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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
2-1011-1011.1004-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.1004 $0.0$ 0 ✓ ✓ $0.183$ $0$ $1.57427$ Modular form 1011.1.bf.a.1004.1
2-1011-1011.1010-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.1010 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.04663$ Modular form 1011.1.c.d.1010.1
2-1011-1011.1010-c0-0-1 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.1010 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $1.53361$ Artin representation 2.1011.4t3.a Artin representation 2.1011.4t3.a.a Modular form 1011.1.c.a Modular form 1011.1.c.a.1010.1
2-1011-1011.1010-c0-0-2 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.1010 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.57558$ Modular form 1011.1.c.d.1010.2
2-1011-1011.1010-c0-0-3 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.1010 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $1.68601$ Artin representation 2.1011.3t2.a Artin representation 2.1011.3t2.a.a Modular form 1011.1.c.b Modular form 1011.1.c.b.1010.1
2-1011-1011.1010-c0-0-4 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.1010 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $2.05427$ Artin representation 2.1011.6t3.a Artin representation 2.1011.6t3.a.a Modular form 1011.1.c.c Modular form 1011.1.c.c.1010.1
2-1011-1011.137-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.137 $0.0$ 0 ✓ ✓ $0.0415$ $0$ $1.82477$ Modular form 1011.1.bf.a.137.1
2-1011-1011.164-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.164 $0.0$ 0 ✓ ✓ $-0.0737$ $0$ $1.38953$ Modular form 1011.1.y.a.164.1
2-1011-1011.173-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.173 $0.0$ 0 ✓ ✓ $-0.384$ $0$ $0.728657$ Modular form 1011.1.y.a.173.1
2-1011-1011.200-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.200 $0.0$ 0 ✓ ✓ $-0.124$ $0$ $0.902794$ Modular form 1011.1.bf.a.200.1
2-1011-1011.281-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.281 $0.0$ 0 ✓ ✓ $0.229$ $0$ $2.02806$ Modular form 1011.1.bf.a.281.1
2-1011-1011.290-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.290 $0.0$ 0 ✓ ✓ $-0.155$ $0$ $1.16660$ Modular form 1011.1.bf.a.290.1
2-1011-1011.329-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.329 $0.0$ 0 ✓ ✓ $-0.0701$ $0$ $1.11368$ Modular form 1011.1.q.a.329.1
2-1011-1011.344-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.344 $0.0$ 0 ✓ ✓ $0.0331$ $0$ $1.93920$ Modular form 1011.1.bf.a.344.1
2-1011-1011.362-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.362 $0.0$ 0 ✓ ✓ $0.265$ $0$ $1.95965$ Modular form 1011.1.bf.a.362.1
2-1011-1011.380-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.380 $0.0$ 0 ✓ ✓ $0.155$ $0$ $1.82916$ Modular form 1011.1.bf.a.380.1
2-1011-1011.386-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.386 $0.0$ 0 ✓ ✓ $-0.211$ $0$ $1.17745$ Modular form 1011.1.y.a.386.1
2-1011-1011.389-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.389 $0.0$ 0 ✓ ✓ $0.138$ $0$ $1.19139$ Modular form 1011.1.r.a.389.1
2-1011-1011.392-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.392 $0.0$ 0 ✓ ✓ $-0.139$ $0$ $1.05849$ Modular form 1011.1.y.a.392.1
2-1011-1011.401-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.401 $0.0$ 0 ✓ ✓ $0.453$ $0$ $0.247920$ Modular form 1011.1.r.a.401.1
2-1011-1011.416-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.416 $0.0$ 0 ✓ ✓ $-0.453$ $0$ $2.63994$ Modular form 1011.1.r.a.416.1
2-1011-1011.422-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.422 $0.0$ 0 ✓ ✓ $-0.176$ $0$ $1.33211$ Modular form 1011.1.l.a.422.1
2-1011-1011.440-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.440 $0.0$ 0 ✓ ✓ $0.411$ $0$ $2.05985$ Modular form 1011.1.y.a.440.1
