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 (50 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
2-30e2-100.11-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	100.11	$0.0$	✓	✓			$0.280$	$0$	$2.47470$	Modular form 900.1.x.a.811.1
2-30e2-100.19-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	100.19	$0.0$	✓	✓			$0.0400$	$0$	$1.50391$	Modular form 900.1.bb.a.19.1
2-30e2-100.19-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	100.19	$0.0$	✓	✓			$0.0400$	$0$	$1.71336$	Modular form 900.1.bb.a.19.2
2-30e2-100.31-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	100.31	$0.0$	✓	✓			$0.0400$	$0$	$1.13851$	Modular form 900.1.x.a.631.1
2-30e2-100.39-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	100.39	$0.0$	✓	✓			$-0.220$	$0$	$0.404534$	Modular form 900.1.bb.a.739.1
2-30e2-100.39-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	100.39	$0.0$	✓	✓			$-0.220$	$0$	$1.45088$	Modular form 900.1.bb.a.739.2
2-30e2-100.59-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	100.59	$0.0$	✓	✓			$0.220$	$0$	$1.87223$	Modular form 900.1.bb.a.559.1
2-30e2-100.59-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	100.59	$0.0$	✓	✓			$0.220$	$0$	$2.02795$	Modular form 900.1.bb.a.559.2
2-30e2-100.71-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	100.71	$0.0$	✓	✓			$-0.0400$	$0$	$1.70109$	Modular form 900.1.x.a.271.1
2-30e2-100.79-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	100.79	$0.0$	✓	✓			$-0.0400$	$0$	$1.22645$	Modular form 900.1.bb.a.379.1
2-30e2-100.79-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	100.79	$0.0$	✓	✓			$-0.0400$	$0$	$1.76848$	Modular form 900.1.bb.a.379.2
2-30e2-100.91-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	100.91	$0.0$	✓	✓			$-0.280$	$0$	$1.23149$	Modular form 900.1.x.a.91.1
2-30e2-180.167-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	180.167	$0.0$	✓	✓			$-0.356$	$0$	$1.25355$	Modular form 900.1.bd.a.707.1
2-30e2-180.167-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	180.167	$0.0$	✓	✓			$-0.356$	$0$	$3.12301$	Modular form 900.1.bd.a.707.2
2-30e2-180.23-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	180.23	$0.0$	✓	✓			$-0.0325$	$0$	$1.24402$	Modular form 900.1.bd.a.743.1
2-30e2-180.23-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	180.23	$0.0$	✓	✓			$-0.0325$	$0$	$1.75272$	Modular form 900.1.bd.a.743.2
2-30e2-180.47-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	180.47	$0.0$	✓	✓			$0.0325$	$0$	$1.48653$	Modular form 900.1.bd.a.407.2
2-30e2-180.47-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	180.47	$0.0$	✓	✓			$0.0325$	$0$	$1.72323$	Modular form 900.1.bd.a.407.1
2-30e2-180.83-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	180.83	$0.0$	✓	✓			$0.356$	$0$	$0.412503$	Modular form 900.1.bd.a.443.2
2-30e2-180.83-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	180.83	$0.0$	✓	✓			$0.356$	$0$	$1.91623$	Modular form 900.1.bd.a.443.1
2-30e2-300.167-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.167	$0.0$	✓	✓			$0.192$	$0$	$1.39622$	Modular form 900.1.bh.a.467.1
2-30e2-300.167-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.167	$0.0$	✓	✓			$-0.112$	$0$	$1.94411$	Modular form 900.1.bh.a.467.2
2-30e2-300.203-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.203	$0.0$	✓	✓			$-0.192$	$0$	$0.800737$	Modular form 900.1.bh.a.503.1
2-30e2-300.203-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.203	$0.0$	✓	✓			$0.112$	$0$	$2.10943$	Modular form 900.1.bh.a.503.2
2-30e2-300.227-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.227	$0.0$	✓	✓			$-0.122$	$0$	$1.25331$	Modular form 900.1.bh.a.827.1
2-30e2-300.227-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.227	$0.0$	✓	✓			$0.182$	$0$	$1.57849$	Modular form 900.1.bh.a.827.2
