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 54 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-245-245.102-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.102	$1$	✓	✓	$-0.207$	$0$	$0.498494$	Character $\chi_{245}(102, \cdot)$
1-245-245.104-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.104	$1$	✓	✓	$-0.127$	$0$	$0.146725$	Character $\chi_{245}(104, \cdot)$
1-245-245.107-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.107	$1$	✓	✓	$0.247$	$0$	$1.31947$	Character $\chi_{245}(107, \cdot)$
1-245-245.113-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.113	$1$	✓	✓	$-0.261$	$0$	$0.293503$	Character $\chi_{245}(113, \cdot)$
1-245-245.123-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.123	$1$	✓	✓	$0.405$	$0$	$0.169175$	Character $\chi_{245}(123, \cdot)$
1-245-245.124-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.124	$1$	✓	✓	$-0.0459$	$0$	$1.36887$	Character $\chi_{245}(124, \cdot)$
1-245-245.127-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.127	$1$	✓	✓	$0.384$	$0$	$1.29220$	Character $\chi_{245}(127, \cdot)$
1-245-245.137-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.137	$1$	✓	✓	$0.0438$	$0$	$0.440221$	Character $\chi_{245}(137, \cdot)$
1-245-245.139-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.139	$1$	✓	✓	$0.127$	$0$	$1.63233$	Character $\chi_{245}(139, \cdot)$
1-245-245.142-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.142	$1$	✓	✓	$0.132$	$0$	$1.05308$	Character $\chi_{245}(142, \cdot)$
1-245-245.158-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.158	$1$	✓	✓	$-0.247$	$0$	$0.196646$	Character $\chi_{245}(158, \cdot)$
1-245-245.159-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.159	$1$	✓	✓	$0.0459$	$0$	$0.785226$	Character $\chi_{245}(159, \cdot)$
1-245-245.162-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.162	$1$	✓	✓	$-0.0853$	$0$	$0.806504$	Character $\chi_{245}(162, \cdot)$
1-245-245.163-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.163	$1$	✓	✓	$0.201$	$0$	$1.26664$	Character $\chi_{245}(163, \cdot)$
1-245-245.164-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.164	$1$	✓	✓	$0.0459$	$0$	$1.52331$	Character $\chi_{245}(164, \cdot)$
1-245-245.172-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.172	$1$	✓	✓	$-0.418$	$0$	$2.27962$	Character $\chi_{245}(172, \cdot)$
1-245-245.174-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.174	$1$	✓	✓	$-0.0459$	$0$	$0.577905$	Character $\chi_{245}(174, \cdot)$
1-245-245.183-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.183	$1$	✓	✓	$0.0853$	$0$	$0.545319$	Character $\chi_{245}(183, \cdot)$
1-245-245.193-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.193	$1$	✓	✓	$-0.377$	$0$	$0.340459$	Character $\chi_{245}(193, \cdot)$
1-245-245.194-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.194	$1$	✓	✓	$-0.243$	$0$	$0.543570$	Character $\chi_{245}(194, \cdot)$
1-245-245.198-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.198	$1$	✓	✓	$0.418$	$0$	$0.543196$	Character $\chi_{245}(198, \cdot)$
1-245-245.199-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.199	$1$	✓	✓	$0.460$	$0$	$1.56287$	Character $\chi_{245}(199, \cdot)$
1-245-245.2-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.2	$1$	✓	✓	$-0.405$	$0$	$1.27114$	Character $\chi_{245}(2, \cdot)$
1-245-245.207-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.207	$1$	✓	✓	$-0.0717$	$0$	$1.20600$	Character $\chi_{245}(207, \cdot)$
1-245-245.209-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.209	$1$	✓	✓	$0.423$	$0$	$1.97855$	Character $\chi_{245}(209, \cdot)$
1-245-245.212-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.212	$1$	✓	✓	$0.377$	$0$	$1.53415$	Character $\chi_{245}(212, \cdot)$
1-245-245.218-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.218	$1$	✓	✓	$-0.384$	$0$	$0.659754$	Character $\chi_{245}(218, \cdot)$
1-245-245.22-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.22	$1$	✓	✓	$-0.207$	$0$	$0.0329158$	Character $\chi_{245}(22, \cdot)$
1-245-245.228-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.228	$1$	✓	✓	$0.207$	$0$	$0.622191$	Character $\chi_{245}(228, \cdot)$
1-245-245.229-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.229	$1$	✓	✓	$-0.460$	$0$	$0.435029$	Character $\chi_{245}(229, \cdot)$
1-245-245.23-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.23	$1$	✓	✓	$-0.384$	$0$	$1.82105$	Character $\chi_{245}(23, \cdot)$
1-245-245.232-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.232	$1$	✓	✓	$0.261$	$0$	$1.75320$	Character $\chi_{245}(232, \cdot)$
1-245-245.233-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.233	$1$	✓	✓	$0.207$	$0$	$1.41427$	Character $\chi_{245}(233, \cdot)$
1-245-245.234-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.234	$1$	✓	✓	$0.0901$	$0$	$0.923367$	Character $\chi_{245}(234, \cdot)$
1-245-245.24-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.24	$1$	✓	✓	$0.243$	$0$	$0.750426$	Character $\chi_{245}(24, \cdot)$
1-245-245.242-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.242	$1$	✓	✓	$-0.201$	$0$	$0.732070$	Character $\chi_{245}(242, \cdot)$
1-245-245.32-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.32	$1$	✓	✓	$0.384$	$0$	$0.442708$	Character $\chi_{245}(32, \cdot)$
1-245-245.34-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.34	$1$	✓	✓	$-0.423$	$0$	$0.162141$	Character $\chi_{245}(34, \cdot)$
1-245-245.37-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.37	$1$	✓	✓	$0.384$	$0$	$1.59769$	Character $\chi_{245}(37, \cdot)$
1-245-245.43-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.43	$1$	✓	✓	$-0.465$	$0$	$1.23867$	Character $\chi_{245}(43, \cdot)$
1-245-245.53-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.53	$1$	✓	✓	$-0.384$	$0$	$0.439598$	Character $\chi_{245}(53, \cdot)$
1-245-245.54-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.54	$1$	✓	✓	$-0.205$	$0$	$0.167097$	Character $\chi_{245}(54, \cdot)$
1-245-245.57-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.57	$1$	✓	✓	$0.465$	$0$	$0.0535285$	Character $\chi_{245}(57, \cdot)$
1-245-245.58-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.58	$1$	✓	✓	$0.0717$	$0$	$1.16927$	Character $\chi_{245}(58, \cdot)$
1-245-245.59-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.59	$1$	✓	✓	$0.205$	$0$	$1.25676$	Character $\chi_{245}(59, \cdot)$
1-245-245.69-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.69	$1$	✓	✓	$0.0459$	$0$	$0.843354$	Character $\chi_{245}(69, \cdot)$
1-245-245.72-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.72	$1$	✓	✓	$-0.207$	$0$	$0.858403$	Character $\chi_{245}(72, \cdot)$
1-245-245.78-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.78	$1$	✓	✓	$0.207$	$0$	$1.63617$	Character $\chi_{245}(78, \cdot)$
1-245-245.8-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.8	$1$	✓	✓	$0.289$	$0$	$2.05771$	Character $\chi_{245}(8, \cdot)$
1-245-245.88-r1-0-0	$26.3$	$26.3$	$1$	$5 \cdot 7^{2}$	245.88	$1$	✓	✓	$-0.132$	$0$	$1.11569$	Character $\chi_{245}(88, \cdot)$

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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.