LMFDB - L-function search results

Refine search

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

		Sort order	Select

Results (1-50 of 144 matches)

Next Download displayed columns for results to

Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2028-2028.1031-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1031	$0$	✓	✓	$-0.0828$	$0$	$0.747792$	Character $\chi_{2028}(1031, \cdot)$
1-2028-2028.1043-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1043	$0$	✓	✓	$-0.155$	$0$	$0.770729$	Character $\chi_{2028}(1043, \cdot)$
1-2028-2028.1067-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1067	$0$	✓	✓	$-0.0828$	$0$	$0.591043$	Character $\chi_{2028}(1067, \cdot)$
1-2028-2028.107-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.107	$0$	✓	✓	$0.238$	$0$	$1.30318$	Character $\chi_{2028}(107, \cdot)$
1-2028-2028.1091-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1091	$0$	✓	✓	$-0.298$	$0$	$0.431092$	Character $\chi_{2028}(1091, \cdot)$
1-2028-2028.1115-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1115	$0$	✓	✓	$-0.407$	$0$	$0.0902382$	Character $\chi_{2028}(1115, \cdot)$
1-2028-2028.1127-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1127	$0$	✓	✓	$0.0394$	$0$	$0.588092$	Character $\chi_{2028}(1127, \cdot)$
1-2028-2028.1187-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1187	$0$	✓	✓	$-0.298$	$0$	$0.378723$	Character $\chi_{2028}(1187, \cdot)$
1-2028-2028.1199-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1199	$0$	✓	✓	$0.428$	$0$	$1.37986$	Character $\chi_{2028}(1199, \cdot)$
1-2028-2028.1223-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1223	$0$	✓	✓	$-0.177$	$0$	$0.549347$	Character $\chi_{2028}(1223, \cdot)$
1-2028-2028.1247-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1247	$0$	✓	✓	$-0.127$	$0$	$0.930082$	Character $\chi_{2028}(1247, \cdot)$
1-2028-2028.1271-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1271	$0$	✓	✓	$-0.298$	$0$	$0.340124$	Character $\chi_{2028}(1271, \cdot)$
1-2028-2028.1283-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1283	$0$	✓	✓	$0.293$	$0$	$1.22052$	Character $\chi_{2028}(1283, \cdot)$
1-2028-2028.131-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.131	$0$	✓	✓	$0.177$	$0$	$1.19613$	Character $\chi_{2028}(131, \cdot)$
1-2028-2028.1343-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1343	$0$	✓	✓	$-0.489$	$0$	$1.64993$	Character $\chi_{2028}(1343, \cdot)$
1-2028-2028.1355-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1355	$0$	✓	✓	$-0.0394$	$0$	$0.712224$	Character $\chi_{2028}(1355, \cdot)$
1-2028-2028.1379-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1379	$0$	✓	✓	$-0.426$	$0$	$0.303428$	Character $\chi_{2028}(1379, \cdot)$
1-2028-2028.1403-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1403	$0$	✓	✓	$0.0828$	$0$	$1.02918$	Character $\chi_{2028}(1403, \cdot)$
1-2028-2028.1427-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1427	$0$	✓	✓	$0.489$	$0$	$0.242563$	Character $\chi_{2028}(1427, \cdot)$
1-2028-2028.1439-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1439	$0$	✓	✓	$-0.0927$	$0$	$0.847181$	Character $\chi_{2028}(1439, \cdot)$
1-2028-2028.1511-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1511	$0$	✓	✓	$0.0828$	$0$	$1.07199$	Character $\chi_{2028}(1511, \cdot)$
1-2028-2028.1535-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1535	$0$	✓	✓	$0.0946$	$0$	$0.811762$	Character $\chi_{2028}(1535, \cdot)$
1-2028-2028.155-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.155	$0$	✓	✓	$0.0946$	$0$	$0.962123$	Character $\chi_{2028}(155, \cdot)$
1-2028-2028.1559-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1559	$0$	✓	✓	$0.177$	$0$	$0.923377$	Character $\chi_{2028}(1559, \cdot)$
