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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
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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
2-59-59.58-c0-0-0 $0.171$ $0.0294$ $2$ $59$ 59.58 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $3.43180$ Artin representation 2.59.3t2.a Artin representation 2.59.3t2.a.a Modular form 59.1.b.a Modular form 59.1.b.a.58.1
2-59-1.1-c1-0-0 $0.686$ $0.471$ $2$ $59$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.52770$ Modular form 59.2.a.a.1.1
2-59-1.1-c1-0-1 $0.686$ $0.471$ $2$ $59$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.37759$ Modular form 59.2.a.a.1.2
2-59-1.1-c1-0-2 $0.686$ $0.471$ $2$ $59$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.92810$ Modular form 59.2.a.a.1.3
2-59-1.1-c1-0-3 $0.686$ $0.471$ $2$ $59$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $3.57516$ Modular form 59.2.a.a.1.4
2-59-1.1-c1-0-4 $0.686$ $0.471$ $2$ $59$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $3.58771$ Modular form 59.2.a.a.1.5
2-59-59.12-c1-0-0 $0.686$ $0.471$ $2$ $59$ 59.12 $1.0$ $1$ ✓ ✓ $-0.300$ $0$ $1.05960$ Modular form 59.2.c.a.12.2
2-59-59.12-c1-0-1 $0.686$ $0.471$ $2$ $59$ 59.12 $1.0$ $1$ ✓ ✓ $-0.0690$ $0$ $1.98933$ Modular form 59.2.c.a.12.1
2-59-59.12-c1-0-2 $0.686$ $0.471$ $2$ $59$ 59.12 $1.0$ $1$ ✓ ✓ $0.0346$ $0$ $3.20226$ Modular form 59.2.c.a.12.3
2-59-59.12-c1-0-3 $0.686$ $0.471$ $2$ $59$ 59.12 $1.0$ $1$ ✓ ✓ $0.0406$ $0$ $3.49745$ Modular form 59.2.c.a.12.4
2-59-59.15-c1-0-0 $0.686$ $0.471$ $2$ $59$ 59.15 $1.0$ $1$ ✓ ✓ $0.0687$ $0$ $2.27661$ Modular form 59.2.c.a.15.1
2-59-59.15-c1-0-1 $0.686$ $0.471$ $2$ $59$ 59.15 $1.0$ $1$ ✓ ✓ $-0.0421$ $0$ $2.82688$ Modular form 59.2.c.a.15.3
2-59-59.15-c1-0-2 $0.686$ $0.471$ $2$ $59$ 59.15 $1.0$ $1$ ✓ ✓ $0.0750$ $0$ $4.19477$ Modular form 59.2.c.a.15.4
2-59-59.15-c1-0-3 $0.686$ $0.471$ $2$ $59$ 59.15 $1.0$ $1$ ✓ ✓ $0.463$ $0$ $4.32342$ Modular form 59.2.c.a.15.2
2-59-59.16-c1-0-0 $0.686$ $0.471$ $2$ $59$ 59.16 $1.0$ $1$ ✓ ✓ $-0.181$ $0$ $1.52413$ Modular form 59.2.c.a.16.2
2-59-59.16-c1-0-1 $0.686$ $0.471$ $2$ $59$ 59.16 $1.0$ $1$ ✓ ✓ $0.277$ $0$ $2.82775$ Modular form 59.2.c.a.16.1
2-59-59.16-c1-0-2 $0.686$ $0.471$ $2$ $59$ 59.16 $1.0$ $1$ ✓ ✓ $-0.00352$ $0$ $3.30022$ Modular form 59.2.c.a.16.4
2-59-59.16-c1-0-3 $0.686$ $0.471$ $2$ $59$ 59.16 $1.0$ $1$ ✓ ✓ $0.234$ $0$ $3.96368$ Modular form 59.2.c.a.16.3
2-59-59.17-c1-0-0 $0.686$ $0.471$ $2$ $59$ 59.17 $1.0$ $1$ ✓ ✓ $-0.339$ $0$ $1.52112$ Modular form 59.2.c.a.17.1
2-59-59.17-c1-0-1 $0.686$ $0.471$ $2$ $59$ 59.17 $1.0$ $1$ ✓ ✓ $-0.0360$ $0$ $2.52220$ Modular form 59.2.c.a.17.2
2-59-59.17-c1-0-2 $0.686$ $0.471$ $2$ $59$ 59.17 $1.0$ $1$ ✓ ✓ $0.114$ $0$ $3.51460$ Modular form 59.2.c.a.17.4
2-59-59.17-c1-0-3 $0.686$ $0.471$ $2$ $59$ 59.17 $1.0$ $1$ ✓ ✓ $0.159$ $0$ $3.97488$ Modular form 59.2.c.a.17.3
2-59-59.19-c1-0-0 $0.686$ $0.471$ $2$ $59$ 59.19 $1.0$ $1$ ✓ ✓ $-0.497$ $0$ $1.05934$ Modular form 59.2.c.a.19.1
