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 189 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-191-191.10-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.10	$0$	✓	✓	$0.319$	$0$	$0.0526540$	Character $\chi_{191}(10, \cdot)$
1-191-191.100-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.100	$0$	✓	✓	$-0.149$	$0$	$1.00347$	Character $\chi_{191}(100, \cdot)$
1-191-191.102-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.102	$0$	✓	✓	$-0.125$	$0$	$1.30964$	Character $\chi_{191}(102, \cdot)$
1-191-191.103-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.103	$0$	✓	✓	$0.125$	$0$	$0.989140$	Character $\chi_{191}(103, \cdot)$
1-191-191.104-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.104	$0$	✓	✓	$0.0280$	$0$	$1.45548$	Character $\chi_{191}(104, \cdot)$
1-191-191.107-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.107	$0$	✓	✓	$-0.321$	$0$	$1.43696$	Character $\chi_{191}(107, \cdot)$
1-191-191.108-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.108	$0$	✓	✓	$0.0311$	$0$	$1.82606$	Character $\chi_{191}(108, \cdot)$
1-191-191.109-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.109	$0$	✓	✓	$-0.0744$	$0$	$0.923136$	Character $\chi_{191}(109, \cdot)$
1-191-191.115-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.115	$0$	✓	✓	$-0.236$	$0$	$0.341672$	Character $\chi_{191}(115, \cdot)$
1-191-191.117-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.117	$0$	✓	✓	$-0.318$	$0$	$0.773993$	Character $\chi_{191}(117, \cdot)$
1-191-191.118-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.118	$0$	✓	✓	$0.496$	$0$	$2.67179$	Character $\chi_{191}(118, \cdot)$
1-191-191.12-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.12	$0$	✓	✓	$0.279$	$0$	$1.18641$	Character $\chi_{191}(12, \cdot)$
1-191-191.120-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.120	$0$	✓	✓	$0.0364$	$0$	$2.19124$	Character $\chi_{191}(120, \cdot)$
1-191-191.121-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.121	$0$	✓	✓	$-0.167$	$0$	$1.04094$	Character $\chi_{191}(121, \cdot)$
1-191-191.125-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.125	$0$	✓	✓	$-0.129$	$0$	$1.11704$	Character $\chi_{191}(125, \cdot)$
1-191-191.128-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.128	$0$	✓	✓	$0.227$	$0$	$1.80259$	Character $\chi_{191}(128, \cdot)$
1-191-191.129-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.129	$0$	✓	✓	$0.198$	$0$	$0.139216$	Character $\chi_{191}(129, \cdot)$
1-191-191.13-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.13	$0$	✓	✓	$-0.130$	$0$	$1.08423$	Character $\chi_{191}(13, \cdot)$
1-191-191.130-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.130	$0$	✓	✓	$0.0335$	$0$	$1.76860$	Character $\chi_{191}(130, \cdot)$
1-191-191.133-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.133	$0$	✓	✓	$-0.187$	$0$	$1.53357$	Character $\chi_{191}(133, \cdot)$
1-191-191.134-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.134	$0$	✓	✓	$0.0647$	$0$	$1.26429$	Character $\chi_{191}(134, \cdot)$
1-191-191.135-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.135	$0$	✓	✓	$0.187$	$0$	$1.89558$	Character $\chi_{191}(135, \cdot)$
1-191-191.136-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.136	$0$	✓	✓	$0.129$	$0$	$0.805888$	Character $\chi_{191}(136, \cdot)$
1-191-191.138-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.138	$0$	✓	✓	$-0.470$	$0$	$2.64992$	Character $\chi_{191}(138, \cdot)$
1-191-191.144-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.144	$0$	✓	✓	$0.388$	$0$	$2.32002$	Character $\chi_{191}(144, \cdot)$
1-191-191.147-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.147	$0$	✓	✓	$0.130$	$0$	$1.66384$	Character $\chi_{191}(147, \cdot)$
1-191-191.149-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.149	$0$	✓	✓	$0.110$	$0$	$2.00136$	Character $\chi_{191}(149, \cdot)$
1-191-191.15-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.15	$0$	✓	✓	$0.0215$	$0$	$0.727970$	Character $\chi_{191}(15, \cdot)$
1-191-191.150-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.150	$0$	✓	✓	$0.353$	$0$	$1.83718$	Character $\chi_{191}(150, \cdot)$
1-191-191.153-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.153	$0$	✓	✓	$-0.152$	$0$	$0.708999$	Character $\chi_{191}(153, \cdot)$
1-191-191.154-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.154	$0$	✓	✓	$0.127$	$0$	$1.63035$	Character $\chi_{191}(154, \cdot)$
1-191-191.156-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.156	$0$	✓	✓	$0.298$	$0$	$2.40372$	Character $\chi_{191}(156, \cdot)$
1-191-191.158-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.158	$0$	✓	✓	$0.420$	$0$	$0.199786$	Character $\chi_{191}(158, \cdot)$
1-191-191.16-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.16	$0$	✓	✓	$-0.279$	$0$	$0.576986$	Character $\chi_{191}(16, \cdot)$
1-191-191.160-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.160	$0$	✓	✓	$-0.127$	$0$	$1.49739$	Character $\chi_{191}(160, \cdot)$
1-191-191.162-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.162	$0$	✓	✓	$0.146$	$0$	$1.79546$	Character $\chi_{191}(162, \cdot)$
1-191-191.163-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.163	$0$	✓	✓	$0.0975$	$0$	$2.42542$	Character $\chi_{191}(163, \cdot)$
1-191-191.169-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.169	$0$	✓	✓	$-0.406$	$0$	$1.18555$	Character $\chi_{191}(169, \cdot)$
1-191-191.17-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.17	$0$	✓	✓	$-0.436$	$0$	$0.944647$	Character $\chi_{191}(17, \cdot)$
1-191-191.170-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.170	$0$	✓	✓	$0.149$	$0$	$1.16440$	Character $\chi_{191}(170, \cdot)$
1-191-191.172-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.172	$0$	✓	✓	$-0.319$	$0$	$2.50490$	Character $\chi_{191}(172, \cdot)$
1-191-191.177-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.177	$0$	✓	✓	$-0.353$	$0$	$0.608496$	Character $\chi_{191}(177, \cdot)$
1-191-191.18-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.18	$0$	✓	✓	$0.470$	$0$	$0.310070$	Character $\chi_{191}(18, \cdot)$
1-191-191.180-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.180	$0$	✓	✓	$-0.216$	$0$	$1.22243$	Character $\chi_{191}(180, \cdot)$
1-191-191.184-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.184	$0$	✓	✓	$0.0744$	$0$	$1.27714$	Character $\chi_{191}(184, \cdot)$
1-191-191.2-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.2	$0$	✓	✓	$-0.176$	$0$	$0.652061$	Character $\chi_{191}(2, \cdot)$
1-191-191.20-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.20	$0$	✓	✓	$0.193$	$0$	$2.38516$	Character $\chi_{191}(20, \cdot)$
1-191-191.23-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.23	$0$	✓	✓	$-0.0311$	$0$	$1.70574$	Character $\chi_{191}(23, \cdot)$
1-191-191.24-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.24	$0$	✓	✓	$0.376$	$0$	$1.61798$	Character $\chi_{191}(24, \cdot)$
1-191-191.25-r0-0-0	$0.887$	$0.887$	$1$	$191$	191.25	$0$	✓	✓	$0.321$	$0$	$2.44157$	Character $\chi_{191}(25, \cdot)$

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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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Results (1-50 of 189 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.