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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
2-812-203.115-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 203.115 $0.0$ 0 ✓ ✓ $-0.186$ $0$ $0.883678$ Modular form 812.1.o.a.521.1
2-812-203.128-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 203.128 $0.0$ 0 ✓ ✓ $0.292$ $0$ $2.21535$ Modular form 812.1.x.a.737.1
2-812-203.173-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 203.173 $0.0$ 0 ✓ ✓ $0.186$ $0$ $1.79953$ Modular form 812.1.o.a.173.1
2-812-203.186-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 203.186 $0.0$ 0 ✓ ✓ $0.146$ $0$ $1.68873$ Modular form 812.1.x.a.389.1
2-812-203.191-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 203.191 $0.0$ 0 ✓ ✓ $-0.146$ $0$ $0.880105$ Modular form 812.1.x.a.597.1
2-812-203.202-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 203.202 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $0.982292$ Modular form 812.1.g.c.405.1
2-812-203.202-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 203.202 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $1.26433$ Artin representation 2.812.3t2.a Artin representation 2.812.3t2.a.a Modular form 812.1.g.a Modular form 812.1.g.a.405.1
2-812-203.202-c0-0-2 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 203.202 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $1.83906$ Artin representation 2.812.6t3.a Artin representation 2.812.6t3.a.a Modular form 812.1.g.b Modular form 812.1.g.b.405.1
2-812-203.202-c0-0-3 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 203.202 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.94871$ Modular form 812.1.g.c.405.2
2-812-203.46-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 203.46 $0.0$ 0 ✓ ✓ $-0.292$ $0$ $1.04751$ Modular form 812.1.x.a.249.1
2-812-812.195-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.195 $0.0$ 0 ✓ ✓ $-0.472$ $0$ $0.439152$ Modular form 812.1.bi.b.195.1
2-812-812.195-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.195 $0.0$ 0 ✓ ✓ $-0.0439$ $0$ $1.70342$ Modular form 812.1.bi.a.195.1
2-812-812.251-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.251 $0.0$ 0 ✓ ✓ $-0.0860$ $0$ $1.10607$ Modular form 812.1.bi.b.251.1
2-812-812.251-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.251 $0.0$ 0 ✓ ✓ $0.199$ $0$ $1.92457$ Modular form 812.1.bi.a.251.1
2-812-812.27-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.27 $0.0$ 0 ✓ ✓ $-0.101$ $0$ $1.24935$ Modular form 812.1.bi.a.27.1
2-812-812.27-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.27 $0.0$ 0 ✓ ✓ $-0.243$ $0$ $1.29284$ Modular form 812.1.bi.b.27.1
2-812-812.279-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.279 $0.0$ 0 ✓ ✓ $0.0439$ $0$ $1.08282$ Modular form 812.1.bi.a.279.1
2-812-812.279-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.279 $0.0$ 0 ✓ ✓ $0.472$ $0$ $2.12261$ Modular form 812.1.bi.b.279.1
2-812-812.307-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.307 $0.0$ 0 ✓ ✓ $0.0302$ $0$ $1.04313$ Modular form 812.1.l.a.307.1
2-812-812.307-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.307 $0.0$ 0 ✓ ✓ $-0.344$ $0$ $1.16408$ Modular form 812.1.l.d.307.2
2-812-812.307-c0-0-2 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.307 $0.0$ 0 ✓ ✓ $0.405$ $0$ $1.49635$ Modular form 812.1.l.c.307.1
2-812-812.307-c0-0-3 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.307 $0.0$ 0 ✓ ✓ $0.155$ $0$ $1.66171$ Modular form 812.1.l.d.307.1
2-812-812.307-c0-0-4 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.307 $0.0$ 0 ✓ ✓ $-0.0947$ $0$ $1.73048$ Modular form 812.1.l.c.307.2
2-812-812.307-c0-0-5 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.307 $0.0$ 0 ✓ ✓ $0.0302$ $0$ $2.09785$ Modular form 812.1.l.b.307.1
