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 82 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2652-2652.1007-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1007	$1$	✓	✓	$0.182$	$0$	$0.879169$	Character $\chi_{2652}(1007, \cdot)$
1-2652-2652.1019-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1019	$1$	✓	✓	$-0.203$	$0$	$0.437257$	Character $\chi_{2652}(1019, \cdot)$
1-2652-2652.1031-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1031	$1$	✓	✓	$-0.371$	$0$	$1.52985$	Character $\chi_{2652}(1031, \cdot)$
1-2652-2652.1043-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1043	$1$	✓	✓	$0.408$	$0$	$0.992222$	Character $\chi_{2652}(1043, \cdot)$
1-2652-2652.107-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.107	$1$	✓	✓	$0.224$	$0$	$0.734775$	Character $\chi_{2652}(107, \cdot)$
1-2652-2652.1091-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1091	$1$	✓	✓	$0.467$	$0$	$0.0277028$	Character $\chi_{2652}(1091, \cdot)$
1-2652-2652.1103-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1103	$1$	✓	✓	$0.0357$	$0$	$0.612025$	Character $\chi_{2652}(1103, \cdot)$
1-2652-2652.1115-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1115	$1$	✓	✓	$0.293$	$0$	$1.18973$	Character $\chi_{2652}(1115, \cdot)$
1-2652-2652.1127-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1127	$1$	✓	✓	$0.472$	$0$	$1.33744$	Character $\chi_{2652}(1127, \cdot)$
1-2652-2652.1175-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1175	$1$	✓	✓	$0.289$	$0$	$0.607935$	Character $\chi_{2652}(1175, \cdot)$
1-2652-2652.1187-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1187	$1$	✓	✓	$0.208$	$0$	$0.881923$	Character $\chi_{2652}(1187, \cdot)$
1-2652-2652.1211-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1211	$1$	✓	✓	$-0.0652$	$0$	$0.680133$	Character $\chi_{2652}(1211, \cdot)$
1-2652-2652.1247-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1247	$1$	✓	✓	$-0.467$	$0$	$1.21989$	Character $\chi_{2652}(1247, \cdot)$
1-2652-2652.1307-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1307	$1$	✓	✓	$0.283$	$0$	$0.887868$	Character $\chi_{2652}(1307, \cdot)$
1-2652-2652.1355-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1355	$1$	✓	✓	$0.164$	$0$	$0.720172$	Character $\chi_{2652}(1355, \cdot)$
1-2652-2652.1415-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1415	$1$	✓	✓	$0.0283$	$0$	$0.464554$	Character $\chi_{2652}(1415, \cdot)$
1-2652-2652.1439-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1439	$1$	✓	✓	$0.333$	$0$	$0.144177$	Character $\chi_{2652}(1439, \cdot)$
1-2652-2652.1475-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1475	$1$	✓	✓	$-0.0283$	$0$	$0.592648$	Character $\chi_{2652}(1475, \cdot)$
1-2652-2652.1487-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1487	$1$	✓	✓	$-0.316$	$0$	$0.264588$	Character $\chi_{2652}(1487, \cdot)$
1-2652-2652.1499-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1499	$1$	✓	✓	$-0.114$	$0$	$0.307429$	Character $\chi_{2652}(1499, \cdot)$
1-2652-2652.1559-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1559	$1$	✓	✓	$0.288$	$0$	$1.23652$	Character $\chi_{2652}(1559, \cdot)$
1-2652-2652.1595-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1595	$1$	✓	✓	$-0.0857$	$0$	$0.349831$	Character $\chi_{2652}(1595, \cdot)$
1-2652-2652.1607-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1607	$1$	✓	✓	$-0.289$	$0$	$0.121683$	Character $\chi_{2652}(1607, \cdot)$
1-2652-2652.1619-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1619	$1$	✓	✓	$0.276$	$0$	$0.0276479$	Character $\chi_{2652}(1619, \cdot)$
1-2652-2652.1631-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1631	$1$	✓	✓	$0.0771$	$0$	$0.378899$	Character $\chi_{2652}(1631, \cdot)$
