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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
2-875-35.34-c0-0-0 $0.660$ $0.436$ $2$ $5^{3} \cdot 7$ 35.34 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.29464$ Artin representation 2.875.5t2.a.b Modular form 875.1.c.a.874.1
2-875-35.34-c0-0-1 $0.660$ $0.436$ $2$ $5^{3} \cdot 7$ 35.34 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.39370$ Modular form 875.1.c.b.874.1
2-875-35.34-c0-0-2 $0.660$ $0.436$ $2$ $5^{3} \cdot 7$ 35.34 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.97610$ Artin representation 2.875.5t2.a.a Modular form 875.1.c.a.874.2
2-875-35.34-c0-0-3 $0.660$ $0.436$ $2$ $5^{3} \cdot 7$ 35.34 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $2.16228$ Modular form 875.1.c.b.874.2
2-875-7.6-c0-0-0 $0.660$ $0.436$ $2$ $5^{3} \cdot 7$ 7.6 $0.0$ 0 ✓ ✓ $0.5$ $0$ $0.519222$ Modular form 875.1.d.a.251.4
2-875-7.6-c0-0-1 $0.660$ $0.436$ $2$ $5^{3} \cdot 7$ 7.6 $0.0$ 0 ✓ ✓ $0$ $0$ $1.16340$ Modular form 875.1.d.a.251.2
2-875-7.6-c0-0-2 $0.660$ $0.436$ $2$ $5^{3} \cdot 7$ 7.6 $0.0$ 0 ✓ ✓ $0$ $0$ $1.41170$ Modular form 875.1.d.a.251.3
2-875-7.6-c0-0-3 $0.660$ $0.436$ $2$ $5^{3} \cdot 7$ 7.6 $0.0$ 0 ✓ ✓ $0.5$ $0$ $2.68996$ Modular form 875.1.d.a.251.1
2-875-1.1-c1-0-0 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.474004$ Modular form 875.2.a.j.1.2
2-875-1.1-c1-0-1 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.501970$ Modular form 875.2.a.j.1.3
2-875-1.1-c1-0-10 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.847546$ Modular form 875.2.a.c.1.1
2-875-1.1-c1-0-11 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.858255$ Modular form 875.2.a.g.1.2
2-875-1.1-c1-0-12 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.937385$ Modular form 875.2.a.g.1.4
2-875-1.1-c1-0-13 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.969226$ Modular form 875.2.a.g.1.1
2-875-1.1-c1-0-14 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.978282$ Modular form 875.2.a.j.1.5
2-875-1.1-c1-0-15 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.07177$ Modular form 875.2.a.g.1.5
2-875-1.1-c1-0-16 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.14369$ Modular form 875.2.a.h.1.3
2-875-1.1-c1-0-17 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.15480$ Modular form 875.2.a.j.1.4
2-875-1.1-c1-0-18 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.23083$ Modular form 875.2.a.e.1.2
2-875-1.1-c1-0-19 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.23826$ Modular form 875.2.a.i.1.3
2-875-1.1-c1-0-2 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.569135$ Modular form 875.2.a.j.1.1
2-875-1.1-c1-0-20 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.24472$ Modular form 875.2.a.f.1.1
2-875-1.1-c1-0-21 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.26105$ Modular form 875.2.a.i.1.2
2-875-1.1-c1-0-22 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.26541$ Modular form 875.2.a.f.1.4
2-875-1.1-c1-0-23 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.29776$ Modular form 875.2.a.j.1.7
2-875-1.1-c1-0-24 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.31121$ Modular form 875.2.a.h.1.1
2-875-1.1-c1-0-25 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.44545$ Modular form 875.2.a.g.1.3
2-875-1.1-c1-0-26 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.52109$ Modular form 875.2.a.b.1.2
2-875-1.1-c1-0-27 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.54253$ Modular form 875.2.a.d.1.1
2-875-1.1-c1-0-28 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.54446$ Modular form 875.2.a.i.1.6
2-875-1.1-c1-0-29 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.57722$ Modular form 875.2.a.e.1.4
2-875-1.1-c1-0-3 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.608119$ Modular form 875.2.a.h.1.2
2-875-1.1-c1-0-30 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.65670$ Modular form 875.2.a.h.1.6
2-875-1.1-c1-0-31 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.68202$ Modular form 875.2.a.e.1.1
2-875-1.1-c1-0-32 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.72705$ Modular form 875.2.a.a.1.1
2-875-1.1-c1-0-33 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.80420$ Modular form 875.2.a.f.1.3
2-875-1.1-c1-0-34 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.95841$ Modular form 875.2.a.e.1.6
2-875-1.1-c1-0-35 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.96625$ Modular form 875.2.a.i.1.8
2-875-1.1-c1-0-36 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.00290$ Modular form 875.2.a.h.1.5
2-875-1.1-c1-0-37 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.08102$ Modular form 875.2.a.f.1.2
2-875-1.1-c1-0-38 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.08209$ Modular form 875.2.a.i.1.7
2-875-1.1-c1-0-39 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.09800$ Modular form 875.2.a.c.1.2
2-875-1.1-c1-0-4 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.641625$ Modular form 875.2.a.i.1.5
2-875-1.1-c1-0-40 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.09962$ Modular form 875.2.a.e.1.3
2-875-1.1-c1-0-41 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.10321$ Modular form 875.2.a.g.1.6
2-875-1.1-c1-0-42 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.20237$ Modular form 875.2.a.j.1.8
2-875-1.1-c1-0-43 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.21542$ Modular form 875.2.a.a.1.2
2-875-1.1-c1-0-44 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.30871$ Modular form 875.2.a.d.1.2
2-875-1.1-c1-0-45 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.38067$ Modular form 875.2.a.f.1.5
2-875-1.1-c1-0-46 $2.64$ $6.98$ $2$ $5^{3} \cdot 7$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.42877$ Modular form 875.2.a.e.1.5
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