2-1011-1011.458-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.458 $0.0$ 0 ✓ ✓ $0.413$ $0$ $0.253075$ Modular form 1011.1.bf.a.458.1
2-1011-1011.47-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.47 $0.0$ 0 ✓ ✓ $0.0858$ $0$ $1.13116$ Modular form 1011.1.bf.a.47.1
2-1011-1011.485-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.485 $0.0$ 0 ✓ ✓ $0.334$ $0$ $0.576452$ Modular form 1011.1.f.b.485.2
2-1011-1011.485-c0-0-1 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.485 $0.0$ 0 ✓ ✓ $-0.165$ $0$ $1.35323$ Modular form 1011.1.f.a.485.1
2-1011-1011.485-c0-0-2 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.485 $0.0$ 0 ✓ ✓ $0.334$ $0$ $2.07655$ Modular form 1011.1.f.b.485.1
2-1011-1011.512-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.512 $0.0$ 0 ✓ ✓ $-0.138$ $0$ $0.843069$ Modular form 1011.1.r.a.512.1
2-1011-1011.524-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.524 $0.0$ 0 ✓ ✓ $0.0737$ $0$ $2.06035$ Modular form 1011.1.y.a.524.1
2-1011-1011.551-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.551 $0.0$ 0 ✓ ✓ $0.124$ $0$ $1.60320$ Modular form 1011.1.bf.a.551.1
2-1011-1011.56-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.56 $0.0$ 0 ✓ ✓ $-0.103$ $0$ $1.44784$ Modular form 1011.1.bf.a.56.1
2-1011-1011.563-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.563 $0.0$ 0 ✓ ✓ $0.176$ $0$ $2.43747$ Modular form 1011.1.l.a.563.1
2-1011-1011.626-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.626 $0.0$ 0 ✓ ✓ $-0.0331$ $0$ $1.62442$ Modular form 1011.1.bf.a.626.1
2-1011-1011.632-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.632 $0.0$ 0 ✓ ✓ $0.190$ $0$ $2.20981$ Modular form 1011.1.r.a.632.1
2-1011-1011.635-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.635 $0.0$ 0 ✓ ✓ $0.171$ $0$ $1.79082$ Modular form 1011.1.bf.a.635.1
2-1011-1011.638-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.638 $0.0$ 0 ✓ ✓ $-0.202$ $0$ $1.18197$ Modular form 1011.1.y.a.638.1
2-1011-1011.647-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.647 $0.0$ 0 ✓ ✓ $-0.302$ $0$ $1.08972$ Modular form 1011.1.bf.a.647.1
2-1011-1011.668-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.668 $0.0$ 0 ✓ ✓ $0.103$ $0$ $1.80768$ Modular form 1011.1.bf.a.668.1
2-1011-1011.680-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.680 $0.0$ 0 ✓ ✓ $-0.229$ $0$ $1.33324$ Modular form 1011.1.bf.a.680.1
2-1011-1011.701-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.701 $0.0$ 0 ✓ ✓ $-0.265$ $0$ $0.545922$ Modular form 1011.1.bf.a.701.1
2-1011-1011.710-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.710 $0.0$ 0 ✓ ✓ $-0.411$ $0$ $0.357152$ Modular form 1011.1.y.a.710.1
2-1011-1011.713-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.713 $0.0$ 0 ✓ ✓ $-0.413$ $0$ $2.86587$ Modular form 1011.1.bf.a.713.1
2-1011-1011.716-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.716 $0.0$ 0 ✓ ✓ $0.0701$ $0$ $1.71434$ Modular form 1011.1.q.a.716.1
2-1011-1011.722-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.722 $0.0$ 0 ✓ ✓ $-0.183$ $0$ $1.25584$ Modular form 1011.1.bf.a.722.1
2-1011-1011.785-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.785 $0.0$ 0 ✓ ✓ $-0.0109$ $0$ $1.47645$ Modular form 1011.1.l.a.785.1
2-1011-1011.797-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.797 $0.0$ 0 ✓ ✓ $-0.0415$ $0$ $1.77868$ Modular form 1011.1.bf.a.797.1
2-1011-1011.8-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.8 $0.0$ 0 ✓ ✓ $-0.190$ $0$ $1.53834$ Modular form 1011.1.r.a.8.1
2-1011-1011.824-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.824 $0.0$ 0 ✓ ✓ $0.384$ $0$ $2.34214$ Modular form 1011.1.y.a.824.1
2-1011-1011.836-c0-0-0 $0.710$ $0.504$ $2$ $3 \cdot 337$ 1011.836 $0.0$ 0 ✓ ✓ $0.186$ $0$ $1.98373$ Modular form 1011.1.q.a.836.1
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