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

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1723-1723.10-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.10	$0$	✓	✓	$0.0571$	$0$	$0.971471$	Character $\chi_{1723}(10, \cdot)$
1-1723-1723.100-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.100	$0$	✓	✓	$-0.245$	$0$	$0.319636$	Character $\chi_{1723}(100, \cdot)$
1-1723-1723.1000-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1000	$0$	✓	✓	$0.284$	$0$	$1.21696$	Character $\chi_{1723}(1000, \cdot)$
1-1723-1723.1001-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1001	$0$	✓	✓	$0.459$	$0$	$0.145357$	Character $\chi_{1723}(1001, \cdot)$
1-1723-1723.1002-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1002	$0$	✓	✓	$0.350$	$0$	$0.989033$	Character $\chi_{1723}(1002, \cdot)$
1-1723-1723.1003-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1003	$0$	✓	✓	$0.440$	$0$	$0.651501$	Character $\chi_{1723}(1003, \cdot)$
1-1723-1723.1005-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1005	$0$	✓	✓	$-0.280$	$0$	$0.153616$	Character $\chi_{1723}(1005, \cdot)$
1-1723-1723.101-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.101	$0$	✓	✓	$0.183$	$0$	$1.18644$	Character $\chi_{1723}(101, \cdot)$
1-1723-1723.1010-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1010	$0$	✓	✓	$0.314$	$0$	$1.27920$	Character $\chi_{1723}(1010, \cdot)$
1-1723-1723.1011-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1011	$0$	✓	✓	$0.391$	$0$	$1.63932$	Character $\chi_{1723}(1011, \cdot)$
1-1723-1723.1012-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1012	$0$	✓	✓	$-0.386$	$0$	$0.513042$	Character $\chi_{1723}(1012, \cdot)$
1-1723-1723.1013-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1013	$0$	✓	✓	$-0.0315$	$0$	$1.28837$	Character $\chi_{1723}(1013, \cdot)$
1-1723-1723.1014-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1014	$0$	✓	✓	$-0.472$	$0$	$0.598980$	Character $\chi_{1723}(1014, \cdot)$
1-1723-1723.1016-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1016	$0$	✓	✓	$-0.477$	$0$	$0.240402$	Character $\chi_{1723}(1016, \cdot)$
1-1723-1723.1017-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1017	$0$	✓	✓	$-0.110$	$0$	$0.276399$	Character $\chi_{1723}(1017, \cdot)$
1-1723-1723.1021-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1021	$0$	✓	✓	$0.211$	$0$	$0.595130$	Character $\chi_{1723}(1021, \cdot)$
1-1723-1723.1023-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1023	$0$	✓	✓	$0.266$	$0$	$1.70249$	Character $\chi_{1723}(1023, \cdot)$
1-1723-1723.1024-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1024	$0$	✓	✓	$-0.00989$	$0$	$1.06112$	Character $\chi_{1723}(1024, \cdot)$
1-1723-1723.1025-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1025	$0$	✓	✓	$-0.270$	$0$	$1.86850$	Character $\chi_{1723}(1025, \cdot)$
1-1723-1723.1026-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1026	$0$	✓	✓	$0.477$	$0$	$1.27916$	Character $\chi_{1723}(1026, \cdot)$
1-1723-1723.1027-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1027	$0$	✓	✓	$0.135$	$0$	$0.874696$	Character $\chi_{1723}(1027, \cdot)$
1-1723-1723.1029-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1029	$0$	✓	✓	$-0.437$	$0$	$0.0660613$	Character $\chi_{1723}(1029, \cdot)$
1-1723-1723.103-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.103	$0$	✓	✓	$0.321$	$0$	$0.791273$	Character $\chi_{1723}(103, \cdot)$
1-1723-1723.1030-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1030	$0$	✓	✓	$0.0253$	$0$	$1.00791$	Character $\chi_{1723}(1030, \cdot)$
1-1723-1723.1031-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1031	$0$	✓	✓	$-0.476$	$0$	$1.44602$	Character $\chi_{1723}(1031, \cdot)$
