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 885 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\mathbb{Q}$	self-dual	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1037-1037.10-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.10	$0$	✓	✓			$0.0460$	$0$	$1.04559$	Character $\chi_{1037}(10, \cdot)$
1-1037-1037.100-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.100	$0$	✓	✓			$-0.0822$	$0$	$1.42972$	Character $\chi_{1037}(100, \cdot)$
1-1037-1037.1000-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1000	$0$	✓	✓			$0.271$	$0$	$1.46978$	Character $\chi_{1037}(1000, \cdot)$
1-1037-1037.1001-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1001	$0$	✓	✓			$-0.214$	$0$	$1.21022$	Character $\chi_{1037}(1001, \cdot)$
1-1037-1037.1006-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1006	$0$	✓	✓			$-0.115$	$0$	$0.626887$	Character $\chi_{1037}(1006, \cdot)$
1-1037-1037.1008-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1008	$0$	✓	✓			$0.0741$	$0$	$0.621509$	Character $\chi_{1037}(1008, \cdot)$
1-1037-1037.1009-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1009	$0$	✓	✓			$0.136$	$0$	$0.901068$	Character $\chi_{1037}(1009, \cdot)$
1-1037-1037.1012-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1012	$0$	✓	✓			$-0.297$	$0$	$0.816547$	Character $\chi_{1037}(1012, \cdot)$
1-1037-1037.1013-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1013	$0$	✓	✓			$0.357$	$0$	$1.30626$	Character $\chi_{1037}(1013, \cdot)$
1-1037-1037.1014-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1014	$0$	✓	✓			$0.00529$	$0$	$1.03802$	Character $\chi_{1037}(1014, \cdot)$
1-1037-1037.1018-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1018	$0$	✓	✓			$-0.0424$	$0$	$0.576612$	Character $\chi_{1037}(1018, \cdot)$
1-1037-1037.1022-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1022	$0$	✓	✓			$0.0698$	$0$	$0.775176$	Character $\chi_{1037}(1022, \cdot)$
1-1037-1037.1024-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1024	$0$	✓	✓			$0.112$	$0$	$0.837523$	Character $\chi_{1037}(1024, \cdot)$
1-1037-1037.1026-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1026	$0$	✓	✓			$-0.272$	$0$	$0.660755$	Character $\chi_{1037}(1026, \cdot)$
1-1037-1037.1027-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1027	$0$	✓	✓			$-0.144$	$0$	$1.15526$	Character $\chi_{1037}(1027, \cdot)$
1-1037-1037.1028-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1028	$0$	✓	✓			$-0.290$	$0$	$0.477489$	Character $\chi_{1037}(1028, \cdot)$
1-1037-1037.1030-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1030	$0$	✓	✓			$-0.117$	$0$	$1.24021$	Character $\chi_{1037}(1030, \cdot)$
1-1037-1037.1031-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1031	$0$	✓	✓			$0.125$	$0$	$1.52359$	Character $\chi_{1037}(1031, \cdot)$
1-1037-1037.1033-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1033	$0$	✓	✓			$0.0603$	$0$	$1.20399$	Character $\chi_{1037}(1033, \cdot)$
1-1037-1037.1036-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.1036	$0$	✓	✓	✓	✓	$0$	$0$	$0.937230$	Character $\chi_{1037}(1036, \cdot)$
1-1037-1037.105-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.105	$0$	✓	✓			$0.259$	$0$	$0.880262$	Character $\chi_{1037}(105, \cdot)$
1-1037-1037.106-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.106	$0$	✓	✓			$0.377$	$0$	$2.00209$	Character $\chi_{1037}(106, \cdot)$
1-1037-1037.11-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.11	$0$	✓	✓			$-0.234$	$0$	$0.677478$	Character $\chi_{1037}(11, \cdot)$
1-1037-1037.110-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.110	$0$	✓	✓			$0.137$	$0$	$0.993569$	Character $\chi_{1037}(110, \cdot)$
1-1037-1037.112-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.112	$0$	✓	✓			$-0.0843$	$0$	$0.280717$	Character $\chi_{1037}(112, \cdot)$
