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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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Label $\alpha$ $A$ $d$ $N$ $\chi$ $\mu$ $\nu$ $w$ prim arith $\mathbb{Q}$ self-dual $\operatorname{Arg}(\epsilon)$ $r$ First zero Origin
2-231-1.1-c3-0-0 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.449292$ Modular form 231.4.a.j.1.3
2-231-1.1-c3-0-1 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.499131$ Modular form 231.4.a.j.1.1
2-231-1.1-c3-0-10 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.09844$ Modular form 231.4.a.k.1.2
2-231-1.1-c3-0-11 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.11335$ Modular form 231.4.a.k.1.3
2-231-1.1-c3-0-12 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.14935$ Modular form 231.4.a.l.1.3
2-231-1.1-c3-0-13 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.35609$ Modular form 231.4.a.g.1.2
2-231-1.1-c3-0-14 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.40812$ Modular form 231.4.a.a Modular form 231.4.a.a.1.1
2-231-1.1-c3-0-15 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.56122$ Modular form 231.4.a.k.1.5
2-231-1.1-c3-0-16 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.60833$ Modular form 231.4.a.f.1.1
2-231-1.1-c3-0-17 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.73157$ Modular form 231.4.a.h.1.1
2-231-1.1-c3-0-18 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.83209$ Modular form 231.4.a.j.1.5
2-231-1.1-c3-0-19 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.84540$ Modular form 231.4.a.l.1.4
2-231-1.1-c3-0-2 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.639911$ Modular form 231.4.a.k.1.1
2-231-1.1-c3-0-20 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.85193$ Modular form 231.4.a.b Modular form 231.4.a.b.1.1
2-231-1.1-c3-0-21 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0$ $0$ $1.87290$ Modular form 231.4.a.e Modular form 231.4.a.e.1.1
2-231-1.1-c3-0-22 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $2.02296$ Modular form 231.4.a.l.1.5
2-231-1.1-c3-0-23 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $2.04803$ Modular form 231.4.a.i.1.2
2-231-1.1-c3-0-24 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.16745$ Modular form 231.4.a.f.1.2
2-231-1.1-c3-0-25 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.17351$ Modular form 231.4.a.c Modular form 231.4.a.c.1.1
2-231-1.1-c3-0-26 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.44340$ Modular form 231.4.a.h.1.2
2-231-1.1-c3-0-27 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.67828$ Modular form 231.4.a.d Modular form 231.4.a.d.1.1
2-231-1.1-c3-0-3 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.749383$ Modular form 231.4.a.k.1.4
2-231-1.1-c3-0-4 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.760481$ Modular form 231.4.a.l.1.2
2-231-1.1-c3-0-5 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.824061$ Modular form 231.4.a.j.1.2
2-231-1.1-c3-0-6 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.831840$ Modular form 231.4.a.i.1.1
2-231-1.1-c3-0-7 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.897189$ Modular form 231.4.a.j.1.4
2-231-1.1-c3-0-8 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.970801$ Modular form 231.4.a.l.1.1
2-231-1.1-c3-0-9 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.06909$ Modular form 231.4.a.g.1.1
2-231-11.3-c3-0-0 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $0.326$ $0$ $0.0479873$ Modular form 231.4.j.d.190.5
2-231-11.3-c3-0-1 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $-0.407$ $0$ $0.265603$ Modular form 231.4.j.d.190.7
2-231-11.3-c3-0-10 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $-0.120$ $0$ $0.750046$ Modular form 231.4.j.b.190.1
2-231-11.3-c3-0-11 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $-0.451$ $0$ $0.784835$ Modular form 231.4.j.a.190.2
2-231-11.3-c3-0-12 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $-0.354$ $0$ $0.793759$ Modular form 231.4.j.a.190.4
2-231-11.3-c3-0-13 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $-0.104$ $0$ $0.844425$ Modular form 231.4.j.c.190.7
2-231-11.3-c3-0-14 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $-0.163$ $0$ $0.933778$ Modular form 231.4.j.c.190.1
2-231-11.3-c3-0-15 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $0.0366$ $0$ $1.10430$ Modular form 231.4.j.b.190.7
2-231-11.3-c3-0-16 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $0.0616$ $0$ $1.12797$ Modular form 231.4.j.d.190.6
2-231-11.3-c3-0-17 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $0.0325$ $0$ $1.14496$ Modular form 231.4.j.a.190.1
2-231-11.3-c3-0-18 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $-0.135$ $0$ $1.14690$ Modular form 231.4.j.d.190.8
2-231-11.3-c3-0-19 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $-0.0420$ $0$ $1.21388$ Modular form 231.4.j.a.190.7
2-231-11.3-c3-0-2 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $-0.448$ $0$ $0.345879$ Modular form 231.4.j.b.190.3
2-231-11.3-c3-0-20 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $0.186$ $0$ $1.21748$ Modular form 231.4.j.b.190.2
2-231-11.3-c3-0-21 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $0.123$ $0$ $1.21893$ Modular form 231.4.j.c.190.4
2-231-11.3-c3-0-22 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $0.253$ $0$ $1.37117$ Modular form 231.4.j.b.190.5
2-231-11.3-c3-0-23 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $0.0589$ $0$ $1.37598$ Modular form 231.4.j.d.190.9
2-231-11.3-c3-0-24 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $0.225$ $0$ $1.44075$ Modular form 231.4.j.d.190.1
2-231-11.3-c3-0-25 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $0.252$ $0$ $1.49080$ Modular form 231.4.j.a.190.3
2-231-11.3-c3-0-26 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $-0.0223$ $0$ $1.50237$ Modular form 231.4.j.d.190.3
2-231-11.3-c3-0-27 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $0.420$ $0$ $1.70842$ Modular form 231.4.j.c.190.2
2-231-11.3-c3-0-28 $3.69$ $13.6$ $2$ $3 \cdot 7 \cdot 11$ 11.3 $3.0$ $3$ ✓ ✓ $0.346$ $0$ $1.72752$ Modular form 231.4.j.a.190.5
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