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 14575113 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\nu$	prim	arith	$\mathbb{Q}$	self-dual	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
2-23-23.22-c0-0-0	$0.107$	$0.0114$	$2$	$23$	23.22	$0.0$	✓	✓	✓	✓	$0$	$0$	$5.11568$	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	$0.0$	✓	✓	✓	✓	$0$	$0$	$4.16621$	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	$0.0$	✓	✓	✓	✓	$0$	$0$	$4.39582$	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	$0.0$	✓	✓	✓	✓	$0$	$0$	$4.04199$	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
2-47-47.46-c0-0-0	$0.153$	$0.0234$	$2$	$47$	47.46	$0.0$	✓	✓		✓	$0$	$0$	$2.98743$	Artin representation 2.47.5t2.a.a Modular form 47.1.b.a.46.1
2-47-47.46-c0-0-1	$0.153$	$0.0234$	$2$	$47$	47.46	$0.0$	✓	✓		✓	$0$	$0$	$4.44331$	Artin representation 2.47.5t2.a.b Modular form 47.1.b.a.46.2
4-47e2-1.1-c0e2-0-0	$0.153$	$0.000550$	$4$	$47^{2}$	1.1	$0.0, 0.0$		✓	✓	✓	$0$	$0$	$2.98743$	Artin representation 2.47.5t2.a Modular form 47.1.b.a
2-52-52.3-c0-0-0	$0.161$	$0.0259$	$2$	$2^{2} \cdot 13$	52.3	$0.0$	✓	✓			$0.123$	$0$	$4.16168$	Artin representation 2.52.6t5.b.b Modular form 52.1.j.a.3.1
2-52-52.35-c0-0-0	$0.161$	$0.0259$	$2$	$2^{2} \cdot 13$	52.35	$0.0$	✓	✓			$-0.123$	$0$	$3.05212$	Artin representation 2.52.6t5.b.a Modular form 52.1.j.a.35.1
4-52e2-1.1-c0e2-0-0	$0.161$	$0.000673$	$4$	$2^{4} \cdot 13^{2}$	1.1	$0.0, 0.0$		✓	✓	✓	$0$	$0$	$3.05212$	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	$0.0$	✓	✓	✓	✓	$0$	$0$	$3.81577$	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	$0.0$	✓	✓	✓	✓	$0$	$0$	$3.00942$	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
2-57-57.11-c0-0-0	$0.168$	$0.0284$	$2$	$3 \cdot 19$	57.11	$0.0$	✓	✓			$-0.0338$	$0$	$3.30843$	Artin representation 2.57.6t5.a.a Modular form 57.1.h.a.11.1
2-57-57.26-c0-0-0	$0.168$	$0.0284$	$2$	$3 \cdot 19$	57.26	$0.0$	✓	✓			$0.0338$	$0$	$3.89339$	Artin representation 2.57.6t5.a.b Modular form 57.1.h.a.26.1
4-57e2-1.1-c0e2-0-0	$0.168$	$0.000809$	$4$	$3^{2} \cdot 19^{2}$	1.1	$0.0, 0.0$		✓	✓	✓	$0$	$0$	$3.30843$	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	$0.0$	✓	✓	✓	✓	$0$	$0$	$3.43180$	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	$0.0$	✓	✓	✓	✓	$0$	$0$	$3.51328$	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
2-68-68.47-c0-0-0	$0.184$	$0.0339$	$2$	$2^{2} \cdot 17$	68.47	$0.0$	✓	✓			$-0.144$	$0$	$3.03544$	Artin representation 2.68.8t17.a.b Modular form 68.1.f.a.47.1
2-68-68.55-c0-0-0	$0.184$	$0.0339$	$2$	$2^{2} \cdot 17$	68.55	$0.0$	✓	✓			$0.144$	$0$	$4.22564$	Artin representation 2.68.8t17.a.a Modular form 68.1.f.a.55.1
2-68-68.67-c0-0-0	$0.184$	$0.0339$	$2$	$2^{2} \cdot 17$	68.67	$0.0$	✓	✓	✓	✓	$0$	$0$	$2.75562$	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	$0.0, 0.0$		✓	✓	✓	$0$	$0$	$3.03544$	Artin representation 2.68.8t17.a Modular form 68.1.f.a
2-71-71.70-c0-0-0	$0.188$	$0.0354$	$2$	$71$	71.70	$0.0$	✓	✓		✓	$0$	$0$	$2.19448$	Artin representation 2.71.7t2.a.c Modular form 71.1.b.a.70.1
2-71-71.70-c0-0-1	$0.188$	$0.0354$	$2$	$71$	71.70	$0.0$	✓	✓		✓	$0$	$0$	$3.39979$	Artin representation 2.71.7t2.a.a Modular form 71.1.b.a.70.2
2-71-71.70-c0-0-2	$0.188$	$0.0354$	$2$	$71$	71.70	$0.0$	✓	✓		✓	$0$	$0$	$3.95531$	Artin representation 2.71.7t2.a.b Modular form 71.1.b.a.70.3
6-71e3-71.70-c0e3-0-0	$0.188$	$4.44\times 10^{-5}$	$6$	$71^{3}$	71.70	$0.0, 0.0, 0.0$		✓	✓	✓	$0$	$0$	$2.19448$	Artin representation 2.71.7t2.a Modular form 71.1.b.a
