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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
2-279-31.15-c0-0-0 $0.373$ $0.139$ $2$ $3^{2} \cdot 31$ 31.15 $0.0$ 0 ✓ ✓ $-0.153$ $0$ $1.42164$ Modular form 279.1.v.a.46.1
2-279-31.23-c0-0-0 $0.373$ $0.139$ $2$ $3^{2} \cdot 31$ 31.23 $0.0$ 0 ✓ ✓ $-0.0416$ $0$ $2.02218$ Modular form 279.1.v.a.271.1
2-279-31.27-c0-0-0 $0.373$ $0.139$ $2$ $3^{2} \cdot 31$ 31.27 $0.0$ 0 ✓ ✓ $0.0416$ $0$ $2.33428$ Modular form 279.1.v.a.244.1
2-279-31.29-c0-0-0 $0.373$ $0.139$ $2$ $3^{2} \cdot 31$ 31.29 $0.0$ 0 ✓ ✓ $0.153$ $0$ $2.67822$ Modular form 279.1.v.a.91.1
2-279-31.30-c0-0-0 $0.373$ $0.139$ $2$ $3^{2} \cdot 31$ 31.30 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.64435$ Modular form 279.1.d.c.154.1
2-279-31.30-c0-0-1 $0.373$ $0.139$ $2$ $3^{2} \cdot 31$ 31.30 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $1.86486$ Artin representation 2.279.4t3.b Artin representation 2.279.4t3.b.a Modular form 279.1.d.a Modular form 279.1.d.a.154.1
2-279-31.30-c0-0-2 $0.373$ $0.139$ $2$ $3^{2} \cdot 31$ 31.30 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $2.50339$ Artin representation 2.279.6t3.a Artin representation 2.279.6t3.a.a Modular form 279.1.d.b Modular form 279.1.d.b.154.1
2-279-31.30-c0-0-3 $0.373$ $0.139$ $2$ $3^{2} \cdot 31$ 31.30 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $3.02032$ Modular form 279.1.d.c.154.2
2-279-1.1-c1-0-0 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.834058$ Modular form 279.2.a.d.1.2
2-279-1.1-c1-0-1 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.15938$ Modular form 279.2.a.d.1.3
2-279-1.1-c1-0-10 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.42198$ Modular form 279.2.a.b.1.2
2-279-1.1-c1-0-11 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.42541$ Modular form 279.2.a.d.1.5
2-279-1.1-c1-0-12 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $3.02280$ Modular form 279.2.a.a.1.2
2-279-1.1-c1-0-2 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.26876$ Modular form 279.2.a.c.1.2
2-279-1.1-c1-0-3 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.29585$ Modular form 279.2.a.c.1.1
2-279-1.1-c1-0-4 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.49747$ Modular form 279.2.a.d.1.1
2-279-1.1-c1-0-5 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.65452$ Modular form 279.2.a.b.1.1
2-279-1.1-c1-0-6 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.69911$ Modular form 279.2.a.d.1.4
2-279-1.1-c1-0-7 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.12507$ Modular form 279.2.a.a.1.1
2-279-1.1-c1-0-8 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.18424$ Modular form 279.2.a.c.1.3
2-279-1.1-c1-0-9 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.29387$ Modular form 279.2.a.d.1.6
2-279-279.103-c1-0-0 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.103$ $0$ $0.197907$ Modular form 279.2.bb.a.103.30
2-279-279.103-c1-0-1 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.245$ $0$ $0.387768$ Modular form 279.2.bb.a.103.3
2-279-279.103-c1-0-10 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.170$ $0$ $1.52480$ Modular form 279.2.bb.a.103.23
2-279-279.103-c1-0-11 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.157$ $0$ $1.54220$ Modular form 279.2.bb.a.103.1
2-279-279.103-c1-0-12 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.0325$ $0$ $1.59674$ Modular form 279.2.bb.a.103.14
2-279-279.103-c1-0-13 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.0234$ $0$ $1.64657$ Modular form 279.2.bb.a.103.17
2-279-279.103-c1-0-14 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.117$ $0$ $1.71595$ Modular form 279.2.bb.a.103.7
2-279-279.103-c1-0-15 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.251$ $0$ $1.89589$ Modular form 279.2.bb.a.103.29
2-279-279.103-c1-0-16 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.0141$ $0$ $1.92115$ Modular form 279.2.bb.a.103.15
2-279-279.103-c1-0-17 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.0798$ $0$ $1.92827$ Modular form 279.2.bb.a.103.18
2-279-279.103-c1-0-18 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.0125$ $0$ $1.94651$ Modular form 279.2.bb.a.103.11
2-279-279.103-c1-0-19 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.178$ $0$ $2.00647$ Modular form 279.2.bb.a.103.9
2-279-279.103-c1-0-2 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.412$ $0$ $0.695384$ Modular form 279.2.bb.a.103.13
2-279-279.103-c1-0-20 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.376$ $0$ $2.10493$ Modular form 279.2.bb.a.103.24
2-279-279.103-c1-0-21 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.0331$ $0$ $2.15450$ Modular form 279.2.bb.a.103.19
2-279-279.103-c1-0-22 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.324$ $0$ $2.30526$ Modular form 279.2.bb.a.103.21
2-279-279.103-c1-0-23 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.304$ $0$ $2.46579$ Modular form 279.2.bb.a.103.5
2-279-279.103-c1-0-24 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.221$ $0$ $2.56416$ Modular form 279.2.bb.a.103.16
2-279-279.103-c1-0-25 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.377$ $0$ $2.56521$ Modular form 279.2.bb.a.103.27
2-279-279.103-c1-0-26 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $0.372$ $0$ $2.57978$ Modular form 279.2.bb.a.103.25
2-279-279.103-c1-0-27 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.405$ $0$ $2.89337$ Modular form 279.2.bb.a.103.20
2-279-279.103-c1-0-28 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.332$ $0$ $3.39103$ Modular form 279.2.bb.a.103.28
2-279-279.103-c1-0-29 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.356$ $0$ $3.80123$ Modular form 279.2.bb.a.103.26
2-279-279.103-c1-0-3 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.451$ $0$ $0.872694$ Modular form 279.2.bb.a.103.8
2-279-279.103-c1-0-4 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.0921$ $0$ $1.18828$ Modular form 279.2.bb.a.103.12
2-279-279.103-c1-0-5 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.442$ $0$ $1.28143$ Modular form 279.2.bb.a.103.6
2-279-279.103-c1-0-6 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.258$ $0$ $1.32413$ Modular form 279.2.bb.a.103.4
2-279-279.103-c1-0-7 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.00629$ $0$ $1.33031$ Modular form 279.2.bb.a.103.22
2-279-279.103-c1-0-8 $1.49$ $2.22$ $2$ $3^{2} \cdot 31$ 279.103 $1.0$ $1$ ✓ ✓ $-0.464$ $0$ $1.33330$ Modular form 279.2.bb.a.103.2
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