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 108 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-245-245.103-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.103	$0$	✓	✓	$-0.293$	$0$	$1.07249$	Character $\chi_{245}(103, \cdot)$
1-245-245.108-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.108	$0$	✓	✓	$0.117$	$0$	$1.55439$	Character $\chi_{245}(108, \cdot)$
1-245-245.109-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.109	$0$	✓	✓	$0.340$	$0$	$1.27018$	Character $\chi_{245}(109, \cdot)$
1-245-245.114-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.114	$0$	✓	✓	$-0.210$	$0$	$1.57487$	Character $\chi_{245}(114, \cdot)$
1-245-245.118-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.118	$0$	✓	✓	$-0.0421$	$0$	$1.60150$	Character $\chi_{245}(118, \cdot)$
1-245-245.12-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.12	$0$	✓	✓	$0.134$	$0$	$2.21815$	Character $\chi_{245}(12, \cdot)$
1-245-245.122-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.122	$0$	✓	✓	$0.331$	$0$	$1.73787$	Character $\chi_{245}(122, \cdot)$
1-245-245.13-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.13	$0$	✓	✓	$0.335$	$0$	$2.15300$	Character $\chi_{245}(13, \cdot)$
1-245-245.132-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.132	$0$	✓	✓	$-0.335$	$0$	$1.10855$	Character $\chi_{245}(132, \cdot)$
1-245-245.134-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.134	$0$	✓	✓	$-0.326$	$0$	$1.15990$	Character $\chi_{245}(134, \cdot)$
1-245-245.138-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.138	$0$	✓	✓	$-0.178$	$0$	$1.45598$	Character $\chi_{245}(138, \cdot)$
1-245-245.143-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.143	$0$	✓	✓	$-0.134$	$0$	$1.66596$	Character $\chi_{245}(143, \cdot)$
1-245-245.144-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.144	$0$	✓	✓	$0.210$	$0$	$2.05791$	Character $\chi_{245}(144, \cdot)$
1-245-245.149-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.149	$0$	✓	✓	$0.00680$	$0$	$1.29467$	Character $\chi_{245}(149, \cdot)$
1-245-245.152-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.152	$0$	✓	✓	$-0.117$	$0$	$0.276893$	Character $\chi_{245}(152, \cdot)$
1-245-245.153-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.153	$0$	✓	✓	$-0.215$	$0$	$0.835785$	Character $\chi_{245}(153, \cdot)$
1-245-245.157-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.157	$0$	✓	✓	$0.293$	$0$	$1.65182$	Character $\chi_{245}(157, \cdot)$
1-245-245.167-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.167	$0$	✓	✓	$0.134$	$0$	$1.24111$	Character $\chi_{245}(167, \cdot)$
1-245-245.169-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.169	$0$	✓	✓	$0.204$	$0$	$1.44344$	Character $\chi_{245}(169, \cdot)$
1-245-245.17-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.17	$0$	✓	✓	$0.134$	$0$	$1.40931$	Character $\chi_{245}(17, \cdot)$
1-245-245.173-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.173	$0$	✓	✓	$-0.134$	$0$	$0.558532$	Character $\chi_{245}(173, \cdot)$
1-245-245.179-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.179	$0$	✓	✓	$-0.204$	$0$	$1.09358$	Character $\chi_{245}(179, \cdot)$
1-245-245.184-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.184	$0$	✓	✓	$-0.204$	$0$	$0.0477212$	Character $\chi_{245}(184, \cdot)$
1-245-245.187-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.187	$0$	✓	✓	$0.00203$	$0$	$0.808302$	Character $\chi_{245}(187, \cdot)$
1-245-245.188-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.188	$0$	✓	✓	$0.0394$	$0$	$1.53407$	Character $\chi_{245}(188, \cdot)$
1-245-245.192-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.192	$0$	✓	✓	$0.0421$	$0$	$0.846288$	Character $\chi_{245}(192, \cdot)$
1-245-245.202-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.202	$0$	✓	✓	$-0.0394$	$0$	$1.27286$	Character $\chi_{245}(202, \cdot)$
1-245-245.204-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.204	$0$	✓	✓	$-0.122$	$0$	$1.00468$	Character $\chi_{245}(204, \cdot)$
1-245-245.208-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.208	$0$	✓	✓	$-0.0421$	$0$	$0.897285$	Character $\chi_{245}(208, \cdot)$
1-245-245.213-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.213	$0$	✓	✓	$-0.0421$	$0$	$0.955067$	Character $\chi_{245}(213, \cdot)$
1-245-245.219-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.219	$0$	✓	✓	$0.204$	$0$	$1.80735$	Character $\chi_{245}(219, \cdot)$
1-245-245.222-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.222	$0$	✓	✓	$0.0421$	$0$	$1.72511$	Character $\chi_{245}(222, \cdot)$
1-245-245.223-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.223	$0$	✓	✓	$-0.134$	$0$	$0.700047$	Character $\chi_{245}(223, \cdot)$
1-245-245.237-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.237	$0$	✓	✓	$0.215$	$0$	$1.75434$	Character $\chi_{245}(237, \cdot)$
1-245-245.239-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.239	$0$	✓	✓	$0.122$	$0$	$1.06722$	Character $\chi_{245}(239, \cdot)$
1-245-245.243-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.243	$0$	✓	✓	$-0.331$	$0$	$0.658726$	Character $\chi_{245}(243, \cdot)$
1-245-245.27-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.27	$0$	✓	✓	$0.0421$	$0$	$1.55098$	Character $\chi_{245}(27, \cdot)$
1-245-245.29-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.29	$0$	✓	✓	$-0.204$	$0$	$1.20055$	Character $\chi_{245}(29, \cdot)$
1-245-245.3-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.3	$0$	✓	✓	$0.372$	$0$	$1.47339$	Character $\chi_{245}(3, \cdot)$
1-245-245.33-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.33	$0$	✓	✓	$0.451$	$0$	$2.48502$	Character $\chi_{245}(33, \cdot)$
1-245-245.38-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.38	$0$	✓	✓	$0.00203$	$0$	$1.28850$	Character $\chi_{245}(38, \cdot)$
1-245-245.39-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.39	$0$	✓	✓	$0.455$	$0$	$1.86451$	Character $\chi_{245}(39, \cdot)$
1-245-245.4-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.4	$0$	✓	✓	$0.204$	$0$	$1.78514$	Character $\chi_{245}(4, \cdot)$
1-245-245.44-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.44	$0$	✓	✓	$-0.455$	$0$	$0.284519$	Character $\chi_{245}(44, \cdot)$
1-245-245.47-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.47	$0$	✓	✓	$-0.155$	$0$	$0.791917$	Character $\chi_{245}(47, \cdot)$
1-245-245.52-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.52	$0$	✓	✓	$-0.451$	$0$	$0.925537$	Character $\chi_{245}(52, \cdot)$
1-245-245.62-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.62	$0$	✓	✓	$-0.488$	$0$	$0.335851$	Character $\chi_{245}(62, \cdot)$
1-245-245.64-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.64	$0$	✓	✓	$0.326$	$0$	$2.38544$	Character $\chi_{245}(64, \cdot)$
1-245-245.73-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.73	$0$	✓	✓	$0.155$	$0$	$1.81997$	Character $\chi_{245}(73, \cdot)$
1-245-245.74-r0-0-0	$1.13$	$1.13$	$1$	$5 \cdot 7^{2}$	245.74	$0$	✓	✓	$-0.00680$	$0$	$1.25404$	Character $\chi_{245}(74, \cdot)$

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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.