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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
2-500-100.11-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 100.11 $0.0$ 0 ✓ ✓ $0.179$ $0$ $2.50481$ Modular form 500.1.j.a.51.1
2-500-100.19-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 100.19 $0.0$ 0 ✓ ✓ $-0.0981$ $0$ $1.27399$ Modular form 500.1.h.a.99.1
2-500-100.19-c0-0-1 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 100.19 $0.0$ 0 ✓ ✓ $0.0781$ $0$ $2.31310$ Modular form 500.1.h.a.99.2
2-500-100.31-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 100.31 $0.0$ 0 ✓ ✓ $0.240$ $0$ $1.83690$ Modular form 500.1.j.a.151.1
2-500-100.39-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 100.39 $0.0$ 0 ✓ ✓ $0.0918$ $0$ $1.41330$ Modular form 500.1.h.a.199.1
2-500-100.39-c0-0-1 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 100.39 $0.0$ 0 ✓ ✓ $-0.231$ $0$ $1.53932$ Modular form 500.1.h.a.199.2
2-500-100.59-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 100.59 $0.0$ 0 ✓ ✓ $-0.0918$ $0$ $1.55826$ Modular form 500.1.h.a.299.1
2-500-100.59-c0-0-1 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 100.59 $0.0$ 0 ✓ ✓ $0.231$ $0$ $2.37563$ Modular form 500.1.h.a.299.2
2-500-100.71-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 100.71 $0.0$ 0 ✓ ✓ $-0.240$ $0$ $1.22639$ Modular form 500.1.j.a.351.1
2-500-100.79-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 100.79 $0.0$ 0 ✓ ✓ $0.0981$ $0$ $1.61333$ Modular form 500.1.h.a.399.1
2-500-100.79-c0-0-1 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 100.79 $0.0$ 0 ✓ ✓ $-0.0781$ $0$ $2.06982$ Modular form 500.1.h.a.399.2
2-500-100.91-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 100.91 $0.0$ 0 ✓ ✓ $-0.179$ $0$ $1.68175$ Modular form 500.1.j.a.451.1
2-500-20.19-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 20.19 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.36592$ Modular form 500.1.d.a.499.1
2-500-20.19-c0-0-1 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 20.19 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.69656$ Artin representation 2.500.5t2.a.a Modular form 500.1.d.b.499.1
2-500-20.19-c0-0-2 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 20.19 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.90018$ Modular form 500.1.d.a.499.2
2-500-20.19-c0-0-3 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 20.19 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $2.41401$ Artin representation 2.500.5t2.a.b Modular form 500.1.d.b.499.2
2-500-4.3-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 4.3 $0.0$ 0 ✓ ✓ $0.5$ $0$ $1.06921$ Modular form 500.1.b.a.251.4
2-500-4.3-c0-0-1 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 4.3 $0.0$ 0 ✓ ✓ $0$ $0$ $1.25276$ Modular form 500.1.b.a.251.2
2-500-4.3-c0-0-2 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 4.3 $0.0$ 0 ✓ ✓ $0$ $0$ $2.00692$ Modular form 500.1.b.a.251.3
2-500-4.3-c0-0-3 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 4.3 $0.0$ 0 ✓ ✓ $0.5$ $0$ $3.07305$ Modular form 500.1.b.a.251.1
2-500-500.11-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.11 $0.0$ 0 ✓ ✓ $0.215$ $0$ $2.68747$ Modular form 500.1.p.a.11.1
2-500-500.111-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.111 $0.0$ 0 ✓ ✓ $0.0160$ $0$ $1.18729$ Modular form 500.1.p.a.111.1
2-500-500.131-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.131 $0.0$ 0 ✓ ✓ $-0.0120$ $0$ $2.30116$ Modular form 500.1.p.a.131.1
2-500-500.171-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.171 $0.0$ 0 ✓ ✓ $-0.188$ $0$ $1.72366$ Modular form 500.1.p.a.171.1
