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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
2-252-21.11-c2-0-0 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 21.11 $2.0$ $2$ ✓ ✓ $-0.431$ $0$ $0.223295$ Modular form 252.3.bk.b.53.2
2-252-21.11-c2-0-1 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 21.11 $2.0$ $2$ ✓ ✓ $-0.127$ $0$ $0.983416$ Modular form 252.3.bk.b.53.3
2-252-21.11-c2-0-2 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 21.11 $2.0$ $2$ ✓ ✓ $-0.0586$ $0$ $1.03890$ Modular form 252.3.bk.a.53.1
2-252-21.11-c2-0-3 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 21.11 $2.0$ $2$ ✓ ✓ $0.147$ $0$ $1.92994$ Modular form 252.3.bk.b.53.4
2-252-21.11-c2-0-4 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 21.11 $2.0$ $2$ ✓ ✓ $0.245$ $0$ $2.02144$ Modular form 252.3.bk.a.53.2
2-252-21.11-c2-0-5 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 21.11 $2.0$ $2$ ✓ ✓ $0.451$ $0$ $2.11903$ Modular form 252.3.bk.b.53.1
2-252-21.2-c2-0-0 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 21.2 $2.0$ $2$ ✓ ✓ $-0.451$ $0$ $0.0538375$ Modular form 252.3.bk.b.233.1
2-252-21.2-c2-0-1 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 21.2 $2.0$ $2$ ✓ ✓ $-0.245$ $0$ $0.752421$ Modular form 252.3.bk.a.233.2
2-252-21.2-c2-0-2 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 21.2 $2.0$ $2$ ✓ ✓ $-0.147$ $0$ $1.13694$ Modular form 252.3.bk.b.233.4
2-252-21.2-c2-0-3 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 21.2 $2.0$ $2$ ✓ ✓ $0.0586$ $0$ $1.29061$ Modular form 252.3.bk.a.233.1
2-252-21.2-c2-0-4 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 21.2 $2.0$ $2$ ✓ ✓ $0.127$ $0$ $1.64099$ Modular form 252.3.bk.b.233.3
2-252-21.2-c2-0-5 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 21.2 $2.0$ $2$ ✓ ✓ $0.431$ $0$ $2.32163$ Modular form 252.3.bk.b.233.2
2-252-252.131-c2-0-0 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.454$ $0$ $0.0116468$ Modular form 252.3.r.a.131.8
2-252-252.131-c2-0-1 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.244$ $0$ $0.0259224$ Modular form 252.3.r.a.131.5
2-252-252.131-c2-0-10 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.402$ $0$ $0.393435$ Modular form 252.3.r.a.131.1
2-252-252.131-c2-0-11 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.192$ $0$ $0.458765$ Modular form 252.3.r.a.131.30
2-252-252.131-c2-0-12 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.321$ $0$ $0.520442$ Modular form 252.3.r.a.131.20
2-252-252.131-c2-0-13 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.00873$ $0$ $0.563126$ Modular form 252.3.r.a.131.22
2-252-252.131-c2-0-14 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $0.372$ $0$ $0.578460$ Modular form 252.3.r.a.131.40
2-252-252.131-c2-0-15 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.276$ $0$ $0.663616$ Modular form 252.3.r.a.131.29
2-252-252.131-c2-0-16 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.194$ $0$ $0.685952$ Modular form 252.3.r.a.131.32
2-252-252.131-c2-0-17 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.440$ $0$ $0.696697$ Modular form 252.3.r.a.131.3
2-252-252.131-c2-0-18 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.295$ $0$ $0.724525$ Modular form 252.3.r.a.131.72
2-252-252.131-c2-0-19 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.393$ $0$ $0.733601$ Modular form 252.3.r.a.131.77
2-252-252.131-c2-0-2 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.174$ $0$ $0.0612475$ Modular form 252.3.r.a.131.38
2-252-252.131-c2-0-20 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.195$ $0$ $0.792850$ Modular form 252.3.r.a.131.11
2-252-252.131-c2-0-21 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.128$ $0$ $0.794904$ Modular form 252.3.r.a.131.57
2-252-252.131-c2-0-22 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.377$ $0$ $0.819040$ Modular form 252.3.r.a.131.28
2-252-252.131-c2-0-23 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.424$ $0$ $0.878277$ Modular form 252.3.r.a.131.70
2-252-252.131-c2-0-24 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.101$ $0$ $0.899655$ Modular form 252.3.r.a.131.51
2-252-252.131-c2-0-25 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.277$ $0$ $0.958215$ Modular form 252.3.r.a.131.35
2-252-252.131-c2-0-26 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.288$ $0$ $0.963522$ Modular form 252.3.r.a.131.53
2-252-252.131-c2-0-27 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $0.0873$ $0$ $1.00129$ Modular form 252.3.r.a.131.15
2-252-252.131-c2-0-28 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.425$ $0$ $1.03763$ Modular form 252.3.r.a.131.46
2-252-252.131-c2-0-29 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $0.0782$ $0$ $1.04654$ Modular form 252.3.r.a.131.14
2-252-252.131-c2-0-3 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $0.423$ $0$ $0.0748217$ Modular form 252.3.r.a.131.33
2-252-252.131-c2-0-30 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $0.0430$ $0$ $1.05158$ Modular form 252.3.r.a.131.9
2-252-252.131-c2-0-31 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.246$ $0$ $1.06884$ Modular form 252.3.r.a.131.91
2-252-252.131-c2-0-32 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.0131$ $0$ $1.07760$ Modular form 252.3.r.a.131.74
2-252-252.131-c2-0-33 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.229$ $0$ $1.08012$ Modular form 252.3.r.a.131.21
2-252-252.131-c2-0-34 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.0280$ $0$ $1.09491$ Modular form 252.3.r.a.131.12
2-252-252.131-c2-0-35 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $0.148$ $0$ $1.12834$ Modular form 252.3.r.a.131.48
2-252-252.131-c2-0-36 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.171$ $0$ $1.13291$ Modular form 252.3.r.a.131.83
2-252-252.131-c2-0-37 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $0.136$ $0$ $1.13889$ Modular form 252.3.r.a.131.36
2-252-252.131-c2-0-38 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.385$ $0$ $1.16768$ Modular form 252.3.r.a.131.60
2-252-252.131-c2-0-39 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.111$ $0$ $1.19630$ Modular form 252.3.r.a.131.19
2-252-252.131-c2-0-4 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.129$ $0$ $0.219763$ Modular form 252.3.r.a.131.44
2-252-252.131-c2-0-40 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $0.321$ $0$ $1.22789$ Modular form 252.3.r.a.131.24
2-252-252.131-c2-0-41 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.261$ $0$ $1.29536$ Modular form 252.3.r.a.131.84
2-252-252.131-c2-0-42 $2.62$ $6.86$ $2$ $2^{2} \cdot 3^{2} \cdot 7$ 252.131 $2.0$ $2$ ✓ ✓ $-0.234$ $0$ $1.29554$ Modular form 252.3.r.a.131.16
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