2-30e2-300.23-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.23	$0.0$	✓	✓			$-0.122$	$0$	$1.52614$	Modular form 900.1.bh.a.323.2
2-30e2-300.23-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.23	$0.0$	✓	✓			$0.182$	$0$	$1.72699$	Modular form 900.1.bh.a.323.1
2-30e2-300.263-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.263	$0.0$	✓	✓			$0.122$	$0$	$1.13257$	Modular form 900.1.bh.a.863.1
2-30e2-300.263-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.263	$0.0$	✓	✓			$-0.182$	$0$	$1.46904$	Modular form 900.1.bh.a.863.2
2-30e2-300.287-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.287	$0.0$	✓	✓			$-0.182$	$0$	$0.998881$	Modular form 900.1.bh.a.287.1
2-30e2-300.287-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.287	$0.0$	✓	✓			$0.122$	$0$	$2.17929$	Modular form 900.1.bh.a.287.2
2-30e2-300.47-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.47	$0.0$	✓	✓			$-0.387$	$0$	$0.968637$	Modular form 900.1.bh.a.647.2
2-30e2-300.47-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.47	$0.0$	✓	✓			$0.307$	$0$	$1.73339$	Modular form 900.1.bh.a.647.1
2-30e2-300.83-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.83	$0.0$	✓	✓			$-0.307$	$0$	$0.968469$	Modular form 900.1.bh.a.683.1
2-30e2-300.83-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	300.83	$0.0$	✓	✓			$0.387$	$0$	$2.37899$	Modular form 900.1.bh.a.683.2
2-30e2-36.31-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	36.31	$0.0$	✓	✓			$0.0555$	$0$	$1.29540$	Artin representation 2.900.24t65.b.b Modular form 900.1.t.a.751.1
2-30e2-36.31-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	36.31	$0.0$	✓	✓			$0.0555$	$0$	$1.99320$	Artin representation 2.900.24t65.b.d Modular form 900.1.t.a.751.2
2-30e2-36.7-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	36.7	$0.0$	✓	✓			$-0.0555$	$0$	$1.02067$	Artin representation 2.900.24t65.b.a Modular form 900.1.t.a.151.1
2-30e2-36.7-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	36.7	$0.0$	✓	✓			$-0.0555$	$0$	$2.02958$	Artin representation 2.900.24t65.b.c Modular form 900.1.t.a.151.2
2-30e2-4.3-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	4.3	$0.0$	✓	✓	✓	✓	$0$	$0$	$1.24960$	Artin representation 2.900.4t3.a Artin representation 2.900.4t3.a.a Modular form 900.1.c.a Modular form 900.1.c.a.451.1
2-30e2-4.3-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	4.3	$0.0$	✓	✓	✓	✓	$0$	$0$	$1.89925$	Artin representation 2.900.4t3.b Artin representation 2.900.4t3.b.a Modular form 900.1.c.b Modular form 900.1.c.b.451.1
2-30e2-5.2-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	5.2	$0.0$	✓	✓			$-0.104$	$0$	$1.23196$	Modular form 900.1.l.a.757.2
2-30e2-5.2-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	5.2	$0.0$	✓	✓			$0.177$	$0$	$1.87344$	Modular form 900.1.l.a.757.1
2-30e2-5.3-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	5.3	$0.0$	✓	✓			$-0.177$	$0$	$0.913355$	Modular form 900.1.l.a.793.1
2-30e2-5.3-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	5.3	$0.0$	✓	✓			$0.104$	$0$	$1.88259$	Modular form 900.1.l.a.793.2
2-30e2-60.23-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	60.23	$0.0$	✓	✓			$0.0639$	$0$	$1.17460$	Modular form 900.1.m.a.143.1
2-30e2-60.23-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	60.23	$0.0$	✓	✓			$-0.240$	$0$	$1.31908$	Modular form 900.1.m.a.143.2
2-30e2-60.47-c0-0-0	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	60.47	$0.0$	✓	✓			$-0.0639$	$0$	$1.35560$	Modular form 900.1.m.a.107.1
2-30e2-60.47-c0-0-1	$0.670$	$0.449$	$2$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	60.47	$0.0$	✓	✓			$0.240$	$0$	$2.09895$	Modular form 900.1.m.a.107.2

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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.