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 951 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-953-953.100-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.100	$0$	✓	✓	$0.228$	$0$	$1.56225$	Character $\chi_{953}(100, \cdot)$
1-953-953.103-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.103	$0$	✓	✓	$0.0123$	$0$	$0.978120$	Character $\chi_{953}(103, \cdot)$
1-953-953.104-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.104	$0$	✓	✓	$0.309$	$0$	$1.11845$	Character $\chi_{953}(104, \cdot)$
1-953-953.105-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.105	$0$	✓	✓	$-0.212$	$0$	$1.17179$	Character $\chi_{953}(105, \cdot)$
1-953-953.106-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.106	$0$	✓	✓	$0.0356$	$0$	$1.58122$	Character $\chi_{953}(106, \cdot)$
1-953-953.109-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.109	$0$	✓	✓	$0.337$	$0$	$1.74391$	Character $\chi_{953}(109, \cdot)$
1-953-953.110-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.110	$0$	✓	✓	$-0.0215$	$0$	$1.05164$	Character $\chi_{953}(110, \cdot)$
1-953-953.112-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.112	$0$	✓	✓	$0.259$	$0$	$0.830640$	Character $\chi_{953}(112, \cdot)$
1-953-953.113-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.113	$0$	✓	✓	$0.338$	$0$	$0.305130$	Character $\chi_{953}(113, \cdot)$
1-953-953.114-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.114	$0$	✓	✓	$0.0647$	$0$	$1.16177$	Character $\chi_{953}(114, \cdot)$
1-953-953.115-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.115	$0$	✓	✓	$-0.348$	$0$	$1.43909$	Character $\chi_{953}(115, \cdot)$
1-953-953.116-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.116	$0$	✓	✓	$0.221$	$0$	$0.806107$	Character $\chi_{953}(116, \cdot)$
1-953-953.117-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.117	$0$	✓	✓	$-0.443$	$0$	$1.37435$	Character $\chi_{953}(117, \cdot)$
1-953-953.118-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.118	$0$	✓	✓	$0.212$	$0$	$0.988080$	Character $\chi_{953}(118, \cdot)$
1-953-953.119-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.119	$0$	✓	✓	$-0.0514$	$0$	$1.55471$	Character $\chi_{953}(119, \cdot)$
1-953-953.120-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.120	$0$	✓	✓	$0.200$	$0$	$1.16098$	Character $\chi_{953}(120, \cdot)$
1-953-953.121-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.121	$0$	✓	✓	$-0.347$	$0$	$0.164457$	Character $\chi_{953}(121, \cdot)$
1-953-953.126-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.126	$0$	✓	✓	$0.104$	$0$	$1.17206$	Character $\chi_{953}(126, \cdot)$
1-953-953.127-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.127	$0$	✓	✓	$0.468$	$0$	$0.0411849$	Character $\chi_{953}(127, \cdot)$
1-953-953.128-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.128	$0$	✓	✓	$-0.329$	$0$	$1.06275$	Character $\chi_{953}(128, \cdot)$
1-953-953.129-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.129	$0$	✓	✓	$0.418$	$0$	$0.688360$	Character $\chi_{953}(129, \cdot)$
1-953-953.13-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.13	$0$	✓	✓	$-0.130$	$0$	$0.393850$	Character $\chi_{953}(13, \cdot)$
1-953-953.131-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.131	$0$	✓	✓	$0.0135$	$0$	$0.595120$	Character $\chi_{953}(131, \cdot)$
1-953-953.132-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.132	$0$	✓	✓	$0.208$	$0$	$1.24951$	Character $\chi_{953}(132, \cdot)$
1-953-953.134-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.134	$0$	✓	✓	$0.318$	$0$	$1.76686$	Character $\chi_{953}(134, \cdot)$
1-953-953.135-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.135	$0$	✓	✓	$0.177$	$0$	$1.29989$	Character $\chi_{953}(135, \cdot)$
1-953-953.136-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.136	$0$	✓	✓	$-0.360$	$0$	$0.706591$	Character $\chi_{953}(136, \cdot)$
1-953-953.138-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.138	$0$	✓	✓	$-0.144$	$0$	$1.07198$	Character $\chi_{953}(138, \cdot)$
1-953-953.14-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.14	$0$	✓	✓	$0.135$	$0$	$1.56422$	Character $\chi_{953}(14, \cdot)$
1-953-953.141-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.141	$0$	✓	✓	$0.00241$	$0$	$1.21273$	Character $\chi_{953}(141, \cdot)$
1-953-953.142-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.142	$0$	✓	✓	$-0.160$	$0$	$0.289700$	Character $\chi_{953}(142, \cdot)$
1-953-953.144-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.144	$0$	✓	✓	$-0.0840$	$0$	$1.03395$	Character $\chi_{953}(144, \cdot)$
1-953-953.146-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.146	$0$	✓	✓	$0.328$	$0$	$1.47899$	Character $\chi_{953}(146, \cdot)$
1-953-953.148-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.148	$0$	✓	✓	$0.307$	$0$	$1.56842$	Character $\chi_{953}(148, \cdot)$
1-953-953.15-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.15	$0$	✓	✓	$-0.338$	$0$	$1.69337$	Character $\chi_{953}(15, \cdot)$
1-953-953.151-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.151	$0$	✓	✓	$-0.386$	$0$	$1.11934$	Character $\chi_{953}(151, \cdot)$
1-953-953.153-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.153	$0$	✓	✓	$0.299$	$0$	$1.54537$	Character $\chi_{953}(153, \cdot)$
1-953-953.155-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.155	$0$	✓	✓	$0.486$	$0$	$1.45063$	Character $\chi_{953}(155, \cdot)$
1-953-953.157-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.157	$0$	✓	✓	$-0.104$	$0$	$0.422452$	Character $\chi_{953}(157, \cdot)$
1-953-953.158-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.158	$0$	✓	✓	$-0.478$	$0$	$1.03320$	Character $\chi_{953}(158, \cdot)$
1-953-953.16-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.16	$0$	✓	✓	$-0.134$	$0$	$1.10415$	Character $\chi_{953}(16, \cdot)$
1-953-953.162-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.162	$0$	✓	✓	$-0.0191$	$0$	$0.270407$	Character $\chi_{953}(162, \cdot)$
1-953-953.164-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.164	$0$	✓	✓	$-0.401$	$0$	$1.24546$	Character $\chi_{953}(164, \cdot)$
1-953-953.166-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.166	$0$	✓	✓	$-0.304$	$0$	$0.820999$	Character $\chi_{953}(166, \cdot)$
1-953-953.169-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.169	$0$	✓	✓	$0.287$	$0$	$0.361732$	Character $\chi_{953}(169, \cdot)$
1-953-953.17-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.17	$0$	✓	✓	$-0.282$	$0$	$0.0983744$	Character $\chi_{953}(17, \cdot)$
1-953-953.173-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.173	$0$	✓	✓	$0.240$	$0$	$1.95425$	Character $\chi_{953}(173, \cdot)$
1-953-953.175-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.175	$0$	✓	✓	$0.218$	$0$	$1.75383$	Character $\chi_{953}(175, \cdot)$
1-953-953.18-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.18	$0$	✓	✓	$0.0883$	$0$	$1.52268$	Character $\chi_{953}(18, \cdot)$
1-953-953.181-r0-0-0	$4.42$	$4.42$	$1$	$953$	953.181	$0$	✓	✓	$-0.0212$	$0$	$1.40686$	Character $\chi_{953}(181, \cdot)$

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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.