LMFDB - Rational L-function search results

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Results (1-50 of 5117 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\nu$	prim	$\epsilon$	$r$	First zero	Origin
1-1-1.1-r0-0-0	$0.00464$	$0.00464$	$1$	$1$	1.1		✓	$1$	$0$	$14.1347$	Artin representation 1.1.1t1.a Artin representation 1.1.1t1.a.a Character $\chi_{1}(1, \cdot)$ Number field $\Q$
2-23-23.22-c0-0-0	$0.107$	$0.0114$	$2$	$23$	23.22	$0.0$	✓	$1$	$0$	$5.11568$	Artin representation 2.23.3t2.b Artin representation 2.23.3t2.b.a Modular form 23.1.b.a Modular form 23.1.b.a.22.1
2-31-31.30-c0-0-0	$0.124$	$0.0154$	$2$	$31$	31.30	$0.0$	✓	$1$	$0$	$4.16621$	Artin representation 2.31.3t2.b Artin representation 2.31.3t2.b.a Modular form 31.1.b.a Modular form 31.1.b.a.30.1
2-39-39.38-c0-0-0	$0.139$	$0.0194$	$2$	$3 \cdot 13$	39.38	$0.0$	✓	$1$	$0$	$4.39582$	Artin representation 2.39.4t3.a Artin representation 2.39.4t3.a.a Modular form 39.1.d.a Modular form 39.1.d.a.38.1
2-44-11.10-c0-0-0	$0.148$	$0.0219$	$2$	$2^{2} \cdot 11$	11.10	$0.0$	✓	$1$	$0$	$4.04199$	Artin representation 2.44.3t2.b Artin representation 2.44.3t2.b.a Modular form 44.1.d.a Modular form 44.1.d.a.21.1
4-47e2-1.1-c0e2-0-0	$0.153$	$0.000550$	$4$	$47^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$2.98743$	Artin representation 2.47.5t2.a Modular form 47.1.b.a
4-52e2-1.1-c0e2-0-0	$0.161$	$0.000673$	$4$	$2^{4} \cdot 13^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$3.05212$	Artin representation 2.52.6t5.b Modular form 52.1.j.a
2-55-55.54-c0-0-0	$0.165$	$0.0274$	$2$	$5 \cdot 11$	55.54	$0.0$	✓	$1$	$0$	$3.81577$	Artin representation 2.55.4t3.c Artin representation 2.55.4t3.c.a Modular form 55.1.d.a Modular form 55.1.d.a.54.1
2-56-56.13-c0-0-0	$0.167$	$0.0279$	$2$	$2^{3} \cdot 7$	56.13	$0.0$	✓	$1$	$0$	$3.00942$	Artin representation 2.56.4t3.b Artin representation 2.56.4t3.b.a Modular form 56.1.h.a Modular form 56.1.h.a.13.1
4-57e2-1.1-c0e2-0-0	$0.168$	$0.000809$	$4$	$3^{2} \cdot 19^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$3.30843$	Artin representation 2.57.6t5.a Modular form 57.1.h.a
2-59-59.58-c0-0-0	$0.171$	$0.0294$	$2$	$59$	59.58	$0.0$	✓	$1$	$0$	$3.43180$	Artin representation 2.59.3t2.a Artin representation 2.59.3t2.a.a Modular form 59.1.b.a Modular form 59.1.b.a.58.1
2-63-7.6-c0-0-0	$0.177$	$0.0314$	$2$	$3^{2} \cdot 7$	7.6	$0.0$	✓	$1$	$0$	$3.51328$	Artin representation 2.63.4t3.a Artin representation 2.63.4t3.a.a Modular form 63.1.d.a Modular form 63.1.d.a.55.1
2-68-68.67-c0-0-0	$0.184$	$0.0339$	$2$	$2^{2} \cdot 17$	68.67	$0.0$	✓	$1$	$0$	$2.75562$	Artin representation 2.68.4t3.a Artin representation 2.68.4t3.a.a Modular form 68.1.d.a Modular form 68.1.d.a.67.1
4-68e2-1.1-c0e2-0-0	$0.184$	$0.00115$	$4$	$2^{4} \cdot 17^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$3.03544$	Artin representation 2.68.8t17.a Modular form 68.1.f.a
6-71e3-71.70-c0e3-0-0	$0.188$	$4.44\times 10^{-5}$	$6$	$71^{3}$	71.70	$0.0, 0.0, 0.0$		$1$	$0$	$2.19448$	Artin representation 2.71.7t2.a Modular form 71.1.b.a
4-72e2-1.1-c0e2-0-0	$0.189$	$0.00129$	$4$	$2^{6} \cdot 3^{4}$	1.1	$0.0, 0.0$		$1$	$0$	$2.13460$	Artin representation 2.72.6t5.b Modular form 72.1.p.a
