$0$	$1.03903$	Character $\chi_{1380}(563, \cdot)$
1-1380-1380.59-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.59	$0$	✓	✓	$0.115$	$0$	$1.05604$	Character $\chi_{1380}(59, \cdot)$
1-1380-1380.707-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.707	$0$	✓	✓	$-0.164$	$0$	$0.757960$	Character $\chi_{1380}(707, \cdot)$
1-1380-1380.719-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.719	$0$	✓	✓	$-0.405$	$0$	$0.173544$	Character $\chi_{1380}(719, \cdot)$
1-1380-1380.743-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.743	$0$	✓	✓	$-0.342$	$0$	$0.341339$	Character $\chi_{1380}(743, \cdot)$
1-1380-1380.803-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.803	$0$	✓	✓	$-0.189$	$0$	$0.360785$	Character $\chi_{1380}(803, \cdot)$
1-1380-1380.827-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.827	$0$	✓	✓	$-0.411$	$0$	$0.0515789$	Character $\chi_{1380}(827, \cdot)$
1-1380-1380.83-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.83	$0$	✓	✓	$-0.0681$	$0$	$0.579636$	Character $\chi_{1380}(83, \cdot)$
1-1380-1380.899-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.899	$0$	✓	✓	$-0.357$	$0$	$0.470856$	Character $\chi_{1380}(899, \cdot)$
1-1380-1380.959-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.959	$0$	✓	✓	$-0.115$	$0$	$0.702099$	Character $\chi_{1380}(959, \cdot)$
1-1380-1380.983-r0-0-0	$6.40$	$6.40$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 23$	1380.983	$0$	✓	✓	$-0.340$	$0$	$0.250058$	Character $\chi_{1380}(983, \cdot)$

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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.