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 222 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1017-1017.1001-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.1001	$1$	✓	✓	$0.000513$	$0$	$0.780530$	Character $\chi_{1017}(1001, \cdot)$
1-1017-1017.1004-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.1004	$1$	✓	✓	$0.0351$	$0$	$0.639448$	Character $\chi_{1017}(1004, \cdot)$
1-1017-1017.1010-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.1010	$1$	✓	✓	$-0.492$	$0$	$1.79134$	Character $\chi_{1017}(1010, \cdot)$
1-1017-1017.1012-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.1012	$1$	✓	✓	$0.184$	$0$	$0.612479$	Character $\chi_{1017}(1012, \cdot)$
1-1017-1017.1013-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.1013	$1$	✓	✓	$0.0509$	$0$	$0.442561$	Character $\chi_{1017}(1013, \cdot)$
1-1017-1017.103-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.103	$1$	✓	✓	$0.416$	$0$	$1.13192$	Character $\chi_{1017}(103, \cdot)$
1-1017-1017.104-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.104	$1$	✓	✓	$0.406$	$0$	$1.60417$	Character $\chi_{1017}(104, \cdot)$
1-1017-1017.11-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.11	$1$	✓	✓	$0.00868$	$0$	$0.761717$	Character $\chi_{1017}(11, \cdot)$
1-1017-1017.122-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.122	$1$	✓	✓	$0.396$	$0$	$1.25080$	Character $\chi_{1017}(122, \cdot)$
1-1017-1017.128-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.128	$1$	✓	✓	$0.404$	$0$	$0.986731$	Character $\chi_{1017}(128, \cdot)$
1-1017-1017.130-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.130	$1$	✓	✓	$0.0281$	$0$	$0.661982$	Character $\chi_{1017}(130, \cdot)$
1-1017-1017.131-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.131	$1$	✓	✓	$-0.482$	$0$	$0.988951$	Character $\chi_{1017}(131, \cdot)$
1-1017-1017.133-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.133	$1$	✓	✓	$-0.0281$	$0$	$0.153394$	Character $\chi_{1017}(133, \cdot)$
1-1017-1017.14-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.14	$1$	✓	✓	$-0.295$	$0$	$0.625238$	Character $\chi_{1017}(14, \cdot)$
1-1017-1017.142-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.142	$1$	✓	✓	$0.368$	$0$	$0.825391$	Character $\chi_{1017}(142, \cdot)$
1-1017-1017.148-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.148	$1$	✓	✓	$0.495$	$0$	$1.58676$	Character $\chi_{1017}(148, \cdot)$
1-1017-1017.149-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.149	$1$	✓	✓	$-0.460$	$0$	$0.109027$	Character $\chi_{1017}(149, \cdot)$
1-1017-1017.151-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.151	$1$	✓	✓	$0.0608$	$0$	$0.850064$	Character $\chi_{1017}(151, \cdot)$
1-1017-1017.160-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.160	$1$	✓	✓	$0.374$	$0$	$1.60788$	Character $\chi_{1017}(160, \cdot)$
1-1017-1017.164-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.164	$1$	✓	✓	$0.174$	$0$	$1.15444$	Character $\chi_{1017}(164, \cdot)$
1-1017-1017.173-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.173	$1$	✓	✓	$-0.203$	$0$	$0.407815$	Character $\chi_{1017}(173, \cdot)$
1-1017-1017.176-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.176	$1$	✓	✓	$0.408$	$0$	$0.267595$	Character $\chi_{1017}(176, \cdot)$
1-1017-1017.178-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.178	$1$	✓	✓	$-0.111$	$0$	$0.945427$	Character $\chi_{1017}(178, \cdot)$
1-1017-1017.182-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.182	$1$	✓	✓	$-0.106$	$0$	$0.828552$	Character $\chi_{1017}(182, \cdot)$
1-1017-1017.184-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.184	$1$	✓	✓	$0.417$	$0$	$0.200670$	Character $\chi_{1017}(184, \cdot)$