1-1723-1723.1032-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1032	$0$	✓	✓	$-0.282$	$0$	$0.676308$	Character $\chi_{1723}(1032, \cdot)$
1-1723-1723.1033-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1033	$0$	✓	✓	$-0.141$	$0$	$0.771368$	Character $\chi_{1723}(1033, \cdot)$
1-1723-1723.104-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.104	$0$	✓	✓	$0.102$	$0$	$1.02147$	Character $\chi_{1723}(104, \cdot)$
1-1723-1723.1040-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1040	$0$	✓	✓	$0.132$	$0$	$1.24720$	Character $\chi_{1723}(1040, \cdot)$
1-1723-1723.1043-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1043	$0$	✓	✓	$-0.00824$	$0$	$1.06670$	Character $\chi_{1723}(1043, \cdot)$
1-1723-1723.1048-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1048	$0$	✓	✓	$0.139$	$0$	$1.23734$	Character $\chi_{1723}(1048, \cdot)$
1-1723-1723.1051-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1051	$0$	✓	✓	$0.282$	$0$	$0.137441$	Character $\chi_{1723}(1051, \cdot)$
1-1723-1723.1056-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1056	$0$	✓	✓	$-0.136$	$0$	$0.356524$	Character $\chi_{1723}(1056, \cdot)$
1-1723-1723.1057-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1057	$0$	✓	✓	$0.195$	$0$	$1.13604$	Character $\chi_{1723}(1057, \cdot)$
1-1723-1723.106-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.106	$0$	✓	✓	$0.199$	$0$	$0.990932$	Character $\chi_{1723}(106, \cdot)$
1-1723-1723.1060-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1060	$0$	✓	✓	$0.456$	$0$	$0.691058$	Character $\chi_{1723}(1060, \cdot)$
1-1723-1723.1062-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1062	$0$	✓	✓	$0.116$	$0$	$0.269671$	Character $\chi_{1723}(1062, \cdot)$
1-1723-1723.1064-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1064	$0$	✓	✓	$0.322$	$0$	$0.718019$	Character $\chi_{1723}(1064, \cdot)$
1-1723-1723.1066-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1066	$0$	✓	✓	$0.210$	$0$	$0.745882$	Character $\chi_{1723}(1066, \cdot)$
1-1723-1723.1071-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1071	$0$	✓	✓	$0.306$	$0$	$1.19157$	Character $\chi_{1723}(1071, \cdot)$
1-1723-1723.1072-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1072	$0$	✓	✓	$-0.0576$	$0$	$0.548428$	Character $\chi_{1723}(1072, \cdot)$
1-1723-1723.1074-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1074	$0$	✓	✓	$0.135$	$0$	$0.782693$	Character $\chi_{1723}(1074, \cdot)$
1-1723-1723.1075-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1075	$0$	✓	✓	$0.410$	$0$	$0.184823$	Character $\chi_{1723}(1075, \cdot)$
1-1723-1723.1079-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1079	$0$	✓	✓	$0.472$	$0$	$1.16270$	Character $\chi_{1723}(1079, \cdot)$
1-1723-1723.1081-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1081	$0$	✓	✓	$-0.0182$	$0$	$0.415040$	Character $\chi_{1723}(1081, \cdot)$
1-1723-1723.1084-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1084	$0$	✓	✓	$0.302$	$0$	$1.61076$	Character $\chi_{1723}(1084, \cdot)$
1-1723-1723.1086-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1086	$0$	✓	✓	$0.118$	$0$	$1.40543$	Character $\chi_{1723}(1086, \cdot)$
1-1723-1723.1089-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1089	$0$	✓	✓	$-0.484$	$0$	$1.57220$	Character $\chi_{1723}(1089, \cdot)$
1-1723-1723.109-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.109	$0$	✓	✓	$-0.478$	$0$	$1.92748$	Character $\chi_{1723}(109, \cdot)$
1-1723-1723.1090-r0-0-0	$8.00$	$8.00$	$1$	$1723$	1723.1090	$0$	✓	✓	$0.0909$	$0$	$1.21928$	Character $\chi_{1723}(1090, \cdot)$

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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.