2-59-59.19-c1-0-1 $0.686$ $0.471$ $2$ $59$ 59.19 $1.0$ $1$ ✓ ✓ $-0.213$ $0$ $1.56645$ Modular form 59.2.c.a.19.3
2-59-59.19-c1-0-2 $0.686$ $0.471$ $2$ $59$ 59.19 $1.0$ $1$ ✓ ✓ $-0.127$ $0$ $2.38508$ Modular form 59.2.c.a.19.2
2-59-59.19-c1-0-3 $0.686$ $0.471$ $2$ $59$ 59.19 $1.0$ $1$ ✓ ✓ $0.185$ $0$ $3.94308$ Modular form 59.2.c.a.19.4
2-59-59.20-c1-0-0 $0.686$ $0.471$ $2$ $59$ 59.20 $1.0$ $1$ ✓ ✓ $-0.276$ $0$ $0.484291$ Modular form 59.2.c.a.20.1
2-59-59.20-c1-0-1 $0.686$ $0.471$ $2$ $59$ 59.20 $1.0$ $1$ ✓ ✓ $0.163$ $0$ $2.94103$ Modular form 59.2.c.a.20.2
2-59-59.20-c1-0-2 $0.686$ $0.471$ $2$ $59$ 59.20 $1.0$ $1$ ✓ ✓ $-0.0626$ $0$ $3.12322$ Modular form 59.2.c.a.20.4
2-59-59.20-c1-0-3 $0.686$ $0.471$ $2$ $59$ 59.20 $1.0$ $1$ ✓ ✓ $0.0954$ $0$ $3.57896$ Modular form 59.2.c.a.20.3
2-59-59.21-c1-0-0 $0.686$ $0.471$ $2$ $59$ 59.21 $1.0$ $1$ ✓ ✓ $-0.185$ $0$ $2.01268$ Modular form 59.2.c.a.21.3
2-59-59.21-c1-0-1 $0.686$ $0.471$ $2$ $59$ 59.21 $1.0$ $1$ ✓ ✓ $0.134$ $0$ $3.27273$ Modular form 59.2.c.a.21.2
2-59-59.21-c1-0-2 $0.686$ $0.471$ $2$ $59$ 59.21 $1.0$ $1$ ✓ ✓ $-0.0800$ $0$ $3.43027$ Modular form 59.2.c.a.21.4
2-59-59.21-c1-0-3 $0.686$ $0.471$ $2$ $59$ 59.21 $1.0$ $1$ ✓ ✓ $0.387$ $0$ $3.83821$ Modular form 59.2.c.a.21.1
2-59-59.22-c1-0-0 $0.686$ $0.471$ $2$ $59$ 59.22 $1.0$ $1$ ✓ ✓ $-0.306$ $0$ $2.11057$ Modular form 59.2.c.a.22.4
2-59-59.22-c1-0-1 $0.686$ $0.471$ $2$ $59$ 59.22 $1.0$ $1$ ✓ ✓ $-0.121$ $0$ $2.57115$ Modular form 59.2.c.a.22.3
2-59-59.22-c1-0-2 $0.686$ $0.471$ $2$ $59$ 59.22 $1.0$ $1$ ✓ ✓ $0.0585$ $0$ $2.63660$ Modular form 59.2.c.a.22.1
2-59-59.22-c1-0-3 $0.686$ $0.471$ $2$ $59$ 59.22 $1.0$ $1$ ✓ ✓ $0.285$ $0$ $4.17768$ Modular form 59.2.c.a.22.2
2-59-59.25-c1-0-0 $0.686$ $0.471$ $2$ $59$ 59.25 $1.0$ $1$ ✓ ✓ $-0.0193$ $0$ $1.61799$ Modular form 59.2.c.a.25.1
2-59-59.25-c1-0-1 $0.686$ $0.471$ $2$ $59$ 59.25 $1.0$ $1$ ✓ ✓ $-0.0911$ $0$ $2.89479$ Modular form 59.2.c.a.25.4
2-59-59.25-c1-0-2 $0.686$ $0.471$ $2$ $59$ 59.25 $1.0$ $1$ ✓ ✓ $0.293$ $0$ $3.63794$ Modular form 59.2.c.a.25.2
2-59-59.25-c1-0-3 $0.686$ $0.471$ $2$ $59$ 59.25 $1.0$ $1$ ✓ ✓ $0.112$ $0$ $3.76239$ Modular form 59.2.c.a.25.3
2-59-59.26-c1-0-0 $0.686$ $0.471$ $2$ $59$ 59.26 $1.0$ $1$ ✓ ✓ $-0.293$ $0$ $1.31381$ Modular form 59.2.c.a.26.2
2-59-59.26-c1-0-1 $0.686$ $0.471$ $2$ $59$ 59.26 $1.0$ $1$ ✓ ✓ $-0.112$ $0$ $2.10730$ Modular form 59.2.c.a.26.3
2-59-59.26-c1-0-2 $0.686$ $0.471$ $2$ $59$ 59.26 $1.0$ $1$ ✓ ✓ $0.0193$ $0$ $2.65252$ Modular form 59.2.c.a.26.1
2-59-59.26-c1-0-3 $0.686$ $0.471$ $2$ $59$ 59.26 $1.0$ $1$ ✓ ✓ $0.0911$ $0$ $3.62436$ Modular form 59.2.c.a.26.4
2-59-59.27-c1-0-0 $0.686$ $0.471$ $2$ $59$ 59.27 $1.0$ $1$ ✓ ✓ $-0.250$ $0$ $1.82803$ Modular form 59.2.c.a.27.2
2-59-59.27-c1-0-1 $0.686$ $0.471$ $2$ $59$ 59.27 $1.0$ $1$ ✓ ✓ $-0.313$ $0$ $2.32758$ Modular form 59.2.c.a.27.1
2-59-59.27-c1-0-2 $0.686$ $0.471$ $2$ $59$ 59.27 $1.0$ $1$ ✓ ✓ $0.132$ $0$ $3.33955$ Modular form 59.2.c.a.27.3
2-59-59.27-c1-0-3 $0.686$ $0.471$ $2$ $59$ 59.27 $1.0$ $1$ ✓ ✓ $0.259$ $0$ $4.46985$ Modular form 59.2.c.a.27.4
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