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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-c1-0-0 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.947419$ Modular form 197.2.a.c.1.4
2-197-1.1-c1-0-1 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.30354$ Modular form 197.2.a.c.1.1
2-197-1.1-c1-0-10 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.52687$ Modular form 197.2.a.c.1.8
2-197-1.1-c1-0-11 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.85993$ Modular form 197.2.a.c.1.10
2-197-1.1-c1-0-12 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.88828$ Modular form 197.2.a.b.1.3
2-197-1.1-c1-0-13 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.98265$ Modular form 197.2.a.b.1.2
2-197-1.1-c1-0-14 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $3.22931$ Modular form 197.2.a.b.1.4
2-197-1.1-c1-0-15 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $3.71400$ Modular form 197.2.a.b.1.5
2-197-1.1-c1-0-2 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.49549$ Modular form 197.2.a.c.1.3
2-197-1.1-c1-0-3 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.69597$ Modular form 197.2.a.c.1.5
2-197-1.1-c1-0-4 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.81345$ Modular form 197.2.a.b.1.1
2-197-1.1-c1-0-5 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.97674$ Modular form 197.2.a.c.1.2
2-197-1.1-c1-0-6 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.10030$ Modular form 197.2.a.c.1.6
2-197-1.1-c1-0-7 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.19232$ Modular form 197.2.a.c.1.9
2-197-1.1-c1-0-8 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.33277$ Elliptic curve 197.a Modular form 197.2.a.a Modular form 197.2.a.a.1.1
2-197-1.1-c1-0-9 $1.25$ $1.57$ $2$ $197$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.47236$ Modular form 197.2.a.c.1.7
2-197-197.10-c1-0-0 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $-0.159$ $0$ $0.105275$ Modular form 197.2.h.a.10.4
2-197-197.10-c1-0-1 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $0.266$ $0$ $0.124919$ Modular form 197.2.h.a.10.15
2-197-197.10-c1-0-10 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $0.271$ $0$ $2.36922$ Modular form 197.2.h.a.10.2
2-197-197.10-c1-0-11 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $0.312$ $0$ $2.40784$ Modular form 197.2.h.a.10.9
2-197-197.10-c1-0-12 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $0.409$ $0$ $2.50344$ Modular form 197.2.h.a.10.3
2-197-197.10-c1-0-13 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $0.151$ $0$ $2.51077$ Modular form 197.2.h.a.10.6
2-197-197.10-c1-0-14 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $-0.476$ $0$ $2.99505$ Modular form 197.2.h.a.10.5
2-197-197.10-c1-0-15 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $-0.191$ $0$ $4.16315$ Modular form 197.2.h.a.10.1
2-197-197.10-c1-0-2 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $-0.484$ $0$ $0.294512$ Modular form 197.2.h.a.10.11
2-197-197.10-c1-0-3 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $-0.398$ $0$ $1.39535$ Modular form 197.2.h.a.10.14
2-197-197.10-c1-0-4 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $-0.199$ $0$ $1.65761$ Modular form 197.2.h.a.10.13
2-197-197.10-c1-0-5 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $-0.188$ $0$ $1.96615$ Modular form 197.2.h.a.10.12
2-197-197.10-c1-0-6 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $-0.391$ $0$ $2.00504$ Modular form 197.2.h.a.10.16
2-197-197.10-c1-0-7 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $0.149$ $0$ $2.03277$ Modular form 197.2.h.a.10.8
2-197-197.10-c1-0-8 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $0.0317$ $0$ $2.05613$ Modular form 197.2.h.a.10.7
2-197-197.10-c1-0-9 $1.25$ $1.57$ $2$ $197$ 197.10 $1.0$ $1$ ✓ ✓ $-0.0236$ $0$ $2.15683$ Modular form 197.2.h.a.10.10
2-197-197.100-c1-0-0 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $-0.404$ $0$ $0.230420$ Modular form 197.2.g.a.100.10
2-197-197.100-c1-0-1 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $-0.0741$ $0$ $0.541379$ Modular form 197.2.g.a.100.5
2-197-197.100-c1-0-10 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $0.304$ $0$ $2.19104$ Modular form 197.2.g.a.100.6
2-197-197.100-c1-0-11 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $0.0549$ $0$ $2.36482$ Modular form 197.2.g.a.100.13
2-197-197.100-c1-0-12 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $0.0313$ $0$ $2.59213$ Modular form 197.2.g.a.100.15
2-197-197.100-c1-0-13 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $0.306$ $0$ $2.72477$ Modular form 197.2.g.a.100.11
2-197-197.100-c1-0-14 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $0.240$ $0$ $3.17291$ Modular form 197.2.g.a.100.14
2-197-197.100-c1-0-2 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $-0.487$ $0$ $0.570663$ Modular form 197.2.g.a.100.2
2-197-197.100-c1-0-3 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $-0.334$ $0$ $0.904666$ Modular form 197.2.g.a.100.7
2-197-197.100-c1-0-4 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $0.0516$ $0$ $1.43511$ Modular form 197.2.g.a.100.8
2-197-197.100-c1-0-5 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $-0.0414$ $0$ $1.66553$ Modular form 197.2.g.a.100.4
2-197-197.100-c1-0-6 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $-0.145$ $0$ $1.70194$ Modular form 197.2.g.a.100.12
2-197-197.100-c1-0-7 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $0.305$ $0$ $1.90757$ Modular form 197.2.g.a.100.1
2-197-197.100-c1-0-8 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $0.412$ $0$ $1.92558$ Modular form 197.2.g.a.100.3
2-197-197.100-c1-0-9 $1.25$ $1.57$ $2$ $197$ 197.100 $1.0$ $1$ ✓ ✓ $-0.0603$ $0$ $1.94170$ Modular form 197.2.g.a.100.9
2-197-197.101-c1-0-0 $1.25$ $1.57$ $2$ $197$ 197.101 $1.0$ $1$ ✓ ✓ $-0.245$ $0$ $0.0186456$ Modular form 197.2.g.a.101.2
2-197-197.101-c1-0-1 $1.25$ $1.57$ $2$ $197$ 197.101 $1.0$ $1$ ✓ ✓ $0.494$ $0$ $0.142294$ Modular form 197.2.g.a.101.12
2-197-197.101-c1-0-10 $1.25$ $1.57$ $2$ $197$ 197.101 $1.0$ $1$ ✓ ✓ $0.255$ $0$ $2.35617$ Modular form 197.2.g.a.101.8
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