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 (40 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-83-83.10-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.10	$0$	✓	✓	$0.229$	$0$	$1.59445$	Character $\chi_{83}(10, \cdot)$
1-83-83.11-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.11	$0$	✓	✓	$0.232$	$0$	$2.17347$	Character $\chi_{83}(11, \cdot)$
1-83-83.12-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.12	$0$	✓	✓	$-0.113$	$0$	$2.29855$	Character $\chi_{83}(12, \cdot)$
1-83-83.16-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.16	$0$	✓	✓	$0.232$	$0$	$2.62640$	Character $\chi_{83}(16, \cdot)$
1-83-83.17-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.17	$0$	✓	✓	$0.259$	$0$	$2.70642$	Character $\chi_{83}(17, \cdot)$
1-83-83.21-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.21	$0$	✓	✓	$0.112$	$0$	$2.65508$	Character $\chi_{83}(21, \cdot)$
1-83-83.23-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.23	$0$	✓	✓	$0.480$	$0$	$0.838582$	Character $\chi_{83}(23, \cdot)$
1-83-83.25-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.25	$0$	✓	✓	$-0.229$	$0$	$0.918246$	Character $\chi_{83}(25, \cdot)$
1-83-83.26-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.26	$0$	✓	✓	$-0.232$	$0$	$1.16681$	Character $\chi_{83}(26, \cdot)$
1-83-83.27-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.27	$0$	✓	✓	$-0.116$	$0$	$1.58683$	Character $\chi_{83}(27, \cdot)$
1-83-83.28-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.28	$0$	✓	✓	$0.113$	$0$	$2.28320$	Character $\chi_{83}(28, \cdot)$
1-83-83.29-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.29	$0$	✓	✓	$0.240$	$0$	$2.23432$	Character $\chi_{83}(29, \cdot)$
1-83-83.3-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.3	$0$	✓	✓	$-0.113$	$0$	$1.79824$	Character $\chi_{83}(3, \cdot)$
1-83-83.30-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.30	$0$	✓	✓	$0.00362$	$0$	$1.53263$	Character $\chi_{83}(30, \cdot)$
1-83-83.31-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.31	$0$	✓	✓	$-0.136$	$0$	$0.605351$	Character $\chi_{83}(31, \cdot)$
1-83-83.33-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.33	$0$	✓	✓	$0.479$	$0$	$3.45795$	Character $\chi_{83}(33, \cdot)$
1-83-83.36-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.36	$0$	✓	✓	$0.00362$	$0$	$2.27120$	Character $\chi_{83}(36, \cdot)$
1-83-83.37-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.37	$0$	✓	✓	$-0.0774$	$0$	$0.774247$	Character $\chi_{83}(37, \cdot)$
1-83-83.38-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.38	$0$	✓	✓	$-0.0595$	$0$	$1.49899$	Character $\chi_{83}(38, \cdot)$
1-83-83.4-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.4	$0$	✓	✓	$-0.112$	$0$	$1.80443$	Character $\chi_{83}(4, \cdot)$
1-83-83.40-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.40	$0$	✓	✓	$0.116$	$0$	$1.33403$	Character $\chi_{83}(40, \cdot)$
1-83-83.41-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.41	$0$	✓	✓	$0.151$	$0$	$2.07015$	Character $\chi_{83}(41, \cdot)$
1-83-83.44-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.44	$0$	✓	✓	$-0.259$	$0$	$0.565529$	Character $\chi_{83}(44, \cdot)$
1-83-83.48-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.48	$0$	✓	✓	$-0.215$	$0$	$1.86642$	Character $\chi_{83}(48, \cdot)$
1-83-83.49-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.49	$0$	✓	✓	$0.315$	$0$	$3.13751$	Character $\chi_{83}(49, \cdot)$
1-83-83.51-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.51	$0$	✓	✓	$0.359$	$0$	$2.30749$	Character $\chi_{83}(51, \cdot)$
1-83-83.59-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.59	$0$	✓	✓	$0.0595$	$0$	$1.73785$	Character $\chi_{83}(59, \cdot)$
1-83-83.61-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.61	$0$	✓	✓	$-0.315$	$0$	$1.46558$	Character $\chi_{83}(61, \cdot)$
1-83-83.63-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.63	$0$	✓	✓	$-0.240$	$0$	$1.31135$	Character $\chi_{83}(63, \cdot)$
1-83-83.64-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.64	$0$	✓	✓	$0.215$	$0$	$2.84225$	Character $\chi_{83}(64, \cdot)$
1-83-83.65-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.65	$0$	✓	✓	$-0.480$	$0$	$3.07067$	Character $\chi_{83}(65, \cdot)$
1-83-83.68-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.68	$0$	✓	✓	$-0.232$	$0$	$1.62553$	Character $\chi_{83}(68, \cdot)$
1-83-83.69-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.69	$0$	✓	✓	$-0.260$	$0$	$1.17190$	Character $\chi_{83}(69, \cdot)$
1-83-83.7-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.7	$0$	✓	✓	$0.113$	$0$	$2.46557$	Character $\chi_{83}(7, \cdot)$
1-83-83.70-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.70	$0$	✓	✓	$-0.359$	$0$	$0.492479$	Character $\chi_{83}(70, \cdot)$
1-83-83.75-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.75	$0$	✓	✓	$0.136$	$0$	$1.57291$	Character $\chi_{83}(75, \cdot)$
1-83-83.77-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.77	$0$	✓	✓	$0.260$	$0$	$2.07848$	Character $\chi_{83}(77, \cdot)$
1-83-83.78-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.78	$0$	✓	✓	$-0.479$	$0$	$0.815236$	Character $\chi_{83}(78, \cdot)$
1-83-83.81-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.81	$0$	✓	✓	$-0.151$	$0$	$1.53861$	Character $\chi_{83}(81, \cdot)$
1-83-83.9-r0-0-0	$0.385$	$0.385$	$1$	$83$	83.9	$0$	✓	✓	$0.0774$	$0$	$1.80514$	Character $\chi_{83}(9, \cdot)$

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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.