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 (32 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-200-200.109-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.109	$0$	✓	✓	$-0.120$	$0$	$0.668666$	Character $\chi_{200}(109, \cdot)$
1-200-200.123-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.123	$0$	✓	✓	$-0.130$	$0$	$1.27602$	Character $\chi_{200}(123, \cdot)$
1-200-200.141-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.141	$0$	✓	✓	$-0.120$	$0$	$1.38271$	Character $\chi_{200}(141, \cdot)$
1-200-200.147-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.147	$0$	✓	✓	$-0.160$	$0$	$1.16450$	Character $\chi_{200}(147, \cdot)$
1-200-200.163-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.163	$0$	✓	✓	$0.130$	$0$	$1.59714$	Character $\chi_{200}(163, \cdot)$
1-200-200.181-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.181	$0$	✓	✓	$0.160$	$0$	$1.51913$	Character $\chi_{200}(181, \cdot)$
1-200-200.187-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.187	$0$	✓	✓	$0.130$	$0$	$1.66382$	Character $\chi_{200}(187, \cdot)$
1-200-200.189-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.189	$0$	✓	✓	$0.120$	$0$	$1.37562$	Character $\chi_{200}(189, \cdot)$
1-200-200.21-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.21	$0$	✓	✓	$-0.160$	$0$	$1.16678$	Character $\chi_{200}(21, \cdot)$
1-200-200.27-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.27	$0$	✓	✓	$-0.130$	$0$	$0.707510$	Character $\chi_{200}(27, \cdot)$
1-200-200.29-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.29	$0$	✓	✓	$0.339$	$0$	$2.14526$	Character $\chi_{200}(29, \cdot)$
1-200-200.3-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.3	$0$	✓	✓	$0.339$	$0$	$1.78874$	Character $\chi_{200}(3, \cdot)$
1-200-200.61-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.61	$0$	✓	✓	$0.120$	$0$	$1.84240$	Character $\chi_{200}(61, \cdot)$
1-200-200.67-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.67	$0$	✓	✓	$-0.339$	$0$	$0.481083$	Character $\chi_{200}(67, \cdot)$
1-200-200.69-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.69	$0$	✓	✓	$-0.339$	$0$	$0.693891$	Character $\chi_{200}(69, \cdot)$
1-200-200.83-r0-0-0	$0.928$	$0.928$	$1$	$2^{3} \cdot 5^{2}$	200.83	$0$	✓	✓	$0.160$	$0$	$2.06791$	Character $\chi_{200}(83, \cdot)$
1-200-200.11-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.11	$1$	✓	✓	$0.120$	$0$	$0.916747$	Character $\chi_{200}(11, \cdot)$
1-200-200.117-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.117	$1$	✓	✓	$0.160$	$0$	$1.50246$	Character $\chi_{200}(117, \cdot)$
1-200-200.13-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.13	$1$	✓	✓	$-0.370$	$0$	$0.129151$	Character $\chi_{200}(13, \cdot)$
1-200-200.131-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.131	$1$	✓	✓	$0.160$	$0$	$1.31873$	Character $\chi_{200}(131, \cdot)$
1-200-200.133-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.133	$1$	✓	✓	$-0.339$	$0$	$0.426093$	Character $\chi_{200}(133, \cdot)$
1-200-200.139-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.139	$1$	✓	✓	$0.120$	$0$	$1.38289$	Character $\chi_{200}(139, \cdot)$
1-200-200.171-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.171	$1$	✓	✓	$-0.160$	$0$	$0.396518$	Character $\chi_{200}(171, \cdot)$
1-200-200.173-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.173	$1$	✓	✓	$0.370$	$0$	$1.34457$	Character $\chi_{200}(173, \cdot)$
1-200-200.179-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.179	$1$	✓	✓	$0.339$	$0$	$1.55288$	Character $\chi_{200}(179, \cdot)$
1-200-200.19-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.19	$1$	✓	✓	$-0.339$	$0$	$0.0484146$	Character $\chi_{200}(19, \cdot)$
1-200-200.197-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.197	$1$	✓	✓	$0.339$	$0$	$1.33802$	Character $\chi_{200}(197, \cdot)$
1-200-200.37-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.37	$1$	✓	✓	$-0.370$	$0$	$0.348704$	Character $\chi_{200}(37, \cdot)$
1-200-200.53-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.53	$1$	✓	✓	$-0.160$	$0$	$0.959862$	Character $\chi_{200}(53, \cdot)$
1-200-200.59-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.59	$1$	✓	✓	$-0.120$	$0$	$1.11842$	Character $\chi_{200}(59, \cdot)$
1-200-200.77-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.77	$1$	✓	✓	$0.370$	$0$	$1.95261$	Character $\chi_{200}(77, \cdot)$
1-200-200.91-r1-0-0	$21.4$	$21.4$	$1$	$2^{3} \cdot 5^{2}$	200.91	$1$	✓	✓	$-0.120$	$0$	$0.366626$	Character $\chi_{200}(91, \cdot)$

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Overview	Random
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.