2-72-72.43-c0-0-0	$0.189$	$0.0359$	$2$	$2^{3} \cdot 3^{2}$	72.43	$0.0$	✓	✓			$-0.222$	$0$	$2.13460$	Artin representation 2.72.6t5.b.a Modular form 72.1.p.a.43.1
2-72-72.67-c0-0-0	$0.189$	$0.0359$	$2$	$2^{3} \cdot 3^{2}$	72.67	$0.0$	✓	✓			$0.222$	$0$	$4.17397$	Artin representation 2.72.6t5.b.b Modular form 72.1.p.a.67.1
4-72e2-1.1-c0e2-0-0	$0.189$	$0.00129$	$4$	$2^{6} \cdot 3^{4}$	1.1	$0.0, 0.0$		✓	✓	✓	$0$	$0$	$2.13460$	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	$0.0$	✓	✓	✓	✓	$0$	$0$	$3.27623$	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
2-77-77.20-c0-0-0	$0.196$	$0.0384$	$2$	$7 \cdot 11$	77.20	$0.0$	✓	✓			$-0.257$	$0$	$2.35278$	Modular form 77.1.j.a.20.1
2-77-77.27-c0-0-0	$0.196$	$0.0384$	$2$	$7 \cdot 11$	77.27	$0.0$	✓	✓			$0.257$	$0$	$4.11400$	Modular form 77.1.j.a.27.1
2-77-77.48-c0-0-0	$0.196$	$0.0384$	$2$	$7 \cdot 11$	77.48	$0.0$	✓	✓			$0.0962$	$0$	$3.35405$	Modular form 77.1.j.a.48.1
2-77-77.69-c0-0-0	$0.196$	$0.0384$	$2$	$7 \cdot 11$	77.69	$0.0$	✓	✓			$-0.0962$	$0$	$2.48329$	Modular form 77.1.j.a.69.1
8-77e4-1.1-c0e4-0-0	$0.196$	$2.18\times 10^{-6}$	$8$	$7^{4} \cdot 11^{4}$	1.1	$0.0, 0.0, 0.0, 0.0$		✓	✓	✓	$0$	$0$	$2.35278$	Modular form 77.1.j.a
2-79-79.78-c0-0-0	$0.198$	$0.0394$	$2$	$79$	79.78	$0.0$	✓	✓		✓	$0$	$0$	$2.25042$	Artin representation 2.79.5t2.a.a Modular form 79.1.b.a.78.1
2-79-79.78-c0-0-1	$0.198$	$0.0394$	$2$	$79$	79.78	$0.0$	✓	✓		✓	$0$	$0$	$3.84845$	Artin representation 2.79.5t2.a.b Modular form 79.1.b.a.78.2
4-79e2-1.1-c0e2-0-0	$0.198$	$0.00155$	$4$	$79^{2}$	1.1	$0.0, 0.0$		✓	✓	✓	$0$	$0$	$2.25042$	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	$0.0$	✓	✓	✓	✓	$0$	$0$	$3.18874$	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	$0.0$	✓	✓	✓	✓	$0$	$0$	$2.91606$	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
2-84-21.11-c0-0-0	$0.204$	$0.0419$	$2$	$2^{2} \cdot 3 \cdot 7$	21.11	$0.0$	✓	✓			$-0.0732$	$0$	$2.56497$	Artin representation 2.84.6t5.b.a Modular form 84.1.p.a.53.1
2-84-21.2-c0-0-0	$0.204$	$0.0419$	$2$	$2^{2} \cdot 3 \cdot 7$	21.2	$0.0$	✓	✓			$0.0732$	$0$	$3.52084$	Artin representation 2.84.6t5.b.b Modular form 84.1.p.a.65.1
4-84e2-1.1-c0e2-0-0	$0.204$	$0.00175$	$4$	$2^{4} \cdot 3^{2} \cdot 7^{2}$	1.1	$0.0, 0.0$		✓	✓	✓	$0$	$0$	$2.56497$	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	$0.0$	✓	✓	✓	✓	$0$	$0$	$2.68368$	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	$0.0$	✓	✓	✓	✓	$0$	$0$	$3.53215$	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
2-88-88.27-c0-0-0	$0.209$	$0.0439$	$2$	$2^{3} \cdot 11$	88.27	$0.0$	✓	✓			$-0.142$	$0$	$2.68791$	Modular form 88.1.l.a.27.1
2-88-88.3-c0-0-0	$0.209$	$0.0439$	$2$	$2^{3} \cdot 11$	88.3	$0.0$	✓	✓			$0.103$	$0$	$3.29597$	Modular form 88.1.l.a.3.1
2-88-88.59-c0-0-0	$0.209$	$0.0439$	$2$	$2^{3} \cdot 11$	88.59	$0.0$	✓	✓			$-0.103$	$0$	$1.80284$	Modular form 88.1.l.a.59.1
2-88-88.75-c0-0-0	$0.209$	$0.0439$	$2$	$2^{3} \cdot 11$	88.75	$0.0$	✓	✓			$0.142$	$0$	$3.67884$	Modular form 88.1.l.a.75.1
8-88e4-1.1-c0e4-0-0	$0.209$	$3.72\times 10^{-6}$	$8$	$2^{12} \cdot 11^{4}$	1.1	$0.0, 0.0, 0.0, 0.0$		✓	✓	✓	$0$	$0$	$1.80284$	Modular form 88.1.l.a
2-93-93.2-c0-0-0	$0.215$	$0.0464$	$2$	$3 \cdot 31$	93.2	$0.0$	✓	✓			$-0.0976$	$0$	$2.26669$	Modular form 93.1.l.a.2.1

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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.