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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
2-403-403.185-c0-0-0 $0.448$ $0.201$ $2$ $13 \cdot 31$ 403.185 $0.0$ 0 ✓ ✓ $0.290$ $0$ $1.97586$ Artin representation 2.403.16t60.a.c Modular form 403.1.p.a.185.1
2-403-403.185-c0-0-1 $0.448$ $0.201$ $2$ $13 \cdot 31$ 403.185 $0.0$ 0 ✓ ✓ $0.290$ $0$ $2.66549$ Artin representation 2.403.16t60.a.b Modular form 403.1.p.a.185.2
2-403-403.61-c0-0-0 $0.448$ $0.201$ $2$ $13 \cdot 31$ 403.61 $0.0$ 0 ✓ ✓ $-0.290$ $0$ $0.977486$ Artin representation 2.403.16t60.a.d Modular form 403.1.p.a.61.1
2-403-403.61-c0-0-1 $0.448$ $0.201$ $2$ $13 \cdot 31$ 403.61 $0.0$ 0 ✓ ✓ $-0.290$ $0$ $1.60641$ Artin representation 2.403.16t60.a.a Modular form 403.1.p.a.61.2
2-403-1.1-c1-0-0 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.526203$ Modular form 403.2.a.e.1.2
2-403-1.1-c1-0-1 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.856550$ Modular form 403.2.a.a.1.1
2-403-1.1-c1-0-10 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.60986$ Modular form 403.2.a.d.1.4
2-403-1.1-c1-0-11 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.62980$ Modular form 403.2.a.e.1.1
2-403-1.1-c1-0-12 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.71468$ Modular form 403.2.a.b.1.1
2-403-1.1-c1-0-13 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.82460$ Modular form 403.2.a.b.1.2
2-403-1.1-c1-0-14 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.84577$ Modular form 403.2.a.c.1.3
2-403-1.1-c1-0-15 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.96422$ Modular form 403.2.a.a.1.2
2-403-1.1-c1-0-16 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.97859$ Modular form 403.2.a.e.1.8
2-403-1.1-c1-0-17 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.03133$ Modular form 403.2.a.c.1.6
2-403-1.1-c1-0-18 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.06326$ Modular form 403.2.a.d.1.1
2-403-1.1-c1-0-19 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.08649$ Modular form 403.2.a.c.1.5
2-403-1.1-c1-0-2 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.925480$ Modular form 403.2.a.c.1.1
2-403-1.1-c1-0-20 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.11848$ Modular form 403.2.a.e.1.6
2-403-1.1-c1-0-21 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.14198$ Modular form 403.2.a.d.1.5
2-403-1.1-c1-0-22 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.31023$ Modular form 403.2.a.d.1.3
2-403-1.1-c1-0-23 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.38455$ Modular form 403.2.a.c.1.7
2-403-1.1-c1-0-24 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.50978$ Modular form 403.2.a.b.1.4
2-403-1.1-c1-0-25 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.51402$ Modular form 403.2.a.e.1.7
2-403-1.1-c1-0-26 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.74397$ Modular form 403.2.a.d.1.8
2-403-1.1-c1-0-27 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.79025$ Modular form 403.2.a.d.1.7
2-403-1.1-c1-0-28 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.83362$ Modular form 403.2.a.b.1.5
2-403-1.1-c1-0-29 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $3.13445$ Modular form 403.2.a.b.1.6
2-403-1.1-c1-0-3 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.977114$ Modular form 403.2.a.e.1.5
2-403-1.1-c1-0-30 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $3.14247$ Modular form 403.2.a.d.1.6
2-403-1.1-c1-0-4 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.14071$ Modular form 403.2.a.d.1.2
2-403-1.1-c1-0-5 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.22041$ Modular form 403.2.a.c.1.2
2-403-1.1-c1-0-6 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.36156$ Modular form 403.2.a.c.1.4
2-403-1.1-c1-0-7 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.43535$ Modular form 403.2.a.e.1.4
2-403-1.1-c1-0-8 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.47699$ Modular form 403.2.a.e.1.3
2-403-1.1-c1-0-9 $1.79$ $3.21$ $2$ $13 \cdot 31$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.59069$ Modular form 403.2.a.b.1.3
2-403-13.10-c1-0-0 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $0.343$ $0$ $0.0237992$ Modular form 403.2.r.a.218.3
2-403-13.10-c1-0-1 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $0.478$ $0$ $0.0758186$ Modular form 403.2.r.a.218.19
2-403-13.10-c1-0-10 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $-0.388$ $0$ $1.13811$ Modular form 403.2.r.a.218.17
2-403-13.10-c1-0-11 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $-0.219$ $0$ $1.13947$ Modular form 403.2.r.a.218.21
2-403-13.10-c1-0-12 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $-0.163$ $0$ $1.19870$ Modular form 403.2.r.a.218.25
2-403-13.10-c1-0-13 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $-0.0838$ $0$ $1.28253$ Modular form 403.2.r.a.218.5
2-403-13.10-c1-0-14 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $-0.00644$ $0$ $1.29924$ Modular form 403.2.r.a.218.10
2-403-13.10-c1-0-15 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $0.00637$ $0$ $1.30594$ Modular form 403.2.r.a.218.4
2-403-13.10-c1-0-16 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $0.242$ $0$ $1.42693$ Modular form 403.2.r.a.218.16
2-403-13.10-c1-0-17 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $-0.136$ $0$ $1.43041$ Modular form 403.2.r.a.218.27
2-403-13.10-c1-0-18 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $-0.217$ $0$ $1.48012$ Modular form 403.2.r.a.218.8
2-403-13.10-c1-0-19 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $0.111$ $0$ $1.57198$ Modular form 403.2.r.a.218.18
2-403-13.10-c1-0-2 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $-0.177$ $0$ $0.481994$ Modular form 403.2.r.a.218.22
2-403-13.10-c1-0-20 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $0.0635$ $0$ $1.64148$ Modular form 403.2.r.a.218.30
2-403-13.10-c1-0-21 $1.79$ $3.21$ $2$ $13 \cdot 31$ 13.10 $1.0$ $1$ ✓ ✓ $0.142$ $0$ $1.76187$ Modular form 403.2.r.a.218.23
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