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 108 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2784-2784.101-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.101	$0$	✓	✓	$-0.409$	$0$	$0.420930$	Character $\chi_{2784}(101, \cdot)$
1-2784-2784.1013-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1013	$0$	✓	✓	$-0.0284$	$0$	$1.13580$	Character $\chi_{2784}(1013, \cdot)$
1-2784-2784.1019-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1019	$0$	✓	✓	$-0.472$	$0$	$1.44834$	Character $\chi_{2784}(1019, \cdot)$
1-2784-2784.1043-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1043	$0$	✓	✓	$0.343$	$0$	$1.17630$	Character $\chi_{2784}(1043, \cdot)$
1-2784-2784.1061-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1061	$0$	✓	✓	$0.375$	$0$	$1.34274$	Character $\chi_{2784}(1061, \cdot)$
1-2784-2784.1067-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1067	$0$	✓	✓	$0.142$	$0$	$1.17752$	Character $\chi_{2784}(1067, \cdot)$
1-2784-2784.107-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.107	$0$	✓	✓	$-0.108$	$0$	$0.790690$	Character $\chi_{2784}(107, \cdot)$
1-2784-2784.1085-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1085	$0$	✓	✓	$-0.125$	$0$	$0.504541$	Character $\chi_{2784}(1085, \cdot)$
1-2784-2784.1115-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1115	$0$	✓	✓	$0.119$	$0$	$0.739632$	Character $\chi_{2784}(1115, \cdot)$
1-2784-2784.1133-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1133	$0$	✓	✓	$0.0787$	$0$	$0.840450$	Character $\chi_{2784}(1133, \cdot)$
1-2784-2784.1157-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1157	$0$	✓	✓	$0.177$	$0$	$0.916709$	Character $\chi_{2784}(1157, \cdot)$
1-2784-2784.1181-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1181	$0$	✓	✓	$0.0305$	$0$	$0.710211$	Character $\chi_{2784}(1181, \cdot)$
1-2784-2784.1211-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1211	$0$	✓	✓	$-0.215$	$0$	$0.574596$	Character $\chi_{2784}(1211, \cdot)$
1-2784-2784.1229-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1229	$0$	✓	✓	$0.160$	$0$	$1.02424$	Character $\chi_{2784}(1229, \cdot)$
1-2784-2784.1283-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1283	$0$	✓	✓	$0.0931$	$0$	$0.622324$	Character $\chi_{2784}(1283, \cdot)$
1-2784-2784.1349-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1349	$0$	✓	✓	$-0.0787$	$0$	$0.801110$	Character $\chi_{2784}(1349, \cdot)$
1-2784-2784.1373-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1373	$0$	✓	✓	$-0.0650$	$0$	$0.817026$	Character $\chi_{2784}(1373, \cdot)$
1-2784-2784.1379-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1379	$0$	✓	✓	$0.108$	$0$	$1.13367$	Character $\chi_{2784}(1379, \cdot)$
1-2784-2784.1427-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1427	$0$	✓	✓	$-0.321$	$0$	$0.379675$	Character $\chi_{2784}(1427, \cdot)$
1-2784-2784.1469-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1469	$0$	✓	✓	$0.0726$	$0$	$0.804359$	Character $\chi_{2784}(1469, \cdot)$
1-2784-2784.1475-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1475	$0$	✓	✓	$0.0943$	$0$	$0.887668$	Character $\chi_{2784}(1475, \cdot)$
1-2784-2784.1493-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1493	$0$	✓	✓	$0.340$	$0$	$1.04101$	Character $\chi_{2784}(1493, \cdot)$
1-2784-2784.1499-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1499	$0$	✓	✓	$0.141$	$0$	$1.03559$	Character $\chi_{2784}(1499, \cdot)$
1-2784-2784.1571-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1571	$0$	✓	✓	$0.259$	$0$	$1.00189$	Character $\chi_{2784}(1571, \cdot)$
1-2784-2784.1613-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1613	$0$	✓	✓	$0.406$	$0$	$1.30836$	Character $\chi_{2784}(1613, \cdot)$
