⌂
→
L-functions
→
Rational
→
4
→
14^4
→
1.1
→
c3e2-0
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 (9 matches)
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
4-14e4-1.1-c3e2-0-0
3.40
3.40
3
.
4
0
133.
133.
1
3
3
.
4
4
4
2
4
⋅
7
4
2^{4} \cdot 7^{4}
2
4
⋅
7
4
1.1
3.0
,
3.0
3.0, 3.0
3
.
0
,
3
.
0
3
3
3
1
1
1
0
0
0
0.242484
0.242484
0
.
2
4
2
4
8
4
Modular form 196.4.e.c
4-14e4-1.1-c3e2-0-1
3.40
3.40
3
.
4
0
133.
133.
1
3
3
.
4
4
4
2
4
⋅
7
4
2^{4} \cdot 7^{4}
2
4
⋅
7
4
1.1
3.0
,
3.0
3.0, 3.0
3
.
0
,
3
.
0
3
3
3
1
1
1
0
0
0
0.527163
0.527163
0
.
5
2
7
1
6
3
Modular form 196.4.e.a
4-14e4-1.1-c3e2-0-2
3.40
3.40
3
.
4
0
133.
133.
1
3
3
.
4
4
4
2
4
⋅
7
4
2^{4} \cdot 7^{4}
2
4
⋅
7
4
1.1
3.0
,
3.0
3.0, 3.0
3
.
0
,
3
.
0
3
3
3
1
1
1
0
0
0
0.607872
0.607872
0
.
6
0
7
8
7
2
Modular form 196.4.e.b
4-14e4-1.1-c3e2-0-3
3.40
3.40
3
.
4
0
133.
133.
1
3
3
.
4
4
4
2
4
⋅
7
4
2^{4} \cdot 7^{4}
2
4
⋅
7
4
1.1
3.0
,
3.0
3.0, 3.0
3
.
0
,
3
.
0
3
3
3
1
1
1
0
0
0
0.842118
0.842118
0
.
8
4
2
1
1
8
Modular form 196.4.e.e
4-14e4-1.1-c3e2-0-4
3.40
3.40
3
.
4
0
133.
133.
1
3
3
.
4
4
4
2
4
⋅
7
4
2^{4} \cdot 7^{4}
2
4
⋅
7
4
1.1
3.0
,
3.0
3.0, 3.0
3
.
0
,
3
.
0
3
3
3
1
1
1
0
0
0
0.976235
0.976235
0
.
9
7
6
2
3
5
Modular form 196.4.e.f
4-14e4-1.1-c3e2-0-5
3.40
3.40
3
.
4
0
133.
133.
1
3
3
.
4
4
4
2
4
⋅
7
4
2^{4} \cdot 7^{4}
2
4
⋅
7
4
1.1
3.0
,
3.0
3.0, 3.0
3
.
0
,
3
.
0
3
3
3
1
1
1
0
0
0
1.07761
1.07761
1
.
0
7
7
6
1
Modular form 196.4.a.g
4-14e4-1.1-c3e2-0-6
3.40
3.40
3
.
4
0
133.
133.
1
3
3
.
4
4
4
2
4
⋅
7
4
2^{4} \cdot 7^{4}
2
4
⋅
7
4
1.1
3.0
,
3.0
3.0, 3.0
3
.
0
,
3
.
0
3
3
3
1
1
1
0
0
0
1.28683
1.28683
1
.
2
8
6
8
3
Modular form 196.4.e.d
4-14e4-1.1-c3e2-0-7
3.40
3.40
3
.
4
0
133.
133.
1
3
3
.
4
4
4
2
4
⋅
7
4
2^{4} \cdot 7^{4}
2
4
⋅
7
4
1.1
3.0
,
3.0
3.0, 3.0
3
.
0
,
3
.
0
3
3
3
1
1
1
2
2
2
1.87397
1.87397
1
.
8
7
3
9
7
Modular form 196.4.a.e
4-14e4-1.1-c3e2-0-8
3.40
3.40
3
.
4
0
133.
133.
1
3
3
.
4
4
4
2
4
⋅
7
4
2^{4} \cdot 7^{4}
2
4
⋅
7
4
1.1
3.0
,
3.0
3.0, 3.0
3
.
0
,
3
.
0
3
3
3
1
1
1
2
2
2
2.14463
2.14463
2
.
1
4
4
6
3
Modular form 196.4.a.f
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV