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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
2-575-115.114-c0-0-0 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 115.114 $0.0$ 0 ✓ ✓ $0.323$ $0$ $0.937073$ Modular form 575.1.c.b.574.6
2-575-115.114-c0-0-1 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 115.114 $0.0$ 0 ✓ ✓ $-0.323$ $0$ $1.29663$ Modular form 575.1.c.b.574.5
2-575-115.114-c0-0-2 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 115.114 $0.0$ 0 ✓ ✓ $-0.323$ $0$ $1.51211$ Modular form 575.1.c.b.574.4
2-575-115.114-c0-0-3 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 115.114 $0.0$ 0 ✓ ✓ $0.0737$ $0$ $1.68386$ Modular form 575.1.c.a.574.1
2-575-115.114-c0-0-4 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 115.114 $0.0$ 0 ✓ ✓ $-0.0737$ $0$ $1.77729$ Modular form 575.1.c.a.574.2
2-575-115.114-c0-0-5 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 115.114 $0.0$ 0 ✓ ✓ $0.323$ $0$ $2.00583$ Modular form 575.1.c.b.574.2
2-575-115.114-c0-0-6 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 115.114 $0.0$ 0 ✓ ✓ $0.323$ $0$ $2.70668$ Modular form 575.1.c.b.574.3
2-575-115.114-c0-0-7 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 115.114 $0.0$ 0 ✓ ✓ $-0.323$ $0$ $3.51092$ Modular form 575.1.c.b.574.1
2-575-23.22-c0-0-0 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 23.22 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.05692$ Artin representation 2.575.9t3.a.c Modular form 575.1.d.b.551.2
2-575-23.22-c0-0-1 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 23.22 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.12148$ Modular form 575.1.d.c.551.1
2-575-23.22-c0-0-2 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 23.22 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.62923$ Artin representation 2.575.9t3.a.a Modular form 575.1.d.b.551.1
2-575-23.22-c0-0-3 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 23.22 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.89718$ Modular form 575.1.d.c.551.2
2-575-23.22-c0-0-4 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 23.22 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $2.02466$ Modular form 575.1.d.c.551.3
2-575-23.22-c0-0-5 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 23.22 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $2.21996$ Artin representation 2.575.6t3.b Artin representation 2.575.6t3.b.a Modular form 575.1.d.a Modular form 575.1.d.a.551.1
2-575-23.22-c0-0-6 $0.535$ $0.286$ $2$ $5^{2} \cdot 23$ 23.22 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $2.52468$ Artin representation 2.575.9t3.a.b Modular form 575.1.d.b.551.3
2-575-1.1-c1-0-0 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.285013$ Modular form 575.2.a.l.1.2
2-575-1.1-c1-0-1 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.572145$ Modular form 575.2.a.k.1.4
2-575-1.1-c1-0-10 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.20005$ Modular form 575.2.a.k.1.5
2-575-1.1-c1-0-11 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.27175$ Modular form 575.2.a.j.1.1
2-575-1.1-c1-0-12 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.31465$ Modular form 575.2.a.g.1.1
2-575-1.1-c1-0-13 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.33629$ Modular form 575.2.a.h.1.1
2-575-1.1-c1-0-14 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.39515$ Elliptic curve 575.a Modular form 575.2.a.a Modular form 575.2.a.a.1.1
2-575-1.1-c1-0-15 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.45038$ Modular form 575.2.a.k.1.3
2-575-1.1-c1-0-16 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.48363$ Modular form 575.2.a.i.1.2
2-575-1.1-c1-0-17 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.48837$ Modular form 575.2.a.l.1.4
2-575-1.1-c1-0-18 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.55401$ Modular form 575.2.a.j.1.4
2-575-1.1-c1-0-19 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.56084$ Modular form 575.2.a.j.1.3
2-575-1.1-c1-0-2 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.741902$ Modular form 575.2.a.k.1.1
2-575-1.1-c1-0-20 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.71500$ Elliptic curve 575.b Modular form 575.2.a.b Modular form 575.2.a.b.1.1
2-575-1.1-c1-0-21 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.84853$ Elliptic curve 575.c Modular form 575.2.a.c Modular form 575.2.a.c.1.1
2-575-1.1-c1-0-22 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.00160$ Modular form 575.2.a.l.1.7
2-575-1.1-c1-0-23 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.03076$ Modular form 575.2.a.h.1.4
2-575-1.1-c1-0-24 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $2.05368$ Elliptic curve 575.e Modular form 575.2.a.e Modular form 575.2.a.e.1.1
2-575-1.1-c1-0-25 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.07091$ Modular form 575.2.a.k.1.6
2-575-1.1-c1-0-26 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.08583$ Modular form 575.2.a.k.1.7
2-575-1.1-c1-0-27 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.11629$ Modular form 575.2.a.i.1.1
2-575-1.1-c1-0-28 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.19820$ Modular form 575.2.a.g.1.2
2-575-1.1-c1-0-29 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.32708$ Modular form 575.2.a.f.1.2
2-575-1.1-c1-0-3 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.775286$ Modular form 575.2.a.h.1.3
2-575-1.1-c1-0-30 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.38221$ Modular form 575.2.a.f.1.1
2-575-1.1-c1-0-31 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.48372$ Modular form 575.2.a.l.1.6
2-575-1.1-c1-0-32 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.51027$ Elliptic curve 575.d Modular form 575.2.a.d Modular form 575.2.a.d.1.1
2-575-1.1-c1-0-33 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.58035$ Modular form 575.2.a.i.1.3
2-575-1.1-c1-0-34 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.73056$ Modular form 575.2.a.i.1.4
2-575-1.1-c1-0-4 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.798760$ Modular form 575.2.a.k.1.2
2-575-1.1-c1-0-5 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.803561$ Modular form 575.2.a.h.1.2
2-575-1.1-c1-0-6 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.842244$ Modular form 575.2.a.j.1.2
2-575-1.1-c1-0-7 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.944767$ Modular form 575.2.a.l.1.1
2-575-1.1-c1-0-8 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.996550$ Modular form 575.2.a.l.1.3
2-575-1.1-c1-0-9 $2.14$ $4.59$ $2$ $5^{2} \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.02145$ Modular form 575.2.a.l.1.5
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