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 180 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-693-693.104-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.104	$0$	✓	✓	$-0.129$	$0$	$0.173456$	Character $\chi_{693}(104, \cdot)$
1-693-693.128-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.128	$0$	✓	✓	$0.137$	$0$	$1.06771$	Character $\chi_{693}(128, \cdot)$
1-693-693.13-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.13	$0$	✓	✓	$-0.375$	$0$	$0.133563$	Character $\chi_{693}(13, \cdot)$
1-693-693.130-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.130	$0$	✓	✓	$-0.491$	$0$	$1.36703$	Character $\chi_{693}(130, \cdot)$
1-693-693.139-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.139	$0$	✓	✓	$0.0167$	$0$	$1.35365$	Character $\chi_{693}(139, \cdot)$
1-693-693.146-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.146	$0$	✓	✓	$-0.231$	$0$	$0.764522$	Character $\chi_{693}(146, \cdot)$
1-693-693.149-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.149	$0$	✓	✓	$0.108$	$0$	$0.718997$	Character $\chi_{693}(149, \cdot)$
1-693-693.16-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.16	$0$	✓	✓	$0.491$	$0$	$0.434604$	Character $\chi_{693}(16, \cdot)$
1-693-693.160-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.160	$0$	✓	✓	$0.375$	$0$	$1.31050$	Character $\chi_{693}(160, \cdot)$
1-693-693.178-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.178	$0$	✓	✓	$0.255$	$0$	$1.32535$	Character $\chi_{693}(178, \cdot)$
1-693-693.185-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.185	$0$	✓	✓	$0.371$	$0$	$0.0741321$	Character $\chi_{693}(185, \cdot)$
1-693-693.2-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.2	$0$	✓	✓	$-0.245$	$0$	$1.00903$	Character $\chi_{693}(2, \cdot)$
1-693-693.20-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.20	$0$	✓	✓	$0.129$	$0$	$1.37196$	Character $\chi_{693}(20, \cdot)$
1-693-693.200-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.200	$0$	✓	✓	$-0.108$	$0$	$0.708045$	Character $\chi_{693}(200, \cdot)$
1-693-693.214-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.214	$0$	✓	✓	$-0.361$	$0$	$1.72430$	Character $\chi_{693}(214, \cdot)$
1-693-693.236-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.236	$0$	✓	✓	$-0.371$	$0$	$1.54385$	Character $\chi_{693}(236, \cdot)$
1-693-693.241-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.241	$0$	✓	✓	$0.409$	$0$	$1.62262$	Character $\chi_{693}(241, \cdot)$
1-693-693.247-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.247	$0$	✓	✓	$0.0472$	$0$	$1.05251$	Character $\chi_{693}(247, \cdot)$
1-693-693.25-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.25	$0$	✓	✓	$-0.408$	$0$	$0.752123$	Character $\chi_{693}(25, \cdot)$
1-693-693.250-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.250	$0$	✓	✓	$-0.203$	$0$	$0.806900$	Character $\chi_{693}(250, \cdot)$
1-693-693.256-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.256	$0$	✓	✓	$0.147$	$0$	$1.00831$	Character $\chi_{693}(256, \cdot)$
1-693-693.257-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.257	$0$	✓	✓	$0.0447$	$0$	$1.26984$	Character $\chi_{693}(257, \cdot)$
1-693-693.263-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.263	$0$	✓	✓	$0.0454$	$0$	$1.40699$	Character $\chi_{693}(263, \cdot)$
1-693-693.268-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.268	$0$	✓	✓	$-0.147$	$0$	$0.799588$	Character $\chi_{693}(268, \cdot)$
1-693-693.283-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.283	$0$	✓	✓	$-0.274$	$0$	$0.816863$	Character $\chi_{693}(283, \cdot)$
1-693-693.290-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.290	$0$	✓	✓	$0.362$	$0$	$1.50670$	Character $\chi_{693}(290, \cdot)$
1-693-693.292-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.292	$0$	✓	✓	$-0.255$	$0$	$0.798956$	Character $\chi_{693}(292, \cdot)$
1-693-693.304-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.304	$0$	✓	✓	$-0.352$	$0$	$0.616617$	Character $\chi_{693}(304, \cdot)$
1-693-693.311-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.311	$0$	✓	✓	$0.0108$	$0$	$1.41974$	Character $\chi_{693}(311, \cdot)$
1-693-693.32-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.32	$0$	✓	✓	$0.101$	$0$	$1.06317$	Character $\chi_{693}(32, \cdot)$
1-693-693.326-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.326	$0$	✓	✓	$0.284$	$0$	$1.30170$	Character $\chi_{693}(326, \cdot)$
1-693-693.335-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.335	$0$	✓	✓	$-0.185$	$0$	$0.766874$	Character $\chi_{693}(335, \cdot)$
1-693-693.338-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.338	$0$	✓	✓	$-0.284$	$0$	$0.883250$	Character $\chi_{693}(338, \cdot)$
1-693-693.347-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.347	$0$	✓	✓	$0.245$	$0$	$1.77935$	Character $\chi_{693}(347, \cdot)$
1-693-693.349-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.349	$0$	✓	✓	$-0.0167$	$0$	$1.59362$	Character $\chi_{693}(349, \cdot)$
1-693-693.356-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.356	$0$	✓	✓	$0.231$	$0$	$1.52516$	Character $\chi_{693}(356, \cdot)$
1-693-693.376-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.376	$0$	✓	✓	$-0.118$	$0$	$0.767107$	Character $\chi_{693}(376, \cdot)$
1-693-693.38-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.38	$0$	✓	✓	$0.00177$	$0$	$1.37333$	Character $\chi_{693}(38, \cdot)$
1-693-693.380-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.380	$0$	✓	✓	$0.0524$	$0$	$1.42394$	Character $\chi_{693}(380, \cdot)$
1-693-693.383-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.383	$0$	✓	✓	$0.00177$	$0$	$0.905426$	Character $\chi_{693}(383, \cdot)$
1-693-693.391-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.391	$0$	✓	✓	$-0.0687$	$0$	$0.559957$	Character $\chi_{693}(391, \cdot)$
1-693-693.394-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.394	$0$	✓	✓	$-0.193$	$0$	$0.864080$	Character $\chi_{693}(394, \cdot)$
1-693-693.4-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.4	$0$	✓	✓	$-0.445$	$0$	$0.732360$	Character $\chi_{693}(4, \cdot)$
1-693-693.40-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.40	$0$	✓	✓	$-0.170$	$0$	$0.888197$	Character $\chi_{693}(40, \cdot)$
1-693-693.409-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.409	$0$	✓	✓	$-0.188$	$0$	$1.14042$	Character $\chi_{693}(409, \cdot)$
1-693-693.416-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.416	$0$	✓	✓	$0.316$	$0$	$1.79141$	Character $\chi_{693}(416, \cdot)$
1-693-693.439-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.439	$0$	✓	✓	$0.0353$	$0$	$1.17025$	Character $\chi_{693}(439, \cdot)$
1-693-693.445-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.445	$0$	✓	✓	$0.193$	$0$	$1.37103$	Character $\chi_{693}(445, \cdot)$
1-693-693.464-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.464	$0$	✓	✓	$-0.198$	$0$	$0.594216$	Character $\chi_{693}(464, \cdot)$
1-693-693.466-r0-0-0	$3.21$	$3.21$	$1$	$3^{2} \cdot 7 \cdot 11$	693.466	$0$	✓	✓	$0.000747$	$0$	$0.408129$	Character $\chi_{693}(466, \cdot)$

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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.