LMFDB - Rational L-function search results

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Results (1-50 of 13940 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\nu$	$w$	$\epsilon$	$r$	First zero	Origin
16-244e8-1.1-c0e8-0-0	$0.348$	$4.83\times 10^{-8}$	$16$	$2^{16} \cdot 61^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.09615$	Modular form 244.1.u.a
16-255e8-1.1-c0e8-0-0	$0.356$	$6.87\times 10^{-8}$	$16$	$3^{8} \cdot 5^{8} \cdot 17^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.37970$	Modular form 255.1.y.a
16-291e8-1.1-c0e8-0-0	$0.381$	$1.97\times 10^{-7}$	$16$	$3^{8} \cdot 97^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.14316$	Modular form 291.1.o.a
16-325e8-1.1-c0e8-0-0	$0.402$	$4.78\times 10^{-7}$	$16$	$5^{16} \cdot 13^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.01143$	Artin representation 2.325.32t402.a Modular form 325.1.u.a
16-328e8-1.1-c0e8-0-0	$0.404$	$5.15\times 10^{-7}$	$16$	$2^{24} \cdot 41^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.06807$	Modular form 328.1.z.a
16-329e8-1.1-c0e8-0-0	$0.405$	$5.28\times 10^{-7}$	$16$	$7^{8} \cdot 47^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.47036$	Modular form 329.1.f.b
16-340e8-1.1-c0e8-0-0	$0.411$	$6.87\times 10^{-7}$	$16$	$2^{16} \cdot 5^{8} \cdot 17^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.19241$	Modular form 340.1.bc.a
16-340e8-1.1-c0e8-0-1	$0.411$	$6.87\times 10^{-7}$	$16$	$2^{16} \cdot 5^{8} \cdot 17^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.33767$	Modular form 340.1.bj.a
16-341e8-1.1-c0e8-0-0	$0.412$	$7.03\times 10^{-7}$	$16$	$11^{8} \cdot 31^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.14148$	Modular form 341.1.by.a
16-372e8-1.1-c0e8-0-0	$0.430$	$1.41\times 10^{-6}$	$16$	$2^{16} \cdot 3^{8} \cdot 31^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.40585$	Modular form 372.1.be.a
16-383e8-1.1-c0e8-0-0	$0.437$	$1.78\times 10^{-6}$	$16$	$383^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.904508$	Modular form 383.1.b.a
16-388e8-1.1-c0e8-0-0	$0.440$	$1.97\times 10^{-6}$	$16$	$2^{16} \cdot 97^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.30726$	Modular form 388.1.r.a
16-5e16-1.1-c1e8-0-0	$0.446$	$2.52\times 10^{-6}$	$16$	$5^{16}$	1.1	$[1.0]^{8}$	$1$	$1$	$0$	$2.48425$	Modular form 25.2.e.a
16-408e8-1.1-c0e8-0-0	$0.451$	$2.95\times 10^{-6}$	$16$	$2^{24} \cdot 3^{8} \cdot 17^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.995234$	Modular form 408.1.bg.a
16-408e8-1.1-c0e8-0-1	$0.451$	$2.95\times 10^{-6}$	$16$	$2^{24} \cdot 3^{8} \cdot 17^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.11338$	Modular form 408.1.bg.b
16-423e8-1.1-c0e8-0-0	$0.459$	$3.94\times 10^{-6}$	$16$	$3^{16} \cdot 47^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.829276$	Modular form 423.1.f.b
16-429e8-1.1-c0e8-0-0	$0.462$	$4.41\times 10^{-6}$	$16$	$3^{8} \cdot 11^{8} \cdot 13^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.20107$	Modular form 429.1.v.c
16-448e8-1.1-c0e8-0-0	$0.472$	$6.24\times 10^{-6}$	$16$	$2^{48} \cdot 7^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.12583$	Modular form 448.1.bf.a
16-465e8-1.1-c0e8-0-0	$0.481$	$8.41\times 10^{-6}$	$16$	$3^{8} \cdot 5^{8} \cdot 31^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.819544$	Modular form 465.1.bl.b
16-465e8-1.1-c0e8-0-1	$0.481$	$8.41\times 10^{-6}$	$16$	$3^{8} \cdot 5^{8} \cdot 31^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.979127$	Modular form 465.1.bl.a
16-468e8-1.1-c0e8-0-0	$0.483$	$8.85\times 10^{-6}$	$16$	$2^{16} \cdot 3^{16} \cdot 13^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.841174$	Modular form 468.1.bx.a
16-480e8-1.1-c0e8-0-0	$0.489$	$1.08\times 10^{-5}$	$16$	$2^{40} \cdot 3^{8} \cdot 5^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.947679$	Modular form 480.1.bu.a
16-500e8-1.1-c0e8-0-0	$0.499$	$1.50\times 10^{-5}$	$16$	$2^{16} \cdot 5^{24}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.27399$	Modular form 500.1.h.a
16-2e40-1.1-c1e8-0-0	$0.505$	$1.81\times 10^{-5}$	$16$	$2^{40}$	1.1	$[1.0]^{8}$	$1$	$1$	$0$	$1.96593$	Modular form 32.2.g.b