1-2028-2028.1583-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1583	$0$	✓	✓	$0.238$	$0$	$0.991426$	Character $\chi_{2028}(1583, \cdot)$
1-2028-2028.1595-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1595	$0$	✓	✓	$-0.428$	$0$	$0.0700021$	Character $\chi_{2028}(1595, \cdot)$
1-2028-2028.1655-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1655	$0$	✓	✓	$0.155$	$0$	$0.988490$	Character $\chi_{2028}(1655, \cdot)$
1-2028-2028.1715-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1715	$0$	✓	✓	$-0.0739$	$0$	$0.831592$	Character $\chi_{2028}(1715, \cdot)$
1-2028-2028.1739-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1739	$0$	✓	✓	$0.206$	$0$	$1.13882$	Character $\chi_{2028}(1739, \cdot)$
1-2028-2028.1751-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1751	$0$	✓	✓	$0.0828$	$0$	$0.573401$	Character $\chi_{2028}(1751, \cdot)$
1-2028-2028.179-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.179	$0$	✓	✓	$0.0828$	$0$	$0.848983$	Character $\chi_{2028}(179, \cdot)$
1-2028-2028.1811-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1811	$0$	✓	✓	$0.298$	$0$	$1.15727$	Character $\chi_{2028}(1811, \cdot)$
1-2028-2028.1823-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1823	$0$	✓	✓	$-0.0828$	$0$	$0.306817$	Character $\chi_{2028}(1823, \cdot)$
1-2028-2028.1847-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1847	$0$	✓	✓	$-0.0946$	$0$	$0.380519$	Character $\chi_{2028}(1847, \cdot)$
1-2028-2028.1871-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1871	$0$	✓	✓	$-0.0946$	$0$	$0.904662$	Character $\chi_{2028}(1871, \cdot)$
1-2028-2028.1895-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1895	$0$	✓	✓	$-0.0828$	$0$	$0.906257$	Character $\chi_{2028}(1895, \cdot)$
1-2028-2028.1907-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1907	$0$	✓	✓	$-0.201$	$0$	$0.477224$	Character $\chi_{2028}(1907, \cdot)$
1-2028-2028.1967-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1967	$0$	✓	✓	$0.0828$	$0$	$1.11502$	Character $\chi_{2028}(1967, \cdot)$
1-2028-2028.1979-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.1979	$0$	✓	✓	$-0.293$	$0$	$0.352403$	Character $\chi_{2028}(1979, \cdot)$
1-2028-2028.2003-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.2003	$0$	✓	✓	$0.426$	$0$	$1.53264$	Character $\chi_{2028}(2003, \cdot)$
1-2028-2028.251-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.251	$0$	✓	✓	$0.407$	$0$	$1.03829$	Character $\chi_{2028}(251, \cdot)$
1-2028-2028.263-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.263	$0$	✓	✓	$0.489$	$0$	$1.60876$	Character $\chi_{2028}(263, \cdot)$
1-2028-2028.287-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.287	$0$	✓	✓	$0.0828$	$0$	$0.835000$	Character $\chi_{2028}(287, \cdot)$
1-2028-2028.311-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.311	$0$	✓	✓	$0.0739$	$0$	$0.830338$	Character $\chi_{2028}(311, \cdot)$
1-2028-2028.335-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.335	$0$	✓	✓	$0.460$	$0$	$1.70774$	Character $\chi_{2028}(335, \cdot)$
1-2028-2028.347-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.347	$0$	✓	✓	$-0.489$	$0$	$0.359633$	Character $\chi_{2028}(347, \cdot)$
1-2028-2028.35-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.35	$0$	✓	✓	$0.155$	$0$	$1.06097$	Character $\chi_{2028}(35, \cdot)$
1-2028-2028.407-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.407	$0$	✓	✓	$-0.206$	$0$	$0.466845$	Character $\chi_{2028}(407, \cdot)$
1-2028-2028.419-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.419	$0$	✓	✓	$0.201$	$0$	$1.06816$	Character $\chi_{2028}(419, \cdot)$
1-2028-2028.443-r0-0-0	$9.41$	$9.41$	$1$	$2^{2} \cdot 3 \cdot 13^{2}$	2028.443	$0$	✓	✓	$0.372$	$0$	$1.27797$	Character $\chi_{2028}(443, \cdot)$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 144 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.