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 72 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-13e2-169.10-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.10	$0$	✓	✓	$0.00591$	$0$	$1.77046$	Character $\chi_{169}(10, \cdot)$
1-13e2-169.100-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.100	$0$	✓	✓	$0.140$	$0$	$2.08912$	Character $\chi_{169}(100, \cdot)$
1-13e2-169.101-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.101	$0$	✓	✓	$0.0542$	$0$	$1.51906$	Character $\chi_{169}(101, \cdot)$
1-13e2-169.103-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.103	$0$	✓	✓	$-0.0266$	$0$	$1.61420$	Character $\chi_{169}(103, \cdot)$
1-13e2-169.105-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.105	$0$	✓	✓	$-0.473$	$0$	$0.581325$	Character $\chi_{169}(105, \cdot)$
1-13e2-169.107-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.107	$0$	✓	✓	$0.469$	$0$	$0.338235$	Character $\chi_{169}(107, \cdot)$
1-13e2-169.108-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.108	$0$	✓	✓	$0.00591$	$0$	$0.635668$	Character $\chi_{169}(108, \cdot)$
1-13e2-169.113-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.113	$0$	✓	✓	$0.193$	$0$	$1.30501$	Character $\chi_{169}(113, \cdot)$
1-13e2-169.114-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.114	$0$	✓	✓	$0.279$	$0$	$2.17690$	Character $\chi_{169}(114, \cdot)$
1-13e2-169.116-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.116	$0$	✓	✓	$-0.00591$	$0$	$0.480872$	Character $\chi_{169}(116, \cdot)$
1-13e2-169.118-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.118	$0$	✓	✓	$0.00591$	$0$	$0.931410$	Character $\chi_{169}(118, \cdot)$
1-13e2-169.12-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.12	$0$	✓	✓	$0.136$	$0$	$2.28364$	Character $\chi_{169}(12, \cdot)$
1-13e2-169.120-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.120	$0$	✓	✓	$-0.140$	$0$	$1.72820$	Character $\chi_{169}(120, \cdot)$
1-13e2-169.121-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.121	$0$	✓	✓	$-0.0857$	$0$	$1.00713$	Character $\chi_{169}(121, \cdot)$
1-13e2-169.126-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.126	$0$	✓	✓	$0.220$	$0$	$1.63572$	Character $\chi_{169}(126, \cdot)$
1-13e2-169.127-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.127	$0$	✓	✓	$-0.0857$	$0$	$1.29509$	Character $\chi_{169}(127, \cdot)$
1-13e2-169.129-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.129	$0$	✓	✓	$0.130$	$0$	$1.37446$	Character $\chi_{169}(129, \cdot)$
1-13e2-169.131-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.131	$0$	✓	✓	$-0.130$	$0$	$1.20666$	Character $\chi_{169}(131, \cdot)$
1-13e2-169.133-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.133	$0$	✓	✓	$-0.00591$	$0$	$1.61121$	Character $\chi_{169}(133, \cdot)$
1-13e2-169.134-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.134	$0$	✓	✓	$0.463$	$0$	$2.45023$	Character $\chi_{169}(134, \cdot)$
1-13e2-169.139-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.139	$0$	✓	✓	$-0.469$	$0$	$1.88070$	Character $\chi_{169}(139, \cdot)$
1-13e2-169.14-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.14	$0$	✓	✓	$-0.136$	$0$	$1.60673$	Character $\chi_{169}(14, \cdot)$
1-13e2-169.140-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.140	$0$	✓	✓	$-0.463$	$0$	$1.17245$	Character $\chi_{169}(140, \cdot)$
1-13e2-169.142-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.142	$0$	✓	✓	$-0.387$	$0$	$1.19464$	Character $\chi_{169}(142, \cdot)$
1-13e2-169.144-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.144	$0$	✓	✓	$-0.112$	$0$	$0.784255$	Character $\chi_{169}(144, \cdot)$
