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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
2-997-1.1-c1-0-0 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.504851$ Modular form 997.2.a.h.1.25
2-997-1.1-c1-0-1 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.552115$ Modular form 997.2.a.h.1.12
2-997-1.1-c1-0-10 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.788065$ Modular form 997.2.a.h.1.13
2-997-1.1-c1-0-11 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.808882$ Modular form 997.2.a.h.1.1
2-997-1.1-c1-0-12 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $0.841561$ Modular form 997.2.a.f.1.1
2-997-1.1-c1-0-13 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.847131$ Modular form 997.2.a.h.1.15
2-997-1.1-c1-0-14 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.852589$ Modular form 997.2.a.h.1.21
2-997-1.1-c1-0-15 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $0.936358$ Modular form 997.2.a.g.1.11
2-997-1.1-c1-0-16 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.07501$ Modular form 997.2.a.h.1.4
2-997-1.1-c1-0-17 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.11093$ Modular form 997.2.a.h.1.19
2-997-1.1-c1-0-18 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.12194$ Modular form 997.2.a.h.1.30
2-997-1.1-c1-0-19 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.14901$ Modular form 997.2.a.g.1.3
2-997-1.1-c1-0-2 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.566773$ Modular form 997.2.a.h.1.17
2-997-1.1-c1-0-20 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.15510$ Modular form 997.2.a.h.1.14
2-997-1.1-c1-0-21 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.18444$ Modular form 997.2.a.h.1.10
2-997-1.1-c1-0-22 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.18633$ Modular form 997.2.a.h.1.37
2-997-1.1-c1-0-23 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.19420$ Modular form 997.2.a.e.1.2
2-997-1.1-c1-0-24 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.22125$ Modular form 997.2.a.d.1.1
2-997-1.1-c1-0-25 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.23309$ Modular form 997.2.a.h.1.18
2-997-1.1-c1-0-26 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.25432$ Modular form 997.2.a.h.1.23
2-997-1.1-c1-0-27 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.26982$ Modular form 997.2.a.h.1.11
2-997-1.1-c1-0-28 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.28465$ Modular form 997.2.a.f.1.2
2-997-1.1-c1-0-29 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.28564$ Modular form 997.2.a.e.1.4
2-997-1.1-c1-0-3 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.606869$ Modular form 997.2.a.h.1.8
2-997-1.1-c1-0-30 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.30551$ Modular form 997.2.a.h.1.9
2-997-1.1-c1-0-31 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.34810$ Modular form 997.2.a.g.1.7
2-997-1.1-c1-0-32 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.36820$ Modular form 997.2.a.e.1.3
2-997-1.1-c1-0-33 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.38419$ Modular form 997.2.a.g.1.16
2-997-1.1-c1-0-34 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.39045$ Modular form 997.2.a.h.1.31
2-997-1.1-c1-0-35 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.40248$ Modular form 997.2.a.h.1.5
2-997-1.1-c1-0-36 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.40836$ Modular form 997.2.a.h.1.41
2-997-1.1-c1-0-37 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.41532$ Modular form 997.2.a.h.1.2
2-997-1.1-c1-0-38 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.47692$ Modular form 997.2.a.h.1.28
2-997-1.1-c1-0-39 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.48618$ Modular form 997.2.a.g.1.4
2-997-1.1-c1-0-4 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.655682$ Modular form 997.2.a.h.1.27
2-997-1.1-c1-0-40 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.48925$ Elliptic curve 997.b Modular form 997.2.a.b Modular form 997.2.a.b.1.1
2-997-1.1-c1-0-41 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.54610$ Modular form 997.2.a.h.1.24
2-997-1.1-c1-0-42 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.55788$ Modular form 997.2.a.g.1.14
2-997-1.1-c1-0-43 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.60430$ Modular form 997.2.a.g.1.2
2-997-1.1-c1-0-44 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.60622$ Modular form 997.2.a.h.1.16
2-997-1.1-c1-0-45 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.60853$ Modular form 997.2.a.g.1.9
2-997-1.1-c1-0-46 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.63513$ Modular form 997.2.a.h.1.35
2-997-1.1-c1-0-47 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.74432$ Modular form 997.2.a.g.1.10
2-997-1.1-c1-0-48 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.75330$ Modular form 997.2.a.e.1.1
2-997-1.1-c1-0-49 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.76932$ Modular form 997.2.a.d.1.2
2-997-1.1-c1-0-5 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.681445$ Modular form 997.2.a.h.1.6
2-997-1.1-c1-0-50 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.77247$ Modular form 997.2.a.g.1.6
2-997-1.1-c1-0-51 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.79946$ Modular form 997.2.a.h.1.26
2-997-1.1-c1-0-52 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.81522$ Modular form 997.2.a.g.1.1
2-997-1.1-c1-0-53 $2.82$ $7.96$ $2$ $997$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.81910$ Modular form 997.2.a.h.1.34
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