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 54 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-980-980.103-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.103	$1$	✓	✓	$0.110$	$0$	$0.844115$	Character $\chi_{980}(103, \cdot)$
1-980-980.143-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.143	$1$	✓	✓	$-0.246$	$0$	$0.352917$	Character $\chi_{980}(143, \cdot)$
1-980-980.167-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.167	$1$	✓	✓	$-0.0802$	$0$	$0.277551$	Character $\chi_{980}(167, \cdot)$
1-980-980.179-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.179	$1$	✓	✓	$-0.248$	$0$	$0.235356$	Character $\chi_{980}(179, \cdot)$
1-980-980.187-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.187	$1$	✓	✓	$-0.0258$	$0$	$0.834262$	Character $\chi_{980}(187, \cdot)$
1-980-980.219-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.219	$1$	✓	✓	$0.248$	$0$	$1.23012$	Character $\chi_{980}(219, \cdot)$
1-980-980.223-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.223	$1$	✓	✓	$0.0802$	$0$	$0.769999$	Character $\chi_{980}(223, \cdot)$
1-980-980.239-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.239	$1$	✓	✓	$-0.448$	$0$	$1.65689$	Character $\chi_{980}(239, \cdot)$
1-980-980.243-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.243	$1$	✓	✓	$0.359$	$0$	$1.43797$	Character $\chi_{980}(243, \cdot)$
1-980-980.27-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.27	$1$	✓	✓	$0.256$	$0$	$0.794615$	Character $\chi_{980}(27, \cdot)$
1-980-980.283-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.283	$1$	✓	✓	$0.0258$	$0$	$0.526861$	Character $\chi_{980}(283, \cdot)$
1-980-980.3-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.3	$1$	✓	✓	$0.110$	$0$	$0.873045$	Character $\chi_{980}(3, \cdot)$
1-980-980.307-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.307	$1$	✓	✓	$-0.131$	$0$	$0.637465$	Character $\chi_{980}(307, \cdot)$
1-980-980.319-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.319	$1$	✓	✓	$-0.197$	$0$	$0.359124$	Character $\chi_{980}(319, \cdot)$
1-980-980.327-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.327	$1$	✓	✓	$-0.110$	$0$	$0.275499$	Character $\chi_{980}(327, \cdot)$
1-980-980.359-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.359	$1$	✓	✓	$-0.448$	$0$	$1.19419$	Character $\chi_{980}(359, \cdot)$
1-980-980.363-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.363	$1$	✓	✓	$-0.256$	$0$	$0.540156$	Character $\chi_{980}(363, \cdot)$
1-980-980.367-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.367	$1$	✓	✓	$-0.359$	$0$	$0.0976623$	Character $\chi_{980}(367, \cdot)$
1-980-980.379-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.379	$1$	✓	✓	$-0.469$	$0$	$1.13508$	Character $\chi_{980}(379, \cdot)$
1-980-980.383-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.383	$1$	✓	✓	$-0.202$	$0$	$1.70230$	Character $\chi_{980}(383, \cdot)$
1-980-980.39-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.39	$1$	✓	✓	$-0.448$	$0$	$0.387410$	Character $\chi_{980}(39, \cdot)$
1-980-980.447-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.447	$1$	✓	✓	$-0.110$	$0$	$0.761408$	Character $\chi_{980}(447, \cdot)$
1-980-980.467-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.467	$1$	✓	✓	$-0.410$	$0$	$0.224840$	Character $\chi_{980}(467, \cdot)$
1-980-980.47-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.47	$1$	✓	✓	$-0.464$	$0$	$1.13981$	Character $\chi_{980}(47, \cdot)$
1-980-980.499-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.499	$1$	✓	✓	$0.136$	$0$	$0.981511$	Character $\chi_{980}(499, \cdot)$
1-980-980.503-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.503	$1$	✓	✓	$-0.307$	$0$	$0.234453$	Character $\chi_{980}(503, \cdot)$
1-980-980.507-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.507	$1$	✓	✓	$-0.413$	$0$	$0.275190$	Character $\chi_{980}(507, \cdot)$
1-980-980.519-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.519	$1$	✓	✓	$0.0816$	$0$	$0.474604$	Character $\chi_{980}(519, \cdot)$
1-980-980.523-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.523	$1$	✓	✓	$-0.287$	$0$	$0.370967$	Character $\chi_{980}(523, \cdot)$
1-980-980.563-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.563	$1$	✓	✓	$0.464$	$0$	$0.138692$	Character $\chi_{980}(563, \cdot)$
1-980-980.599-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.599	$1$	✓	✓	$-0.136$	$0$	$0.726269$	Character $\chi_{980}(599, \cdot)$
1-980-980.639-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.639	$1$	✓	✓	$0.197$	$0$	$1.00888$	Character $\chi_{980}(639, \cdot)$
1-980-980.643-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.643	$1$	✓	✓	$-0.287$	$0$	$0.0642577$	Character $\chi_{980}(643, \cdot)$
1-980-980.647-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.647	$1$	✓	✓	$-0.110$	$0$	$0.776409$	Character $\chi_{980}(647, \cdot)$
1-980-980.659-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.659	$1$	✓	✓	$-0.0816$	$0$	$0.368172$	Character $\chi_{980}(659, \cdot)$
1-980-980.663-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.663	$1$	✓	✓	$0.413$	$0$	$1.15465$	Character $\chi_{980}(663, \cdot)$
1-980-980.703-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.703	$1$	✓	✓	$0.410$	$0$	$0.932661$	Character $\chi_{980}(703, \cdot)$
1-980-980.727-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.727	$1$	✓	✓	$0.287$	$0$	$0.883537$	Character $\chi_{980}(727, \cdot)$
1-980-980.739-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.739	$1$	✓	✓	$-0.414$	$0$	$1.39978$	Character $\chi_{980}(739, \cdot)$
1-980-980.747-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.747	$1$	✓	✓	$0.246$	$0$	$0.953428$	Character $\chi_{980}(747, \cdot)$
1-980-980.779-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.779	$1$	✓	✓	$0.448$	$0$	$1.30356$	Character $\chi_{980}(779, \cdot)$
1-980-980.787-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.787	$1$	✓	✓	$0.287$	$0$	$0.738226$	Character $\chi_{980}(787, \cdot)$
1-980-980.799-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.799	$1$	✓	✓	$0.469$	$0$	$0.0657169$	Character $\chi_{980}(799, \cdot)$
1-980-980.83-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.83	$1$	✓	✓	$0.131$	$0$	$1.16176$	Character $\chi_{980}(83, \cdot)$
1-980-980.843-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.843	$1$	✓	✓	$-0.287$	$0$	$0.269484$	Character $\chi_{980}(843, \cdot)$
1-980-980.867-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.867	$1$	✓	✓	$0.307$	$0$	$0.893744$	Character $\chi_{980}(867, \cdot)$
1-980-980.87-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.87	$1$	✓	✓	$0.202$	$0$	$0.0399547$	Character $\chi_{980}(87, \cdot)$
1-980-980.879-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.879	$1$	✓	✓	$0.448$	$0$	$0.0598798$	Character $\chi_{980}(879, \cdot)$
1-980-980.887-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.887	$1$	✓	✓	$0.287$	$0$	$1.31453$	Character $\chi_{980}(887, \cdot)$
1-980-980.919-r1-0-0	$105.$	$105.$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.919	$1$	✓	✓	$0.414$	$0$	$0.180890$	Character $\chi_{980}(919, \cdot)$

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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.