2-76-19.18-c0-0-0	$0.194$	$0.0379$	$2$	$2^{2} \cdot 19$	19.18	$0.0$	✓	$1$	$0$	$3.27623$	Artin representation 2.76.3t2.a Artin representation 2.76.3t2.a.a Modular form 76.1.c.a Modular form 76.1.c.a.37.1
4-79e2-1.1-c0e2-0-0	$0.198$	$0.00155$	$4$	$79^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$2.25042$	Artin representation 2.79.5t2.a Modular form 79.1.b.a
2-80-20.19-c0-0-0	$0.199$	$0.0399$	$2$	$2^{4} \cdot 5$	20.19	$0.0$	✓	$1$	$0$	$3.18874$	Artin representation 2.80.4t3.a Artin representation 2.80.4t3.a.a Modular form 80.1.h.a Modular form 80.1.h.a.79.1
2-83-83.82-c0-0-0	$0.203$	$0.0414$	$2$	$83$	83.82	$0.0$	✓	$1$	$0$	$2.91606$	Artin representation 2.83.3t2.a Artin representation 2.83.3t2.a.a Modular form 83.1.b.a Modular form 83.1.b.a.82.1
4-84e2-1.1-c0e2-0-0	$0.204$	$0.00175$	$4$	$2^{4} \cdot 3^{2} \cdot 7^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$2.56497$	Artin representation 2.84.6t5.b Modular form 84.1.p.a
2-87-87.86-c0-0-0	$0.208$	$0.0434$	$2$	$3 \cdot 29$	87.86	$0.0$	✓	$1$	$0$	$2.68368$	Artin representation 2.87.3t2.a Artin representation 2.87.3t2.a.a Modular form 87.1.d.a Modular form 87.1.d.a.86.1
2-87-87.86-c0-0-1	$0.208$	$0.0434$	$2$	$3 \cdot 29$	87.86	$0.0$	✓	$1$	$0$	$3.53215$	Artin representation 2.87.6t3.b Artin representation 2.87.6t3.b.a Modular form 87.1.d.b Modular form 87.1.d.b.86.1
2-95-95.94-c0-0-1	$0.217$	$0.0474$	$2$	$5 \cdot 19$	95.94	$0.0$	✓	$1$	$0$	$2.87350$	Artin representation 2.95.4t3.c Artin representation 2.95.4t3.c.a Modular form 95.1.d.a Modular form 95.1.d.a.94.1
4-95e2-1.1-c0e2-0-0	$0.217$	$0.00224$	$4$	$5^{2} \cdot 19^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$2.51518$	Artin representation 2.95.8t6.a Modular form 95.1.d.b
4-99e2-1.1-c0e2-0-0	$0.222$	$0.00244$	$4$	$3^{4} \cdot 11^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$2.19749$	Artin representation 2.99.6t5.a Modular form 99.1.h.a
4-103e2-1.1-c0e2-0-0	$0.226$	$0.00264$	$4$	$103^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$2.00946$	Artin representation 2.103.5t2.a Modular form 103.1.b.a
2-104-104.51-c0-0-0	$0.227$	$0.0519$	$2$	$2^{3} \cdot 13$	104.51	$0.0$	✓	$1$	$0$	$2.09431$	Artin representation 2.104.6t3.a Artin representation 2.104.6t3.a.a Modular form 104.1.h.a Modular form 104.1.h.a.51.1
2-104-104.51-c0-0-1	$0.227$	$0.0519$	$2$	$2^{3} \cdot 13$	104.51	$0.0$	✓	$1$	$0$	$3.31991$	Artin representation 2.104.3t2.b Artin representation 2.104.3t2.b.a Modular form 104.1.h.b Modular form 104.1.h.b.51.1
2-107-107.106-c0-0-0	$0.231$	$0.0533$	$2$	$107$	107.106	$0.0$	✓	$1$	$0$	$2.61608$	Artin representation 2.107.3t2.a Artin representation 2.107.3t2.a.a Modular form 107.1.b.a Modular form 107.1.b.a.106.1
2-108-3.2-c0-0-0	$0.232$	$0.0538$	$2$	$2^{2} \cdot 3^{3}$	3.2	$0.0$	✓	$1$	$0$	$2.82161$	Artin representation 2.108.3t2.b Artin representation 2.108.3t2.b.a Modular form 108.1.c.a Modular form 108.1.c.a.53.1
2-111-111.110-c0-0-1	$0.235$	$0.0553$	$2$	$3 \cdot 37$	111.110	$0.0$	✓	$1$	$0$	$3.07636$	Artin representation 2.111.4t3.a Artin representation 2.111.4t3.a.a Modular form 111.1.d.a Modular form 111.1.d.a.110.1
4-111e2-1.1-c0e2-0-0	$0.235$	$0.00306$	$4$	$3^{2} \cdot 37^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$1.81269$	Artin representation 2.111.8t6.a Modular form 111.1.d.b
