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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
2-197-1.1-c3-0-0 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.204688$ Modular form 197.4.a.b.1.6
2-197-1.1-c3-0-1 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.364425$ Modular form 197.4.a.b.1.16
2-197-1.1-c3-0-10 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.956534$ Modular form 197.4.a.b.1.20
2-197-1.1-c3-0-11 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.982774$ Modular form 197.4.a.b.1.5
2-197-1.1-c3-0-12 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.02813$ Modular form 197.4.a.a.1.7
2-197-1.1-c3-0-13 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.13820$ Modular form 197.4.a.a.1.1
2-197-1.1-c3-0-14 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.23539$ Modular form 197.4.a.b.1.15
2-197-1.1-c3-0-15 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.26420$ Modular form 197.4.a.b.1.17
2-197-1.1-c3-0-16 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.27519$ Modular form 197.4.a.b.1.7
2-197-1.1-c3-0-17 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.28556$ Modular form 197.4.a.b.1.8
2-197-1.1-c3-0-18 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.31013$ Modular form 197.4.a.a.1.5
2-197-1.1-c3-0-19 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.39370$ Modular form 197.4.a.b.1.12
2-197-1.1-c3-0-2 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.522313$ Modular form 197.4.a.b.1.10
2-197-1.1-c3-0-20 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.39555$ Modular form 197.4.a.a.1.10
2-197-1.1-c3-0-21 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.51536$ Modular form 197.4.a.a.1.11
2-197-1.1-c3-0-22 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.54993$ Modular form 197.4.a.b.1.25
2-197-1.1-c3-0-23 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.60124$ Modular form 197.4.a.a.1.6
2-197-1.1-c3-0-24 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.63735$ Modular form 197.4.a.b.1.1
2-197-1.1-c3-0-25 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.71428$ Modular form 197.4.a.b.1.14
2-197-1.1-c3-0-26 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.72099$ Modular form 197.4.a.a.1.12
2-197-1.1-c3-0-27 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.77105$ Modular form 197.4.a.a.1.3
2-197-1.1-c3-0-28 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.80698$ Modular form 197.4.a.b.1.19
2-197-1.1-c3-0-29 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.86843$ Modular form 197.4.a.b.1.23
2-197-1.1-c3-0-3 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.556162$ Modular form 197.4.a.b.1.2
2-197-1.1-c3-0-30 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.94790$ Modular form 197.4.a.a.1.2
2-197-1.1-c3-0-31 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.00876$ Modular form 197.4.a.a.1.9
2-197-1.1-c3-0-32 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $2.03533$ Modular form 197.4.a.b.1.27
2-197-1.1-c3-0-33 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.04667$ Modular form 197.4.a.a.1.4
2-197-1.1-c3-0-34 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.14294$ Modular form 197.4.a.a.1.8
2-197-1.1-c3-0-35 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $2.14817$ Modular form 197.4.a.b.1.21
2-197-1.1-c3-0-36 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $2.17020$ Modular form 197.4.a.b.1.22
2-197-1.1-c3-0-37 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $2.27095$ Modular form 197.4.a.b.1.24
2-197-1.1-c3-0-38 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.29919$ Modular form 197.4.a.a.1.19
2-197-1.1-c3-0-39 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.39230$ Modular form 197.4.a.a.1.13
2-197-1.1-c3-0-4 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.593551$ Modular form 197.4.a.b.1.11
2-197-1.1-c3-0-40 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.41190$ Modular form 197.4.a.a.1.16
2-197-1.1-c3-0-41 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $2.45592$ Modular form 197.4.a.b.1.26
2-197-1.1-c3-0-42 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.48665$ Modular form 197.4.a.a.1.17
2-197-1.1-c3-0-43 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.72575$ Modular form 197.4.a.a.1.22
2-197-1.1-c3-0-44 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.79202$ Modular form 197.4.a.a.1.14
2-197-1.1-c3-0-45 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.83484$ Modular form 197.4.a.a.1.18
2-197-1.1-c3-0-46 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.87412$ Modular form 197.4.a.a.1.21
2-197-1.1-c3-0-47 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.92335$ Modular form 197.4.a.a.1.20
2-197-1.1-c3-0-48 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.96311$ Modular form 197.4.a.a.1.15
2-197-1.1-c3-0-5 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.685962$ Modular form 197.4.a.b.1.3
2-197-1.1-c3-0-6 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.745775$ Modular form 197.4.a.b.1.9
2-197-1.1-c3-0-7 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.763663$ Modular form 197.4.a.b.1.4
2-197-1.1-c3-0-8 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.791089$ Modular form 197.4.a.b.1.18
2-197-1.1-c3-0-9 $3.40$ $11.6$ $2$ $197$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.934309$ Modular form 197.4.a.b.1.13
2-197-197.10-c3-0-0 $3.40$ $11.6$ $2$ $197$ 197.10 $3.0$ $3$ ✓ ✓ $-0.0953$ $0$ $0.0786759$ Modular form 197.4.h.a.10.5
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