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 (35 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
1-37-37.10-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.10	$0$	✓	✓			$0.190$	$0$	$2.88826$	Character $\chi_{37}(10, \cdot)$
1-37-37.11-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.11	$0$	✓	✓			$-0.286$	$0$	$1.69586$	Character $\chi_{37}(11, \cdot)$
1-37-37.12-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.12	$0$	✓	✓			$-0.121$	$0$	$2.17733$	Character $\chi_{37}(12, \cdot)$
1-37-37.16-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.16	$0$	✓	✓			$0.0647$	$0$	$2.98263$	Character $\chi_{37}(16, \cdot)$
1-37-37.21-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.21	$0$	✓	✓			$-0.165$	$0$	$1.95336$	Character $\chi_{37}(21, \cdot)$
1-37-37.25-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.25	$0$	✓	✓			$0.365$	$0$	$3.79770$	Character $\chi_{37}(25, \cdot)$
1-37-37.26-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.26	$0$	✓	✓			$-0.190$	$0$	$0.898061$	Character $\chi_{37}(26, \cdot)$
1-37-37.27-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.27	$0$	✓	✓			$0.286$	$0$	$3.68644$	Character $\chi_{37}(27, \cdot)$
1-37-37.28-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.28	$0$	✓	✓			$-0.153$	$0$	$1.96857$	Character $\chi_{37}(28, \cdot)$
1-37-37.3-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.3	$0$	✓	✓			$-0.365$	$0$	$1.36111$	Character $\chi_{37}(3, \cdot)$
1-37-37.30-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.30	$0$	✓	✓			$0.165$	$0$	$2.49646$	Character $\chi_{37}(30, \cdot)$
1-37-37.33-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.33	$0$	✓	✓			$-0.200$	$0$	$1.06630$	Character $\chi_{37}(33, \cdot)$
1-37-37.34-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.34	$0$	✓	✓			$0.121$	$0$	$2.54193$	Character $\chi_{37}(34, \cdot)$
1-37-37.36-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.36	$0$	✓	✓	✓	✓	$0$	$0$	$2.05722$	Character $\chi_{37}(36, \cdot)$
1-37-37.4-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.4	$0$	✓	✓			$0.153$	$0$	$3.29169$	Character $\chi_{37}(4, \cdot)$
1-37-37.7-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.7	$0$	✓	✓			$-0.0647$	$0$	$2.96773$	Character $\chi_{37}(7, \cdot)$
1-37-37.9-r0-0-0	$0.171$	$0.171$	$1$	$37$	37.9	$0$	✓	✓			$0.200$	$0$	$2.16828$	Character $\chi_{37}(9, \cdot)$
1-37-37.13-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.13	$1$	✓	✓			$0.0884$	$0$	$1.69684$	Character $\chi_{37}(13, \cdot)$
1-37-37.14-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.14	$1$	✓	✓			$-0.198$	$0$	$1.93799$	Character $\chi_{37}(14, \cdot)$
1-37-37.15-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.15	$1$	✓	✓			$-0.215$	$0$	$0.123527$	Character $\chi_{37}(15, \cdot)$
1-37-37.17-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.17	$1$	✓	✓			$0.364$	$0$	$3.21010$	Character $\chi_{37}(17, \cdot)$
1-37-37.18-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.18	$1$	✓	✓			$0.237$	$0$	$1.85723$	Character $\chi_{37}(18, \cdot)$
1-37-37.19-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.19	$1$	✓	✓			$0.164$	$0$	$2.81510$	Character $\chi_{37}(19, \cdot)$
1-37-37.2-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.2	$1$	✓	✓			$-0.164$	$0$	$1.46430$	Character $\chi_{37}(2, \cdot)$
1-37-37.20-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.20	$1$	✓	✓			$-0.0884$	$0$	$1.89439$	Character $\chi_{37}(20, \cdot)$
1-37-37.22-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.22	$1$	✓	✓			$-0.372$	$0$	$0.771298$	Character $\chi_{37}(22, \cdot)$
1-37-37.23-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.23	$1$	✓	✓			$-0.421$	$0$	$0.285715$	Character $\chi_{37}(23, \cdot)$
1-37-37.24-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.24	$1$	✓	✓			$-0.364$	$0$	$1.16522$	Character $\chi_{37}(24, \cdot)$
1-37-37.29-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.29	$1$	✓	✓			$0.421$	$0$	$2.85855$	Character $\chi_{37}(29, \cdot)$
1-37-37.31-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.31	$1$	✓	✓			$-0.111$	$0$	$0.615496$	Character $\chi_{37}(31, \cdot)$
1-37-37.32-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.32	$1$	✓	✓			$0.372$	$0$	$2.86376$	Character $\chi_{37}(32, \cdot)$
1-37-37.35-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.35	$1$	✓	✓			$-0.237$	$0$	$1.01296$	Character $\chi_{37}(35, \cdot)$
1-37-37.5-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.5	$1$	✓	✓			$0.215$	$0$	$1.71803$	Character $\chi_{37}(5, \cdot)$
1-37-37.6-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.6	$1$	✓	✓			$0.111$	$0$	$1.89103$	Character $\chi_{37}(6, \cdot)$
1-37-37.8-r1-0-0	$3.97$	$3.97$	$1$	$37$	37.8	$1$	✓	✓			$0.198$	$0$	$2.87938$	Character $\chi_{37}(8, \cdot)$

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Universe	Knowledge

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.