4-111e2-1.1-c0e2-0-1	$0.235$	$0.00306$	$4$	$3^{2} \cdot 37^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$1.94869$	Artin representation 2.111.6t5.a Modular form 111.1.i.a
4-112e2-1.1-c0e2-0-0	$0.236$	$0.00312$	$4$	$2^{8} \cdot 7^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$2.27803$	Artin representation 2.112.8t17.a Modular form 112.1.l.a
2-116-116.115-c0-0-0	$0.240$	$0.0578$	$2$	$2^{2} \cdot 29$	116.115	$0.0$	✓	$1$	$0$	$2.51709$	Artin representation 2.116.6t3.b Artin representation 2.116.6t3.b.a Modular form 116.1.d.a Modular form 116.1.d.a.115.1
2-116-116.115-c0-0-1	$0.240$	$0.0578$	$2$	$2^{2} \cdot 29$	116.115	$0.0$	✓	$1$	$0$	$3.11568$	Artin representation 2.116.3t2.a Artin representation 2.116.3t2.a.a Modular form 116.1.d.b Modular form 116.1.d.b.115.1
4-117e2-1.1-c0e2-0-0	$0.241$	$0.00340$	$4$	$3^{4} \cdot 13^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$2.45453$	Artin representation 2.117.8t17.b Modular form 117.1.j.a
4-119e2-1.1-c0e2-0-0	$0.243$	$0.00352$	$4$	$7^{2} \cdot 17^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$1.52402$	Artin representation 2.119.5t2.a Modular form 119.1.d.a
4-120e2-1.1-c0e2-0-0	$0.244$	$0.00358$	$4$	$2^{6} \cdot 3^{2} \cdot 5^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$2.15313$	Artin representation 2.120.8t11.c Modular form 120.1.i.a
8-124e4-1.1-c0e4-0-0	$0.248$	$1.46\times 10^{-5}$	$8$	$2^{8} \cdot 31^{4}$	1.1	$0.0, 0.0, 0.0, 0.0$		$1$	$0$	$1.52908$	Artin representation 2.124.16t60.a Modular form 124.1.i.a
4-127e2-1.1-c0e2-0-0	$0.251$	$0.00401$	$4$	$127^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$1.85920$	Artin representation 2.127.5t2.a Modular form 127.1.b.a
2-2e7-8.3-c0-0-0	$0.252$	$0.0638$	$2$	$2^{7}$	8.3	$0.0$	✓	$1$	$0$	$2.63592$	Artin representation 2.128.4t3.a Artin representation 2.128.4t3.a.a Modular form 128.1.d.a Modular form 128.1.d.a.63.1
4-131e2-1.1-c0e2-0-0	$0.255$	$0.00427$	$4$	$131^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$2.26288$	Artin representation 2.131.5t2.a Modular form 131.1.b.a
4-133e2-1.1-c0e2-0-0	$0.257$	$0.00440$	$4$	$7^{2} \cdot 19^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$2.16502$	Artin representation 2.133.6t5.a Modular form 133.1.r.a
8-133e4-1.1-c0e4-0-0	$0.257$	$1.94\times 10^{-5}$	$8$	$7^{4} \cdot 19^{4}$	1.1	$0.0, 0.0, 0.0, 0.0$		$1$	$0$	$1.69683$	Artin representation 2.133.16t60.a Modular form 133.1.m.a
2-135-15.14-c0-0-0	$0.259$	$0.0673$	$2$	$3^{3} \cdot 5$	15.14	$0.0$	✓	$1$	$0$	$2.04028$	Artin representation 2.135.3t2.b Artin representation 2.135.3t2.b.a Modular form 135.1.d.a Modular form 135.1.d.a.134.1
2-135-15.14-c0-0-1	$0.259$	$0.0673$	$2$	$3^{3} \cdot 5$	15.14	$0.0$	✓	$1$	$0$	$3.20668$	Artin representation 2.135.6t3.b Artin representation 2.135.6t3.b.a Modular form 135.1.d.b Modular form 135.1.d.b.134.1
2-136-136.67-c0-0-0	$0.260$	$0.0678$	$2$	$2^{3} \cdot 17$	136.67	$0.0$	✓	$1$	$0$	$2.11561$	Artin representation 2.136.4t3.b Artin representation 2.136.4t3.b.a Modular form 136.1.e.a Modular form 136.1.e.a.67.1
4-136e2-1.1-c0e2-0-0	$0.260$	$0.00460$	$4$	$2^{6} \cdot 17^{2}$	1.1	$0.0, 0.0$		$1$	$0$	$1.42085$	Artin representation 2.136.8t17.a Modular form 136.1.j.a

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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.