⌂
→
L-functions
→
Rational
→
4
→
855^2
→
1.1
→
c2e2-0
Citation
·
Feedback
·
Hide Menu
Rational L-function search results
Introduction
Overview
Random
Universe
Knowledge
L-functions
Rational
All
Modular forms
Classical
Maass
Hilbert
Bianchi
Varieties
Elliptic curves over
Q
\Q
Q
Elliptic curves over
Q
(
α
)
\Q(\alpha)
Q
(
α
)
Genus 2 curves over
Q
\Q
Q
Higher genus families
Abelian varieties over
F
q
\F_{q}
F
q
Belyi maps
Fields
Number fields
p
p
p
-adic fields
Representations
Dirichlet characters
Artin representations
Groups
Galois groups
Sato-Tate groups
Abstract groups
Database
↑
Learn more
Source and acknowledgments
Completeness of the data
Reliability of the data
L-function labels
ζ
\zeta
ζ
zeros
Refine search
Lowest zero
Conductor
Analytic conductor
Central character
Analytic rank
Degree
Bad
p
p
p
include
exclude
exactly
subset
Root analytic conductor
Motivic weight
Spectral label
Root number
Primitive
Origin
Exclude origin
1
-1
yes
no
Dirichlet character
Artin representation
Elliptic curve/Q
Elliptic curve/NF
Genus 2 curve/Q
Classical modular form
Hilbert modular form
Bianchi modular form
GL3 Maass form
GL4 Maass form
GSp4 Maass form
Dirichlet character
Artin representation
Elliptic curve/Q
Elliptic curve/NF
Genus 2 curve/Q
Classical modular form
Hilbert modular form
Bianchi modular form
GL3 Maass form
GL4 Maass form
GSp4 Maass form
Sort order
Select
Search again
Traces table
Euler factors
Random L-function
▲ root analytic conductor
analytic conductor
first zero
conductor
columns to display
✓ label
✓ root analytic conductor
✓ analytic conductor
✓ degree
✓ conductor
✓ central character
✓ mu
✓ nu
✓ motivic weight
✓ primitive
✓ root number
✓ order of vanishing
✓ first zero
✓ origin
hide all
Results (unique match)
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
Label
α
\alpha
α
A
A
A
d
d
d
N
N
N
χ
\chi
χ
μ
\mu
μ
ν
\nu
ν
w
w
w
prim
ϵ
\epsilon
ϵ
r
r
r
First zero
Origin
4-855e2-1.1-c2e2-0-0
4.82
4.82
4
.
8
2
542.
542.
5
4
2
.
4
4
4
3
4
⋅
5
2
⋅
1
9
2
3^{4} \cdot 5^{2} \cdot 19^{2}
3
4
⋅
5
2
⋅
1
9
2
1.1
2.0
,
2.0
2.0, 2.0
2
.
0
,
2
.
0
2
2
2
1
1
1
0
0
0
0.408279
0.408279
0
.
4
0
8
2
7
9
Modular form 855.3.g.a
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV