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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
2-28-28.19-c1-0-0 $0.472$ $0.223$ $2$ $2^{2} \cdot 7$ 28.19 $1.0$ $1$ ✓ ✓ $-0.0934$ $0$ $2.79175$ Modular form 28.2.f.a.19.1
2-28-28.19-c1-0-1 $0.472$ $0.223$ $2$ $2^{2} \cdot 7$ 28.19 $1.0$ $1$ ✓ ✓ $-0.0934$ $0$ $3.79023$ Modular form 28.2.f.a.19.2
2-28-28.27-c1-0-0 $0.472$ $0.223$ $2$ $2^{2} \cdot 7$ 28.27 $1.0$ $1$ ✓ ✓ $-0.134$ $0$ $3.05576$ Modular form 28.2.d.a.27.2
2-28-28.27-c1-0-1 $0.472$ $0.223$ $2$ $2^{2} \cdot 7$ 28.27 $1.0$ $1$ ✓ ✓ $0.134$ $0$ $4.67922$ Modular form 28.2.d.a.27.1
2-28-28.3-c1-0-0 $0.472$ $0.223$ $2$ $2^{2} \cdot 7$ 28.3 $1.0$ $1$ ✓ ✓ $0.0934$ $0$ $3.97935$ Modular form 28.2.f.a.3.1
2-28-28.3-c1-0-1 $0.472$ $0.223$ $2$ $2^{2} \cdot 7$ 28.3 $1.0$ $1$ ✓ ✓ $0.0934$ $0$ $4.72839$ Modular form 28.2.f.a.3.2
2-28-7.2-c1-0-0 $0.472$ $0.223$ $2$ $2^{2} \cdot 7$ 7.2 $1.0$ $1$ ✓ ✓ $0.0201$ $0$ $4.16290$ Modular form 28.2.e.a.9.1
2-28-7.4-c1-0-0 $0.472$ $0.223$ $2$ $2^{2} \cdot 7$ 7.4 $1.0$ $1$ ✓ ✓ $-0.0201$ $0$ $3.68820$ Modular form 28.2.e.a.25.1
2-28-28.11-c2-0-0 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 28.11 $2.0$ $2$ ✓ ✓ $-0.0830$ $0$ $2.22483$ Modular form 28.3.g.a.11.1
2-28-28.11-c2-0-1 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 28.11 $2.0$ $2$ ✓ ✓ $-0.189$ $0$ $2.47432$ Modular form 28.3.g.a.11.4
2-28-28.11-c2-0-2 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 28.11 $2.0$ $2$ ✓ ✓ $-0.0561$ $0$ $3.37221$ Modular form 28.3.g.a.11.6
2-28-28.11-c2-0-3 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 28.11 $2.0$ $2$ ✓ ✓ $0.108$ $0$ $3.50884$ Modular form 28.3.g.a.11.3
2-28-28.11-c2-0-4 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 28.11 $2.0$ $2$ ✓ ✓ $0.158$ $0$ $4.58637$ Modular form 28.3.g.a.11.5
2-28-28.11-c2-0-5 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 28.11 $2.0$ $2$ ✓ ✓ $0.394$ $0$ $4.97887$ Modular form 28.3.g.a.11.2
2-28-28.23-c2-0-0 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 28.23 $2.0$ $2$ ✓ ✓ $-0.394$ $0$ $0.902243$ Modular form 28.3.g.a.23.2
2-28-28.23-c2-0-1 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 28.23 $2.0$ $2$ ✓ ✓ $-0.158$ $0$ $2.64828$ Modular form 28.3.g.a.23.5
2-28-28.23-c2-0-2 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 28.23 $2.0$ $2$ ✓ ✓ $0.0830$ $0$ $2.98745$ Modular form 28.3.g.a.23.1
2-28-28.23-c2-0-3 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 28.23 $2.0$ $2$ ✓ ✓ $-0.108$ $0$ $3.02206$ Modular form 28.3.g.a.23.3
2-28-28.23-c2-0-4 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 28.23 $2.0$ $2$ ✓ ✓ $0.0561$ $0$ $3.86036$ Modular form 28.3.g.a.23.6
2-28-28.23-c2-0-5 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 28.23 $2.0$ $2$ ✓ ✓ $0.189$ $0$ $4.24505$ Modular form 28.3.g.a.23.4
2-28-4.3-c2-0-0 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 4.3 $2.0$ $2$ ✓ ✓ $-0.162$ $0$ $1.68304$ Modular form 28.3.c.a.15.1
2-28-4.3-c2-0-1 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 4.3 $2.0$ $2$ ✓ ✓ $-0.223$ $0$ $2.18943$ Modular form 28.3.c.a.15.4
2-28-4.3-c2-0-2 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 4.3 $2.0$ $2$ ✓ ✓ $0.162$ $0$ $3.50379$ Modular form 28.3.c.a.15.2
2-28-4.3-c2-0-3 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 4.3 $2.0$ $2$ ✓ ✓ $0.0419$ $0$ $3.66998$ Modular form 28.3.c.a.15.5
2-28-4.3-c2-0-4 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 4.3 $2.0$ $2$ ✓ ✓ $-0.0419$ $0$ $3.75144$ Modular form 28.3.c.a.15.6
2-28-4.3-c2-0-5 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 4.3 $2.0$ $2$ ✓ ✓ $0.223$ $0$ $4.44786$ Modular form 28.3.c.a.15.3
2-28-7.3-c2-0-0 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 7.3 $2.0$ $2$ ✓ ✓ $-0.0201$ $0$ $3.01203$ Modular form 28.3.h.a.17.1
2-28-7.5-c2-0-0 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 7.5 $2.0$ $2$ ✓ ✓ $0.0201$ $0$ $3.28637$ Modular form 28.3.h.a.5.1
2-28-7.6-c2-0-0 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 7.6 $2.0$ $2$ ✓ ✓ $-0.123$ $0$ $2.35788$ Modular form 28.3.b.a.13.2
2-28-7.6-c2-0-1 $0.873$ $0.762$ $2$ $2^{2} \cdot 7$ 7.6 $2.0$ $2$ ✓ ✓ $0.123$ $0$ $4.14483$ Modular form 28.3.b.a.13.1
2-28-1.1-c3-0-0 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0$ $0$ $2.64008$ Modular form 28.4.a.b Modular form 28.4.a.b.1.1
2-28-1.1-c3-0-1 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0.5$ $1$ $4.59778$ Modular form 28.4.a.a Modular form 28.4.a.a.1.1
2-28-28.19-c3-0-0 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.19 $3.0$ $3$ ✓ ✓ $-0.320$ $0$ $1.56183$ Modular form 28.4.f.a.19.5
2-28-28.19-c3-0-1 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.19 $3.0$ $3$ ✓ ✓ $-0.0609$ $0$ $1.76656$ Modular form 28.4.f.a.19.1
2-28-28.19-c3-0-2 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.19 $3.0$ $3$ ✓ ✓ $-0.0567$ $0$ $1.84803$ Modular form 28.4.f.a.19.4
2-28-28.19-c3-0-3 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.19 $3.0$ $3$ ✓ ✓ $-0.201$ $0$ $2.09715$ Modular form 28.4.f.a.19.7
2-28-28.19-c3-0-4 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.19 $3.0$ $3$ ✓ ✓ $-0.109$ $0$ $2.67568$ Modular form 28.4.f.a.19.9
2-28-28.19-c3-0-5 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.19 $3.0$ $3$ ✓ ✓ $0.0663$ $0$ $3.18081$ Modular form 28.4.f.a.19.8
2-28-28.19-c3-0-6 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.19 $3.0$ $3$ ✓ ✓ $0.273$ $0$ $3.39341$ Modular form 28.4.f.a.19.3
2-28-28.19-c3-0-7 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.19 $3.0$ $3$ ✓ ✓ $0.130$ $0$ $3.97099$ Modular form 28.4.f.a.19.10
2-28-28.19-c3-0-8 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.19 $3.0$ $3$ ✓ ✓ $0.465$ $0$ $4.16911$ Modular form 28.4.f.a.19.2
2-28-28.19-c3-0-9 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.19 $3.0$ $3$ ✓ ✓ $0.334$ $0$ $4.45150$ Modular form 28.4.f.a.19.6
2-28-28.27-c3-0-0 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.27 $3.0$ $3$ ✓ ✓ $-0.305$ $0$ $0.483827$ Modular form 28.4.d.b.27.1
2-28-28.27-c3-0-1 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.27 $3.0$ $3$ ✓ ✓ $-0.430$ $0$ $0.827496$ Modular form 28.4.d.b.27.7
2-28-28.27-c3-0-2 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.27 $3.0$ $3$ ✓ ✓ $-0.154$ $0$ $1.80429$ Modular form 28.4.d.b.27.4
2-28-28.27-c3-0-3 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.27 $3.0$ $3$ ✓ ✓ $-0.162$ $0$ $2.58636$ Modular form 28.4.d.b.27.8
2-28-28.27-c3-0-4 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.27 $3.0$ $3$ ✓ ✓ $-0.0950$ $0$ $2.66561$ Modular form 28.4.d.a.27.2
2-28-28.27-c3-0-5 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.27 $3.0$ $3$ ✓ ✓ $0.154$ $0$ $2.74031$ Modular form 28.4.d.b.27.2
2-28-28.27-c3-0-6 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.27 $3.0$ $3$ ✓ ✓ $0.305$ $0$ $3.09369$ Modular form 28.4.d.b.27.3
2-28-28.27-c3-0-7 $1.28$ $1.65$ $2$ $2^{2} \cdot 7$ 28.27 $3.0$ $3$ ✓ ✓ $0.162$ $0$ $3.45690$ Modular form 28.4.d.b.27.6
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