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 at least 1000)

Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	$\nu$	$w$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
2-855-285.113-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.113	$$	$0.0$	$0$	✓	✓	$-0.384$	$0$	$0.590149$	Modular form 855.1.m.a.683.1
2-855-285.113-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.113	$$	$0.0$	$0$	✓	✓	$-0.188$	$0$	$1.04879$	Modular form 855.1.m.a.683.2
2-855-285.113-c0-0-2	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.113	$$	$0.0$	$0$	✓	✓	$-0.134$	$0$	$1.44833$	Modular form 855.1.m.b.683.2
2-855-285.113-c0-0-3	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.113	$$	$0.0$	$0$	✓	✓	$0.0610$	$0$	$1.68239$	Modular form 855.1.m.b.683.1
2-855-285.227-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.227	$$	$0.0$	$0$	✓	✓	$-0.0610$	$0$	$1.18520$	Modular form 855.1.m.b.512.1
2-855-285.227-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.227	$$	$0.0$	$0$	✓	✓	$0.134$	$0$	$1.99465$	Modular form 855.1.m.b.512.2
2-855-285.227-c0-0-2	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.227	$$	$0.0$	$0$	✓	✓	$0.188$	$0$	$2.07441$	Modular form 855.1.m.a.512.2
2-855-285.227-c0-0-3	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.227	$$	$0.0$	$0$	✓	✓	$0.384$	$0$	$2.56780$	Modular form 855.1.m.a.512.1
2-855-285.239-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.239	$$	$0.0$	$0$	✓	✓	$-0.477$	$0$	$0.894409$	Modular form 855.1.u.a.809.2
2-855-285.239-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.239	$$	$0.0$	$0$	✓	✓	$0.0765$	$0$	$1.71119$	Modular form 855.1.u.a.809.1
2-855-285.239-c0-0-2	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.239	$$	$0.0$	$0$	✓	✓	$0.326$	$0$	$2.19635$	Modular form 855.1.u.a.809.3
2-855-285.239-c0-0-3	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.239	$$	$0.0$	$0$	✓	✓	$0.272$	$0$	$2.21657$	Modular form 855.1.u.a.809.4
2-855-285.254-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.254	$$	$0.0$	$0$	✓	✓	$-0.0765$	$0$	$0.461237$	Modular form 855.1.u.a.539.1
2-855-285.254-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.254	$$	$0.0$	$0$	✓	✓	$-0.326$	$0$	$1.33352$	Modular form 855.1.u.a.539.3
2-855-285.254-c0-0-2	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.254	$$	$0.0$	$0$	✓	✓	$-0.272$	$0$	$1.75626$	Modular form 855.1.u.a.539.4
2-855-285.254-c0-0-3	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	285.254	$$	$0.0$	$0$	✓	✓	$0.477$	$0$	$2.18249$	Modular form 855.1.u.a.539.2
2-855-855.664-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.664	$$	$0.0$	$0$	✓	✓	$0.361$	$0$	$0.508674$	Modular form 855.1.z.d.664.1
2-855-855.664-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.664	$$	$0.0$	$0$	✓	✓	$-0.388$	$0$	$1.00250$	Modular form 855.1.z.c.664.1
2-855-855.664-c0-0-2	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.664	$$	$0.0$	$0$	✓	✓	$-0.138$	$0$	$1.20709$	Modular form 855.1.z.d.664.2
2-855-855.664-c0-0-3	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.664	$$	$0.0$	$0$	✓	✓	$0.111$	$0$	$1.58946$	Artin representation 2.855.6t5.b.b Modular form 855.1.z.b.664.1
2-855-855.664-c0-0-4	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.664	$$	$0.0$	$0$	✓	✓	$-0.138$	$0$	$1.71910$	Modular form 855.1.z.d.664.3
2-855-855.664-c0-0-5	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.664	$$	$0.0$	$0$	✓	✓	$0.111$	$0$	$1.97736$	Artin representation 2.855.12t18.b.a Modular form 855.1.z.a.664.1
2-855-855.664-c0-0-6	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.664	$$	$0.0$	$0$	✓	✓	$0.361$	$0$	$2.62117$	Modular form 855.1.z.d.664.4
2-855-855.664-c0-0-7	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.664	$$	$0.0$	$0$	✓	✓	$-0.388$	$0$	$3.06549$	Modular form 855.1.z.c.664.2