1-13e2-169.152-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.152	$0$	✓	✓	$-0.00591$	$0$	$1.31753$	Character $\chi_{169}(152, \cdot)$
1-13e2-169.153-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.153	$0$	✓	✓	$0.197$	$0$	$1.68283$	Character $\chi_{169}(153, \cdot)$
1-13e2-169.155-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.155	$0$	✓	✓	$-0.136$	$0$	$0.871422$	Character $\chi_{169}(155, \cdot)$
1-13e2-169.157-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.157	$0$	✓	✓	$0.136$	$0$	$1.26781$	Character $\chi_{169}(157, \cdot)$
1-13e2-169.159-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.159	$0$	✓	✓	$0.00591$	$0$	$1.80463$	Character $\chi_{169}(159, \cdot)$
1-13e2-169.16-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.16	$0$	✓	✓	$0.197$	$0$	$2.54474$	Character $\chi_{169}(16, \cdot)$
1-13e2-169.160-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.160	$0$	✓	✓	$0.203$	$0$	$2.24122$	Character $\chi_{169}(160, \cdot)$
1-13e2-169.165-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.165	$0$	✓	✓	$-0.414$	$0$	$0.519789$	Character $\chi_{169}(165, \cdot)$
1-13e2-169.166-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.166	$0$	✓	✓	$0.306$	$0$	$1.19281$	Character $\chi_{169}(166, \cdot)$
1-13e2-169.17-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.17	$0$	✓	✓	$-0.00591$	$0$	$2.17322$	Character $\chi_{169}(17, \cdot)$
1-13e2-169.25-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.25	$0$	✓	✓	$0.387$	$0$	$2.64125$	Character $\chi_{169}(25, \cdot)$
1-13e2-169.27-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.27	$0$	✓	✓	$0.112$	$0$	$1.15161$	Character $\chi_{169}(27, \cdot)$
1-13e2-169.29-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.29	$0$	✓	✓	$-0.463$	$0$	$2.39800$	Character $\chi_{169}(29, \cdot)$
1-13e2-169.3-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.3	$0$	✓	✓	$-0.193$	$0$	$1.29952$	Character $\chi_{169}(3, \cdot)$
1-13e2-169.30-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.30	$0$	✓	✓	$-0.469$	$0$	$0.728824$	Character $\chi_{169}(30, \cdot)$
1-13e2-169.35-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.35	$0$	✓	✓	$0.463$	$0$	$0.203193$	Character $\chi_{169}(35, \cdot)$
1-13e2-169.36-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.36	$0$	✓	✓	$-0.00591$	$0$	$1.21017$	Character $\chi_{169}(36, \cdot)$
1-13e2-169.38-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.38	$0$	✓	✓	$-0.130$	$0$	$0.619989$	Character $\chi_{169}(38, \cdot)$
1-13e2-169.4-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.4	$0$	✓	✓	$0.0857$	$0$	$1.98853$	Character $\chi_{169}(4, \cdot)$
1-13e2-169.40-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.40	$0$	✓	✓	$0.130$	$0$	$1.60070$	Character $\chi_{169}(40, \cdot)$
1-13e2-169.42-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.42	$0$	✓	✓	$0.414$	$0$	$1.75966$	Character $\chi_{169}(42, \cdot)$
1-13e2-169.43-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.43	$0$	✓	✓	$-0.279$	$0$	$1.38746$	Character $\chi_{169}(43, \cdot)$
1-13e2-169.48-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.48	$0$	✓	✓	$0.414$	$0$	$0.527213$	Character $\chi_{169}(48, \cdot)$
1-13e2-169.49-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.49	$0$	✓	✓	$0.359$	$0$	$1.91934$	Character $\chi_{169}(49, \cdot)$
1-13e2-169.51-r0-0-0	$0.784$	$0.784$	$1$	$13^{2}$	169.51	$0$	✓	✓	$0.00591$	$0$	$1.38694$	Character $\chi_{169}(51, \cdot)$

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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.