1-2784-2784.1619-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1619	$0$	✓	✓	$-0.392$	$0$	$0.318252$	Character $\chi_{2784}(1619, \cdot)$
1-2784-2784.1661-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1661	$0$	✓	✓	$0.277$	$0$	$1.21393$	Character $\chi_{2784}(1661, \cdot)$
1-2784-2784.1685-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1685	$0$	✓	✓	$0.0650$	$0$	$0.858152$	Character $\chi_{2784}(1685, \cdot)$
1-2784-2784.1691-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1691	$0$	✓	✓	$0.193$	$0$	$0.821661$	Character $\chi_{2784}(1691, \cdot)$
1-2784-2784.1709-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1709	$0$	✓	✓	$0.409$	$0$	$1.51959$	Character $\chi_{2784}(1709, \cdot)$
1-2784-2784.1715-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1715	$0$	✓	✓	$0.215$	$0$	$1.26046$	Character $\chi_{2784}(1715, \cdot)$
1-2784-2784.1739-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1739	$0$	✓	✓	$0.406$	$0$	$1.23926$	Character $\chi_{2784}(1739, \cdot)$
1-2784-2784.1757-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1757	$0$	✓	✓	$-0.186$	$0$	$0.421672$	Character $\chi_{2784}(1757, \cdot)$
1-2784-2784.1763-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1763	$0$	✓	✓	$0.329$	$0$	$0.0284941$	Character $\chi_{2784}(1763, \cdot)$
1-2784-2784.1781-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1781	$0$	✓	✓	$0.186$	$0$	$1.00118$	Character $\chi_{2784}(1781, \cdot)$
1-2784-2784.179-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.179	$0$	✓	✓	$0.00903$	$0$	$0.820662$	Character $\chi_{2784}(179, \cdot)$
1-2784-2784.1811-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1811	$0$	✓	✓	$-0.193$	$0$	$0.400009$	Character $\chi_{2784}(1811, \cdot)$
1-2784-2784.1829-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1829	$0$	✓	✓	$-0.108$	$0$	$0.521382$	Character $\chi_{2784}(1829, \cdot)$
1-2784-2784.1853-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1853	$0$	✓	✓	$-0.385$	$0$	$0.368270$	Character $\chi_{2784}(1853, \cdot)$
1-2784-2784.1877-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1877	$0$	✓	✓	$0.343$	$0$	$0.849974$	Character $\chi_{2784}(1877, \cdot)$
1-2784-2784.1907-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1907	$0$	✓	✓	$0.472$	$0$	$0.140608$	Character $\chi_{2784}(1907, \cdot)$
1-2784-2784.1925-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1925	$0$	✓	✓	$-0.0273$	$0$	$0.706626$	Character $\chi_{2784}(1925, \cdot)$
1-2784-2784.1979-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.1979	$0$	✓	✓	$0.155$	$0$	$1.17119$	Character $\chi_{2784}(1979, \cdot)$
1-2784-2784.2045-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.2045	$0$	✓	✓	$0.358$	$0$	$1.37657$	Character $\chi_{2784}(2045, \cdot)$
1-2784-2784.2069-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.2069	$0$	✓	✓	$0.247$	$0$	$1.24208$	Character $\chi_{2784}(2069, \cdot)$
1-2784-2784.2075-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.2075	$0$	✓	✓	$0.171$	$0$	$0.868304$	Character $\chi_{2784}(2075, \cdot)$
1-2784-2784.2123-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.2123	$0$	✓	✓	$-0.259$	$0$	$0.337765$	Character $\chi_{2784}(2123, \cdot)$
1-2784-2784.2165-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.2165	$0$	✓	✓	$0.385$	$0$	$1.38343$	Character $\chi_{2784}(2165, \cdot)$
1-2784-2784.2171-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.2171	$0$	✓	✓	$0.156$	$0$	$0.979194$	Character $\chi_{2784}(2171, \cdot)$
1-2784-2784.2189-r0-0-0	$12.9$	$12.9$	$1$	$2^{5} \cdot 3 \cdot 29$	2784.2189	$0$	✓	✓	$-0.221$	$0$	$0.202989$	Character $\chi_{2784}(2189, \cdot)$

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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.