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 (36 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-3e4-81.13-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.13	$0$	✓	✓	$0.345$	$0$	$3.04450$	Character $\chi_{81}(13, \cdot)$
1-3e4-81.16-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.16	$0$	✓	✓	$0.0987$	$0$	$2.26893$	Character $\chi_{81}(16, \cdot)$
1-3e4-81.22-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.22	$0$	✓	✓	$0.234$	$0$	$2.05450$	Character $\chi_{81}(22, \cdot)$
1-3e4-81.25-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.25	$0$	✓	✓	$-0.345$	$0$	$1.08184$	Character $\chi_{81}(25, \cdot)$
1-3e4-81.31-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.31	$0$	✓	✓	$0.0123$	$0$	$1.14716$	Character $\chi_{81}(31, \cdot)$
1-3e4-81.34-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.34	$0$	✓	✓	$-0.0123$	$0$	$1.60374$	Character $\chi_{81}(34, \cdot)$
1-3e4-81.4-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.4	$0$	✓	✓	$0.0123$	$0$	$2.12652$	Character $\chi_{81}(4, \cdot)$
1-3e4-81.40-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.40	$0$	✓	✓	$0.0123$	$0$	$1.50120$	Character $\chi_{81}(40, \cdot)$
1-3e4-81.43-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.43	$0$	✓	✓	$0.432$	$0$	$2.36489$	Character $\chi_{81}(43, \cdot)$
1-3e4-81.49-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.49	$0$	✓	✓	$-0.432$	$0$	$0.440708$	Character $\chi_{81}(49, \cdot)$
1-3e4-81.52-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.52	$0$	✓	✓	$0.320$	$0$	$2.71521$	Character $\chi_{81}(52, \cdot)$
1-3e4-81.58-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.58	$0$	✓	✓	$0.0123$	$0$	$2.06180$	Character $\chi_{81}(58, \cdot)$
1-3e4-81.61-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.61	$0$	✓	✓	$-0.0123$	$0$	$2.40911$	Character $\chi_{81}(61, \cdot)$
1-3e4-81.67-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.67	$0$	✓	✓	$-0.320$	$0$	$1.27072$	Character $\chi_{81}(67, \cdot)$
1-3e4-81.7-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.7	$0$	✓	✓	$-0.0123$	$0$	$1.13941$	Character $\chi_{81}(7, \cdot)$
1-3e4-81.70-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.70	$0$	✓	✓	$-0.234$	$0$	$1.44794$	Character $\chi_{81}(70, \cdot)$
1-3e4-81.76-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.76	$0$	✓	✓	$-0.0987$	$0$	$1.94565$	Character $\chi_{81}(76, \cdot)$
1-3e4-81.79-r0-0-0	$0.376$	$0.376$	$1$	$3^{4}$	81.79	$0$	✓	✓	$-0.0123$	$0$	$1.54887$	Character $\chi_{81}(79, \cdot)$
1-3e4-81.11-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.11	$1$	✓	✓	$0.0154$	$0$	$0.756780$	Character $\chi_{81}(11, \cdot)$
1-3e4-81.14-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.14	$1$	✓	✓	$0.429$	$0$	$1.87822$	Character $\chi_{81}(14, \cdot)$
1-3e4-81.2-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.2	$1$	✓	✓	$0.237$	$0$	$2.29940$	Character $\chi_{81}(2, \cdot)$
1-3e4-81.20-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.20	$1$	✓	✓	$0.237$	$0$	$1.29471$	Character $\chi_{81}(20, \cdot)$
1-3e4-81.23-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.23	$1$	✓	✓	$-0.237$	$0$	$0.208943$	Character $\chi_{81}(23, \cdot)$
1-3e4-81.29-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.29	$1$	✓	✓	$-0.429$	$0$	$0.661731$	Character $\chi_{81}(29, \cdot)$
1-3e4-81.32-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.32	$1$	✓	✓	$0.317$	$0$	$2.46008$	Character $\chi_{81}(32, \cdot)$
1-3e4-81.38-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.38	$1$	✓	✓	$-0.317$	$0$	$0.999052$	Character $\chi_{81}(38, \cdot)$
1-3e4-81.41-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.41	$1$	✓	✓	$-0.237$	$0$	$0.926066$	Character $\chi_{81}(41, \cdot)$
1-3e4-81.47-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.47	$1$	✓	✓	$0.237$	$0$	$2.00078$	Character $\chi_{81}(47, \cdot)$
1-3e4-81.5-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.5	$1$	✓	✓	$-0.348$	$0$	$0.386329$	Character $\chi_{81}(5, \cdot)$
1-3e4-81.50-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.50	$1$	✓	✓	$-0.237$	$0$	$1.32328$	Character $\chi_{81}(50, \cdot)$
1-3e4-81.56-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.56	$1$	✓	✓	$-0.0956$	$0$	$0.616840$	Character $\chi_{81}(56, \cdot)$
1-3e4-81.59-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.59	$1$	✓	✓	$-0.0154$	$0$	$1.36647$	Character $\chi_{81}(59, \cdot)$
1-3e4-81.65-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.65	$1$	✓	✓	$0.348$	$0$	$2.08026$	Character $\chi_{81}(65, \cdot)$
1-3e4-81.68-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.68	$1$	✓	✓	$0.0956$	$0$	$1.57357$	Character $\chi_{81}(68, \cdot)$
1-3e4-81.74-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.74	$1$	✓	✓	$0.237$	$0$	$1.98700$	Character $\chi_{81}(74, \cdot)$
1-3e4-81.77-r1-0-0	$8.70$	$8.70$	$1$	$3^{4}$	81.77	$1$	✓	✓	$-0.237$	$0$	$0.460445$	Character $\chi_{81}(77, \cdot)$

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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.