2-855-855.94-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.94	$$	$0.0$	$0$	✓	✓	$0.388$	$0$	$0.767867$	Modular form 855.1.z.c.94.2
2-855-855.94-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.94	$$	$0.0$	$0$	✓	✓	$-0.111$	$0$	$0.910952$	Artin representation 2.855.12t18.b.b Modular form 855.1.z.a.94.1
2-855-855.94-c0-0-2	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.94	$$	$0.0$	$0$	✓	✓	$-0.111$	$0$	$1.35611$	Artin representation 2.855.6t5.b.a Modular form 855.1.z.b.94.1
2-855-855.94-c0-0-3	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.94	$$	$0.0$	$0$	✓	✓	$0.388$	$0$	$1.70010$	Modular form 855.1.z.c.94.1
2-855-855.94-c0-0-4	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.94	$$	$0.0$	$0$	✓	✓	$0.138$	$0$	$1.75394$	Modular form 855.1.z.d.94.2
2-855-855.94-c0-0-5	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.94	$$	$0.0$	$0$	✓	✓	$-0.361$	$0$	$1.86071$	Modular form 855.1.z.d.94.1
2-855-855.94-c0-0-6	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.94	$$	$0.0$	$0$	✓	✓	$-0.361$	$0$	$1.91171$	Modular form 855.1.z.d.94.4
2-855-855.94-c0-0-7	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	855.94	$$	$0.0$	$0$	✓	✓	$0.138$	$0$	$2.33037$	Modular form 855.1.z.d.94.3
2-855-95.14-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.14	$$	$0.0$	$0$	✓	✓	$-0.380$	$0$	$0.547214$	Modular form 855.1.cw.a.109.1
2-855-95.14-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.14	$$	$0.0$	$0$	✓	✓	$0.119$	$0$	$2.13968$	Modular form 855.1.cw.a.109.2
2-855-95.29-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.29	$$	$0.0$	$0$	✓	✓	$-0.225$	$0$	$1.30194$	Modular form 855.1.cw.a.694.2
2-855-95.29-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.29	$$	$0.0$	$0$	✓	✓	$0.274$	$0$	$2.22359$	Modular form 855.1.cw.a.694.1
2-855-95.34-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.34	$$	$0.0$	$0$	✓	✓	$0.380$	$0$	$1.69367$	Modular form 855.1.cw.a.604.1
2-855-95.34-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.34	$$	$0.0$	$0$	✓	✓	$-0.119$	$0$	$1.75334$	Modular form 855.1.cw.a.604.2
2-855-95.59-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.59	$$	$0.0$	$0$	✓	✓	$-0.274$	$0$	$1.27569$	Modular form 855.1.cw.a.154.1
2-855-95.59-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.59	$$	$0.0$	$0$	✓	✓	$0.225$	$0$	$2.03219$	Modular form 855.1.cw.a.154.2
2-855-95.68-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.68	$$	$0.0$	$0$	✓	✓	$-0.154$	$0$	$1.81053$	Modular form 855.1.ck.a.163.2
2-855-95.68-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.68	$$	$0.0$	$0$	✓	✓	$0.345$	$0$	$1.87486$	Modular form 855.1.ck.a.163.1
2-855-95.69-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.69	$$	$0.0$	$0$	✓	✓	$0.182$	$0$	$0.962928$	Modular form 855.1.v.a.829.1
2-855-95.69-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.69	$$	$0.0$	$0$	✓	✓	$-0.317$	$0$	$1.60445$	Modular form 855.1.v.a.829.2
2-855-95.7-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.7	$$	$0.0$	$0$	✓	✓	$-0.345$	$0$	$0.906812$	Modular form 855.1.ck.a.577.1
2-855-95.7-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.7	$$	$0.0$	$0$	✓	✓	$0.154$	$0$	$1.81845$	Modular form 855.1.ck.a.577.2
2-855-95.79-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.79	$$	$0.0$	$0$	✓	✓	$0.138$	$0$	$1.18157$	Modular form 855.1.cw.a.649.1
2-855-95.79-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.79	$$	$0.0$	$0$	✓	✓	$-0.361$	$0$	$1.38831$	Modular form 855.1.cw.a.649.2
2-855-95.83-c0-0-0	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.83	$$	$0.0$	$0$	✓	✓	$-0.419$	$0$	$0.168448$	Modular form 855.1.ck.a.748.1
2-855-95.83-c0-0-1	$0.653$	$0.426$	$2$	$3^{2} \cdot 5 \cdot 19$	95.83	$$	$0.0$	$0$	✓	✓	$0.0803$	$0$	$2.11410$	Modular form 855.1.ck.a.748.2

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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.