2-500-500.191-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.191 $0.0$ 0 ✓ ✓ $0.183$ $0$ $2.55255$ Modular form 500.1.p.a.191.1
2-500-500.211-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.211 $0.0$ 0 ✓ ✓ $0.215$ $0$ $2.02917$ Modular form 500.1.p.a.211.1
2-500-500.231-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.231 $0.0$ 0 ✓ ✓ $0.188$ $0$ $2.19630$ Modular form 500.1.p.a.231.1
2-500-500.271-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.271 $0.0$ 0 ✓ ✓ $0.0120$ $0$ $2.01781$ Modular form 500.1.p.a.271.1
2-500-500.291-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.291 $0.0$ 0 ✓ ✓ $0.183$ $0$ $1.79165$ Modular form 500.1.p.a.291.1
2-500-500.31-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.31 $0.0$ 0 ✓ ✓ $-0.412$ $0$ $0.875338$ Modular form 500.1.p.a.31.1
2-500-500.311-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.311 $0.0$ 0 ✓ ✓ $-0.183$ $0$ $1.63327$ Modular form 500.1.p.a.311.1
2-500-500.331-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.331 $0.0$ 0 ✓ ✓ $0.188$ $0$ $1.57861$ Modular form 500.1.p.a.331.1
2-500-500.371-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.371 $0.0$ 0 ✓ ✓ $0.412$ $0$ $2.62524$ Modular form 500.1.p.a.371.1
2-500-500.391-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.391 $0.0$ 0 ✓ ✓ $-0.215$ $0$ $0.813853$ Modular form 500.1.p.a.391.1
2-500-500.411-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.411 $0.0$ 0 ✓ ✓ $-0.183$ $0$ $1.57786$ Modular form 500.1.p.a.411.1
2-500-500.431-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.431 $0.0$ 0 ✓ ✓ $-0.0120$ $0$ $1.68248$ Modular form 500.1.p.a.431.1
2-500-500.471-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.471 $0.0$ 0 ✓ ✓ $0.0120$ $0$ $1.50190$ Modular form 500.1.p.a.471.1
2-500-500.491-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.491 $0.0$ 0 ✓ ✓ $-0.0160$ $0$ $1.77834$ Modular form 500.1.p.a.491.1
2-500-500.71-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.71 $0.0$ 0 ✓ ✓ $-0.188$ $0$ $1.15237$ Modular form 500.1.p.a.71.1
2-500-500.91-c0-0-0 $0.499$ $0.249$ $2$ $2^{2} \cdot 5^{3}$ 500.91 $0.0$ 0 ✓ ✓ $-0.215$ $0$ $1.72276$ Modular form 500.1.p.a.91.1
2-500-1.1-c1-0-0 $1.99$ $3.99$ $2$ $2^{2} \cdot 5^{3}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.792757$ Modular form 500.2.a.c.1.1
2-500-1.1-c1-0-1 $1.99$ $3.99$ $2$ $2^{2} \cdot 5^{3}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.925094$ Modular form 500.2.a.c.1.2
2-500-1.1-c1-0-2 $1.99$ $3.99$ $2$ $2^{2} \cdot 5^{3}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.26607$ Modular form 500.2.a.b.1.1
2-500-1.1-c1-0-3 $1.99$ $3.99$ $2$ $2^{2} \cdot 5^{3}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.50943$ Modular form 500.2.a.b.1.2
2-500-1.1-c1-0-4 $1.99$ $3.99$ $2$ $2^{2} \cdot 5^{3}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.69036$ Modular form 500.2.a.c.1.3
2-500-1.1-c1-0-5 $1.99$ $3.99$ $2$ $2^{2} \cdot 5^{3}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.84364$ Modular form 500.2.a.c.1.4
2-500-1.1-c1-0-6 $1.99$ $3.99$ $2$ $2^{2} \cdot 5^{3}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.05788$ Modular form 500.2.a.a.1.1
2-500-1.1-c1-0-7 $1.99$ $3.99$ $2$ $2^{2} \cdot 5^{3}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.60231$ Modular form 500.2.a.a.1.2
2-500-100.23-c1-0-0 $1.99$ $3.99$ $2$ $2^{2} \cdot 5^{3}$ 100.23 $1.0$ $1$ ✓ ✓ $0.0181$ $0$ $0.657545$ Modular form 500.2.l.d.343.3
2-500-100.23-c1-0-1 $1.99$ $3.99$ $2$ $2^{2} \cdot 5^{3}$ 100.23 $1.0$ $1$ ✓ ✓ $-0.412$ $0$ $0.842762$ Modular form 500.2.l.f.343.4
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