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 (36 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-588-588.107-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.107	$0$	✓	✓	$-0.197$	$0$	$0.798328$	Character $\chi_{588}(107, \cdot)$
1-588-588.11-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.11	$0$	✓	✓	$0.197$	$0$	$1.53779$	Character $\chi_{588}(11, \cdot)$
1-588-588.155-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.155	$0$	✓	✓	$0.448$	$0$	$1.80024$	Character $\chi_{588}(155, \cdot)$
1-588-588.179-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.179	$0$	✓	✓	$0.0816$	$0$	$1.11066$	Character $\chi_{588}(179, \cdot)$
1-588-588.191-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.191	$0$	✓	✓	$0.115$	$0$	$1.36759$	Character $\chi_{588}(191, \cdot)$
1-588-588.23-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.23	$0$	✓	✓	$-0.0816$	$0$	$0.984829$	Character $\chi_{588}(23, \cdot)$
1-588-588.239-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.239	$0$	✓	✓	$-0.448$	$0$	$0.264762$	Character $\chi_{588}(239, \cdot)$
1-588-588.323-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.323	$0$	✓	✓	$0.0816$	$0$	$1.45473$	Character $\chi_{588}(323, \cdot)$
1-588-588.347-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.347	$0$	✓	✓	$-0.0816$	$0$	$0.664969$	Character $\chi_{588}(347, \cdot)$
1-588-588.359-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.359	$0$	✓	✓	$0.217$	$0$	$1.34765$	Character $\chi_{588}(359, \cdot)$
1-588-588.407-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.407	$0$	✓	✓	$0.469$	$0$	$1.91243$	Character $\chi_{588}(407, \cdot)$
1-588-588.431-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.431	$0$	✓	✓	$-0.115$	$0$	$0.871531$	Character $\chi_{588}(431, \cdot)$
1-588-588.443-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.443	$0$	✓	✓	$-0.136$	$0$	$0.600367$	Character $\chi_{588}(443, \cdot)$
1-588-588.515-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.515	$0$	✓	✓	$0.136$	$0$	$1.09331$	Character $\chi_{588}(515, \cdot)$
1-588-588.527-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.527	$0$	✓	✓	$0.0816$	$0$	$1.02488$	Character $\chi_{588}(527, \cdot)$
1-588-588.575-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.575	$0$	✓	✓	$-0.469$	$0$	$0.182808$	Character $\chi_{588}(575, \cdot)$
1-588-588.71-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.71	$0$	✓	✓	$-0.0816$	$0$	$0.949992$	Character $\chi_{588}(71, \cdot)$
1-588-588.95-r0-0-0	$2.73$	$2.73$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.95	$0$	✓	✓	$-0.217$	$0$	$0.688540$	Character $\chi_{588}(95, \cdot)$
1-588-588.131-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.131	$1$	✓	✓	$-0.0323$	$0$	$0.921966$	Character $\chi_{588}(131, \cdot)$
1-588-588.143-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.143	$1$	✓	✓	$-0.331$	$0$	$0.326802$	Character $\chi_{588}(143, \cdot)$
1-588-588.167-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.167	$1$	✓	✓	$0.331$	$0$	$1.06003$	Character $\chi_{588}(167, \cdot)$
1-588-588.251-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.251	$1$	✓	✓	$0.301$	$0$	$1.24121$	Character $\chi_{588}(251, \cdot)$
1-588-588.299-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.299	$1$	✓	✓	$0.365$	$0$	$0.000693906$	Character $\chi_{588}(299, \cdot)$
1-588-588.311-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.311	$1$	✓	✓	$0.331$	$0$	$1.11340$	Character $\chi_{588}(311, \cdot)$
1-588-588.335-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.335	$1$	✓	✓	$-0.301$	$0$	$0.424992$	Character $\chi_{588}(335, \cdot)$
1-588-588.383-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.383	$1$	✓	✓	$0.0527$	$0$	$0.732898$	Character $\chi_{588}(383, \cdot)$
1-588-588.395-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.395	$1$	✓	✓	$0.0323$	$0$	$0.831358$	Character $\chi_{588}(395, \cdot)$
1-588-588.419-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.419	$1$	✓	✓	$-0.331$	$0$	$0.280842$	Character $\chi_{588}(419, \cdot)$
1-588-588.467-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.467	$1$	✓	✓	$-0.331$	$0$	$0.0321295$	Character $\chi_{588}(467, \cdot)$
1-588-588.47-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.47	$1$	✓	✓	$-0.386$	$0$	$0.319572$	Character $\chi_{588}(47, \cdot)$
1-588-588.479-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.479	$1$	✓	✓	$-0.0527$	$0$	$0.716725$	Character $\chi_{588}(479, \cdot)$
1-588-588.503-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.503	$1$	✓	✓	$0.280$	$0$	$1.09420$	Character $\chi_{588}(503, \cdot)$
1-588-588.551-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.551	$1$	✓	✓	$0.331$	$0$	$1.26281$	Character $\chi_{588}(551, \cdot)$
1-588-588.563-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.563	$1$	✓	✓	$0.386$	$0$	$1.58940$	Character $\chi_{588}(563, \cdot)$
1-588-588.59-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.59	$1$	✓	✓	$-0.365$	$0$	$1.59439$	Character $\chi_{588}(59, \cdot)$
1-588-588.83-r1-0-0	$63.1$	$63.1$	$1$	$2^{2} \cdot 3 \cdot 7^{2}$	588.83	$1$	✓	✓	$-0.280$	$0$	$0.494230$	Character $\chi_{588}(83, \cdot)$

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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.