1-1017-1017.185-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.185	$1$	✓	✓	$-0.00868$	$0$	$1.04909$	Character $\chi_{1017}(185, \cdot)$
1-1017-1017.187-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.187	$1$	✓	✓	$-0.213$	$0$	$0.199817$	Character $\chi_{1017}(187, \cdot)$
1-1017-1017.193-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.193	$1$	✓	✓	$0.399$	$0$	$0.0903240$	Character $\chi_{1017}(193, \cdot)$
1-1017-1017.194-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.194	$1$	✓	✓	$0.203$	$0$	$0.407264$	Character $\chi_{1017}(194, \cdot)$
1-1017-1017.2-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.2	$1$	✓	✓	$0.368$	$0$	$0.0180453$	Character $\chi_{1017}(2, \cdot)$
1-1017-1017.200-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.200	$1$	✓	✓	$0.0240$	$0$	$0.752494$	Character $\chi_{1017}(200, \cdot)$
1-1017-1017.202-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.202	$1$	✓	✓	$0.155$	$0$	$0.803766$	Character $\chi_{1017}(202, \cdot)$
1-1017-1017.205-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.205	$1$	✓	✓	$0.171$	$0$	$0.740846$	Character $\chi_{1017}(205, \cdot)$
1-1017-1017.212-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.212	$1$	✓	✓	$-0.260$	$0$	$0.590343$	Character $\chi_{1017}(212, \cdot)$
1-1017-1017.214-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.214	$1$	✓	✓	$0.0699$	$0$	$0.204950$	Character $\chi_{1017}(214, \cdot)$
1-1017-1017.218-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.218	$1$	✓	✓	$0.295$	$0$	$1.59365$	Character $\chi_{1017}(218, \cdot)$
1-1017-1017.220-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.220	$1$	✓	✓	$0.0315$	$0$	$1.13616$	Character $\chi_{1017}(220, \cdot)$
1-1017-1017.223-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.223	$1$	✓	✓	$-0.284$	$0$	$0.356630$	Character $\chi_{1017}(223, \cdot)$
1-1017-1017.229-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.229	$1$	✓	✓	$-0.0608$	$0$	$0.421589$	Character $\chi_{1017}(229, \cdot)$
1-1017-1017.230-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.230	$1$	✓	✓	$0.326$	$0$	$1.08885$	Character $\chi_{1017}(230, \cdot)$
1-1017-1017.232-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.232	$1$	✓	✓	$0.194$	$0$	$1.10434$	Character $\chi_{1017}(232, \cdot)$
1-1017-1017.238-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.238	$1$	✓	✓	$0.164$	$0$	$1.23650$	Character $\chi_{1017}(238, \cdot)$
1-1017-1017.239-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.239	$1$	✓	✓	$-0.0240$	$0$	$0.201922$	Character $\chi_{1017}(239, \cdot)$
1-1017-1017.247-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.247	$1$	✓	✓	$-0.205$	$0$	$1.45955$	Character $\chi_{1017}(247, \cdot)$
1-1017-1017.248-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.248	$1$	✓	✓	$-0.483$	$0$	$1.53079$	Character $\chi_{1017}(248, \cdot)$
1-1017-1017.250-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.250	$1$	✓	✓	$0.452$	$0$	$0.173965$	Character $\chi_{1017}(250, \cdot)$
1-1017-1017.254-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.254	$1$	✓	✓	$-0.0509$	$0$	$0.561971$	Character $\chi_{1017}(254, \cdot)$
1-1017-1017.257-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.257	$1$	✓	✓	$0.119$	$0$	$0.522190$	Character $\chi_{1017}(257, \cdot)$
1-1017-1017.259-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.259	$1$	✓	✓	$-0.00756$	$0$	$1.12158$	Character $\chi_{1017}(259, \cdot)$
1-1017-1017.265-r1-0-0	$109.$	$109.$	$1$	$3^{2} \cdot 113$	1017.265	$1$	✓	✓	$-0.368$	$0$	$0.592541$	Character $\chi_{1017}(265, \cdot)$

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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.