16-525e8-1.1-c0e8-0-0	$0.511$	$2.22\times 10^{-5}$	$16$	$3^{8} \cdot 5^{16} \cdot 7^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.957285$	Modular form 525.1.be.a
16-33e8-1.1-c1e8-0-0	$0.513$	$2.32\times 10^{-5}$	$16$	$3^{8} \cdot 11^{8}$	1.1	$[1.0]^{8}$	$1$	$1$	$0$	$2.19885$	Modular form 33.2.f.a
16-539e8-1.1-c0e8-0-0	$0.518$	$2.74\times 10^{-5}$	$16$	$7^{16} \cdot 11^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.904180$	Modular form 539.1.t.a
16-539e8-1.1-c0e8-0-1	$0.518$	$2.74\times 10^{-5}$	$16$	$7^{16} \cdot 11^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.27703$	Modular form 539.1.u.a
16-543e8-1.1-c0e8-0-0	$0.520$	$2.90\times 10^{-5}$	$16$	$3^{8} \cdot 181^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.382417$	Modular form 543.1.y.a
16-543e8-1.1-c0e8-0-1	$0.520$	$2.90\times 10^{-5}$	$16$	$3^{8} \cdot 181^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.888284$	Modular form 543.1.z.a
16-544e8-1.1-c0e8-0-0	$0.521$	$2.95\times 10^{-5}$	$16$	$2^{40} \cdot 17^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.781145$	Modular form 544.1.cd.a
16-549e8-1.1-c0e8-0-0	$0.523$	$3.17\times 10^{-5}$	$16$	$3^{16} \cdot 61^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.776987$	Modular form 549.1.bn.a
16-555e8-1.1-c0e8-0-0	$0.526$	$3.46\times 10^{-5}$	$16$	$3^{8} \cdot 5^{8} \cdot 37^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.653143$	Modular form 555.1.b.a
16-6e16-1.1-c1e8-0-0	$0.536$	$4.66\times 10^{-5}$	$16$	$2^{16} \cdot 3^{16}$	1.1	$[1.0]^{8}$	$1$	$1$	$0$	$2.12226$	Modular form 36.2.h.a
16-579e8-1.1-c0e8-0-0	$0.537$	$4.86\times 10^{-5}$	$16$	$3^{8} \cdot 193^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$1.29135$	Modular form 579.1.o.a
16-585e8-1.1-c0e8-0-0	$0.540$	$5.27\times 10^{-5}$	$16$	$3^{16} \cdot 5^{8} \cdot 13^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.762636$	Modular form 585.1.o.a
16-595e8-1.1-c0e8-0-0	$0.544$	$6.04\times 10^{-5}$	$16$	$5^{8} \cdot 7^{8} \cdot 17^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.688905$	Modular form 595.1.be.a
16-595e8-1.1-c0e8-0-1	$0.544$	$6.04\times 10^{-5}$	$16$	$5^{8} \cdot 7^{8} \cdot 17^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.910485$	Modular form 595.1.b.b
16-600e8-1.1-c0e8-0-0	$0.547$	$6.46\times 10^{-5}$	$16$	$2^{24} \cdot 3^{8} \cdot 5^{16}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.794170$	Modular form 600.1.q.b
16-600e8-1.1-c0e8-0-1	$0.547$	$6.46\times 10^{-5}$	$16$	$2^{24} \cdot 3^{8} \cdot 5^{16}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.923675$	Modular form 600.1.z.a
16-605e8-1.1-c0e8-0-0	$0.549$	$6.90\times 10^{-5}$	$16$	$5^{8} \cdot 11^{16}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.631731$	Modular form 605.1.l.a
16-612e8-1.1-c0e8-0-0	$0.552$	$7.57\times 10^{-5}$	$16$	$2^{16} \cdot 3^{16} \cdot 17^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.565189$	Modular form 612.1.bf.a
16-612e8-1.1-c0e8-0-1	$0.552$	$7.57\times 10^{-5}$	$16$	$2^{16} \cdot 3^{16} \cdot 17^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.990123$	Modular form 612.1.bf.b
16-624e8-1.1-c0e8-0-0	$0.558$	$8.84\times 10^{-5}$	$16$	$2^{32} \cdot 3^{8} \cdot 13^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.567998$	Modular form 624.1.bi.a
16-39e8-1.1-c1e8-0-0	$0.558$	$8.84\times 10^{-5}$	$16$	$3^{8} \cdot 13^{8}$	1.1	$[1.0]^{8}$	$1$	$1$	$0$	$1.84816$	Modular form 39.2.k.b
16-633e8-1.1-c0e8-0-0	$0.562$	$9.91\times 10^{-5}$	$16$	$3^{8} \cdot 211^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.152091$	Modular form 633.1.m.b
16-40e8-1.1-c1e8-0-0	$0.565$	$0.000108$	$16$	$2^{24} \cdot 5^{8}$	1.1	$[1.0]^{8}$	$1$	$1$	$0$	$1.77368$	Modular form 40.2.k.a
16-651e8-1.1-c0e8-0-0	$0.569$	$0.000124$	$16$	$3^{8} \cdot 7^{8} \cdot 31^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.352564$	Modular form 651.1.co.a
16-651e8-1.1-c0e8-0-1	$0.569$	$0.000124$	$16$	$3^{8} \cdot 7^{8} \cdot 31^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.456629$	Modular form 651.1.ck.a
16-651e8-1.1-c0e8-0-2	$0.569$	$0.000124$	$16$	$3^{8} \cdot 7^{8} \cdot 31^{8}$	1.1	$[0.0]^{8}$	0	$1$	$0$	$0.923737$	Modular form 651.1.ch.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.