2-812-812.363-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.363 $0.0$ 0 ✓ ✓ $-0.229$ $0$ $0.533873$ Modular form 812.1.bi.a.363.1
2-812-812.363-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.363 $0.0$ 0 ✓ ✓ $-0.0864$ $0$ $1.37438$ Modular form 812.1.bi.b.363.1
2-812-812.391-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.391 $0.0$ 0 ✓ ✓ $0.101$ $0$ $1.49139$ Modular form 812.1.bi.a.391.1
2-812-812.391-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.391 $0.0$ 0 ✓ ✓ $0.243$ $0$ $2.30154$ Modular form 812.1.bi.b.391.1
2-812-812.447-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.447 $0.0$ 0 ✓ ✓ $-0.405$ $0$ $0.121428$ Modular form 812.1.l.c.447.1
2-812-812.447-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.447 $0.0$ 0 ✓ ✓ $-0.155$ $0$ $1.75893$ Modular form 812.1.l.d.447.1
2-812-812.447-c0-0-2 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.447 $0.0$ 0 ✓ ✓ $-0.0302$ $0$ $1.79916$ Modular form 812.1.l.b.447.1
2-812-812.447-c0-0-3 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.447 $0.0$ 0 ✓ ✓ $-0.0302$ $0$ $1.82977$ Modular form 812.1.l.a.447.1
2-812-812.447-c0-0-4 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.447 $0.0$ 0 ✓ ✓ $0.0947$ $0$ $1.89232$ Modular form 812.1.l.c.447.2
2-812-812.447-c0-0-5 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.447 $0.0$ 0 ✓ ✓ $0.344$ $0$ $2.31772$ Modular form 812.1.l.d.447.2
2-812-812.475-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.475 $0.0$ 0 ✓ ✓ $-0.280$ $0$ $1.28193$ Modular form 812.1.bi.b.475.1
2-812-812.475-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.475 $0.0$ 0 ✓ ✓ $0.290$ $0$ $1.71080$ Modular form 812.1.bi.a.475.1
2-812-812.503-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.503 $0.0$ 0 ✓ ✓ $0.0516$ $0$ $1.97554$ Modular form 812.1.bi.b.503.1
2-812-812.503-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.503 $0.0$ 0 ✓ ✓ $0.337$ $0$ $2.51936$ Modular form 812.1.bi.a.503.1
2-812-812.55-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.55 $0.0$ 0 ✓ ✓ $0.0860$ $0$ $1.43393$ Modular form 812.1.bi.b.55.1
2-812-812.55-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.55 $0.0$ 0 ✓ ✓ $-0.199$ $0$ $1.50819$ Modular form 812.1.bi.a.55.1
2-812-812.559-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.559 $0.0$ 0 ✓ ✓ $-0.290$ $0$ $1.01471$ Modular form 812.1.bi.a.559.1
2-812-812.559-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.559 $0.0$ 0 ✓ ✓ $0.280$ $0$ $2.07800$ Modular form 812.1.bi.b.559.1
2-812-812.699-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.699 $0.0$ 0 ✓ ✓ $-0.337$ $0$ $1.03977$ Modular form 812.1.bi.a.699.1
2-812-812.699-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.699 $0.0$ 0 ✓ ✓ $-0.0516$ $0$ $1.88089$ Modular form 812.1.bi.b.699.1
2-812-812.727-c0-0-0 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.727 $0.0$ 0 ✓ ✓ $0.0864$ $0$ $1.34793$ Modular form 812.1.bi.b.727.1
2-812-812.727-c0-0-1 $0.636$ $0.405$ $2$ $2^{2} \cdot 7 \cdot 29$ 812.727 $0.0$ 0 ✓ ✓ $0.229$ $0$ $1.91316$ Modular form 812.1.bi.a.727.1
2-812-1.1-c1-0-0 $2.54$ $6.48$ $2$ $2^{2} \cdot 7 \cdot 29$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.450573$ Modular form 812.2.a.e.1.1
2-812-1.1-c1-0-1 $2.54$ $6.48$ $2$ $2^{2} \cdot 7 \cdot 29$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.702130$ Modular form 812.2.a.c.1.1
2-812-1.1-c1-0-10 $2.54$ $6.48$ $2$ $2^{2} \cdot 7 \cdot 29$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.88392$ Modular form 812.2.a.d.1.2
2-812-1.1-c1-0-11 $2.54$ $6.48$ $2$ $2^{2} \cdot 7 \cdot 29$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.89240$ Modular form 812.2.a.e.1.6
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