1-2652-2652.1655-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1655	$1$	✓	✓	$-0.0484$	$0$	$0.514182$	Character $\chi_{2652}(1655, \cdot)$
1-2652-2652.1679-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1679	$1$	✓	✓	$-0.276$	$0$	$1.36367$	Character $\chi_{2652}(1679, \cdot)$
1-2652-2652.1739-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1739	$1$	✓	✓	$-0.0698$	$0$	$0.622781$	Character $\chi_{2652}(1739, \cdot)$
1-2652-2652.1787-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1787	$1$	✓	✓	$-0.430$	$0$	$0.280083$	Character $\chi_{2652}(1787, \cdot)$
1-2652-2652.1835-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1835	$1$	✓	✓	$-0.170$	$0$	$0.619684$	Character $\chi_{2652}(1835, \cdot)$
1-2652-2652.1883-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1883	$1$	✓	✓	$-0.182$	$0$	$0.639554$	Character $\chi_{2652}(1883, \cdot)$
1-2652-2652.1907-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1907	$1$	✓	✓	$-0.408$	$0$	$0.282492$	Character $\chi_{2652}(1907, \cdot)$
1-2652-2652.1919-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1919	$1$	✓	✓	$0.316$	$0$	$0.795386$	Character $\chi_{2652}(1919, \cdot)$
1-2652-2652.1967-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1967	$1$	✓	✓	$-0.293$	$0$	$0.234760$	Character $\chi_{2652}(1967, \cdot)$
1-2652-2652.1979-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1979	$1$	✓	✓	$-0.472$	$0$	$0.231105$	Character $\chi_{2652}(1979, \cdot)$
1-2652-2652.1991-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.1991	$1$	✓	✓	$0.321$	$0$	$1.01665$	Character $\chi_{2652}(1991, \cdot)$
1-2652-2652.203-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.203	$1$	✓	✓	$0.203$	$0$	$0.764132$	Character $\chi_{2652}(203, \cdot)$
1-2652-2652.2039-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.2039	$1$	✓	✓	$-0.0771$	$0$	$0.0463308$	Character $\chi_{2652}(2039, \cdot)$
1-2652-2652.2051-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.2051	$1$	✓	✓	$-0.208$	$0$	$0.275055$	Character $\chi_{2652}(2051, \cdot)$
1-2652-2652.2063-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.2063	$1$	✓	✓	$-0.343$	$0$	$1.51747$	Character $\chi_{2652}(2063, \cdot)$
1-2652-2652.2087-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.2087	$1$	✓	✓	$0.0652$	$0$	$0.658815$	Character $\chi_{2652}(2087, \cdot)$
1-2652-2652.2099-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.2099	$1$	✓	✓	$-0.0357$	$0$	$0.364855$	Character $\chi_{2652}(2099, \cdot)$
1-2652-2652.2135-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.2135	$1$	✓	✓	$-0.412$	$0$	$1.04474$	Character $\chi_{2652}(2135, \cdot)$
1-2652-2652.2183-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.2183	$1$	✓	✓	$-0.348$	$0$	$1.09103$	Character $\chi_{2652}(2183, \cdot)$
1-2652-2652.2195-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.2195	$1$	✓	✓	$0.415$	$0$	$1.00652$	Character $\chi_{2652}(2195, \cdot)$
1-2652-2652.2207-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.2207	$1$	✓	✓	$0.371$	$0$	$0.135152$	Character $\chi_{2652}(2207, \cdot)$
1-2652-2652.2231-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.2231	$1$	✓	✓	$0.308$	$0$	$0.713160$	Character $\chi_{2652}(2231, \cdot)$
1-2652-2652.2243-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.2243	$1$	✓	✓	$0.170$	$0$	$0.800270$	Character $\chi_{2652}(2243, \cdot)$
1-2652-2652.23-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.23	$1$	✓	✓	$0.114$	$0$	$0.712645$	Character $\chi_{2652}(23, \cdot)$
1-2652-2652.2303-r1-0-0	$284.$	$284.$	$1$	$2^{2} \cdot 3 \cdot 13 \cdot 17$	2652.2303	$1$	✓	✓	$-0.283$	$0$	$0.0869600$	Character $\chi_{2652}(2303, \cdot)$

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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.