1-1037-1037.114-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.114	$0$	✓	✓			$-0.00728$	$0$	$1.51985$	Character $\chi_{1037}(114, \cdot)$
1-1037-1037.116-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.116	$0$	✓	✓			$-0.0440$	$0$	$0.265131$	Character $\chi_{1037}(116, \cdot)$
1-1037-1037.117-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.117	$0$	✓	✓			$0.0526$	$0$	$0.831302$	Character $\chi_{1037}(117, \cdot)$
1-1037-1037.118-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.118	$0$	✓	✓			$-0.334$	$0$	$0.321274$	Character $\chi_{1037}(118, \cdot)$
1-1037-1037.121-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.121	$0$	✓	✓			$0.242$	$0$	$1.53853$	Character $\chi_{1037}(121, \cdot)$
1-1037-1037.124-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.124	$0$	✓	✓			$-0.0943$	$0$	$0.413834$	Character $\chi_{1037}(124, \cdot)$
1-1037-1037.127-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.127	$0$	✓	✓			$0.136$	$0$	$1.36923$	Character $\chi_{1037}(127, \cdot)$
1-1037-1037.129-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.129	$0$	✓	✓			$0.158$	$0$	$1.21030$	Character $\chi_{1037}(129, \cdot)$
1-1037-1037.13-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.13	$0$	✓	✓			$-0.0255$	$0$	$0.319642$	Character $\chi_{1037}(13, \cdot)$
1-1037-1037.130-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.130	$0$	✓	✓			$-0.249$	$0$	$0.0979525$	Character $\chi_{1037}(130, \cdot)$
1-1037-1037.133-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.133	$0$	✓	✓			$-0.404$	$0$	$2.35585$	Character $\chi_{1037}(133, \cdot)$
1-1037-1037.134-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.134	$0$	✓	✓			$-0.326$	$0$	$0.179748$	Character $\chi_{1037}(134, \cdot)$
1-1037-1037.135-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.135	$0$	✓	✓			$-0.420$	$0$	$0.112052$	Character $\chi_{1037}(135, \cdot)$
1-1037-1037.138-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.138	$0$	✓	✓			$0.147$	$0$	$0.876807$	Character $\chi_{1037}(138, \cdot)$
1-1037-1037.139-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.139	$0$	✓	✓			$-0.370$	$0$	$0.551013$	Character $\chi_{1037}(139, \cdot)$
1-1037-1037.143-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.143	$0$	✓	✓			$-0.0741$	$0$	$0.310115$	Character $\chi_{1037}(143, \cdot)$
1-1037-1037.144-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.144	$0$	✓	✓			$0.214$	$0$	$1.77851$	Character $\chi_{1037}(144, \cdot)$
1-1037-1037.146-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.146	$0$	✓	✓			$0.443$	$0$	$2.05439$	Character $\chi_{1037}(146, \cdot)$
1-1037-1037.148-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.148	$0$	✓	✓			$0.117$	$0$	$1.59031$	Character $\chi_{1037}(148, \cdot)$
1-1037-1037.149-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.149	$0$	✓	✓			$-0.177$	$0$	$1.09713$	Character $\chi_{1037}(149, \cdot)$
1-1037-1037.15-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.15	$0$	✓	✓			$0.197$	$0$	$1.57322$	Character $\chi_{1037}(15, \cdot)$
1-1037-1037.150-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.150	$0$	✓	✓			$-0.441$	$0$	$0.637696$	Character $\chi_{1037}(150, \cdot)$
1-1037-1037.159-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.159	$0$	✓	✓			$-0.321$	$0$	$1.03751$	Character $\chi_{1037}(159, \cdot)$
1-1037-1037.16-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.16	$0$	✓	✓			$-0.0946$	$0$	$1.11562$	Character $\chi_{1037}(16, \cdot)$
1-1037-1037.160-r0-0-0	$4.81$	$4.81$	$1$	$17 \cdot 61$	1037.160	$0$	✓	✓			$-0.0532$	$0$	$0.306994$	Character $\chi_{1037}(160, \cdot)$

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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.