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
1-201-201.104-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.104	$1$	✓	✓	$0.0997$	$0$	$1.20522$	Character $\chi_{201}(104, \cdot)$
1-201-201.107-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.107	$1$	✓	✓	$-0.124$	$0$	$0.835184$	Character $\chi_{201}(107, \cdot)$
1-201-201.116-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.116	$1$	✓	✓	$0.259$	$0$	$1.32338$	Character $\chi_{201}(116, \cdot)$
1-201-201.122-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.122	$1$	✓	✓	$-0.289$	$0$	$0.412764$	Character $\chi_{201}(122, \cdot)$
1-201-201.131-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.131	$1$	✓	✓	$-0.216$	$0$	$0.845490$	Character $\chi_{201}(131, \cdot)$
1-201-201.14-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.14	$1$	✓	✓	$-0.355$	$0$	$0.784247$	Character $\chi_{201}(14, \cdot)$
1-201-201.140-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.140	$1$	✓	✓	$0.432$	$0$	$1.81631$	Character $\chi_{201}(140, \cdot)$
1-201-201.143-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.143	$1$	✓	✓	$0.335$	$0$	$1.88655$	Character $\chi_{201}(143, \cdot)$
1-201-201.149-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.149	$1$	✓	✓	$-0.335$	$0$	$0.327841$	Character $\chi_{201}(149, \cdot)$
1-201-201.155-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.155	$1$	✓	✓	$0.447$	$0$	$0.0869434$	Character $\chi_{201}(155, \cdot)$
1-201-201.158-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.158	$1$	✓	✓	$0.355$	$0$	$1.69884$	Character $\chi_{201}(158, \cdot)$
1-201-201.167-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.167	$1$	✓	✓	$-0.0520$	$0$	$1.37220$	Character $\chi_{201}(167, \cdot)$
1-201-201.17-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.17	$1$	✓	✓	$-0.333$	$0$	$0.158719$	Character $\chi_{201}(17, \cdot)$
1-201-201.170-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.170	$1$	✓	✓	$-0.324$	$0$	$0.864798$	Character $\chi_{201}(170, \cdot)$
1-201-201.173-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.173	$1$	✓	✓	$0.289$	$0$	$1.06410$	Character $\chi_{201}(173, \cdot)$
1-201-201.188-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.188	$1$	✓	✓	$0.324$	$0$	$1.17728$	Character $\chi_{201}(188, \cdot)$
1-201-201.194-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.194	$1$	✓	✓	$-0.0886$	$0$	$0.293060$	Character $\chi_{201}(194, \cdot)$
1-201-201.23-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.23	$1$	✓	✓	$-0.371$	$0$	$0.819037$	Character $\chi_{201}(23, \cdot)$
1-201-201.26-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.26	$1$	✓	✓	$-0.259$	$0$	$0.984609$	Character $\chi_{201}(26, \cdot)$
1-201-201.29-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.29	$1$	✓	✓	$-0.0997$	$0$	$0.247619$	Character $\chi_{201}(29, \cdot)$
1-201-201.35-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.35	$1$	✓	✓	$0.371$	$0$	$2.21462$	Character $\chi_{201}(35, \cdot)$
1-201-201.47-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.47	$1$	✓	✓	$-0.172$	$0$	$0.262708$	Character $\chi_{201}(47, \cdot)$
1-201-201.56-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.56	$1$	✓	✓	$-0.432$	$0$	$0.436746$	Character $\chi_{201}(56, \cdot)$
1-201-201.59-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.59	$1$	✓	✓	$-0.428$	$0$	$0.115366$	Character $\chi_{201}(59, \cdot)$
1-201-201.62-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.62	$1$	✓	✓	$0.124$	$0$	$0.620442$	Character $\chi_{201}(62, \cdot)$
1-201-201.65-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.65	$1$	✓	✓	$0.0520$	$0$	$1.39360$	Character $\chi_{201}(65, \cdot)$
1-201-201.71-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.71	$1$	✓	✓	$0.333$	$0$	$1.45954$	Character $\chi_{201}(71, \cdot)$
1-201-201.77-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.77	$1$	✓	✓	$0.172$	$0$	$1.38258$	Character $\chi_{201}(77, \cdot)$
1-201-201.83-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.83	$1$	✓	✓	$-0.447$	$0$	$1.78073$	Character $\chi_{201}(83, \cdot)$
1-201-201.86-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.86	$1$	✓	✓	$0.0886$	$0$	$1.04677$	Character $\chi_{201}(86, \cdot)$
1-201-201.89-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.89	$1$	✓	✓	$0.216$	$0$	$1.27116$	Character $\chi_{201}(89, \cdot)$
1-201-201.92-r1-0-0	$21.6$	$21.6$	$1$	$3 \cdot 67$	201.92	$1$	✓	✓	$0.428$	$0$	$2.28107$	Character $\chi_{201}(92, \cdot)$

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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 $\F_{q}$
Belyi maps

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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.