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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
2-2e9-1.1-c1-0-0 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.607881$ Modular form 512.2.a.g.1.1
2-2e9-1.1-c1-0-1 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.976243$ Modular form 512.2.a.d.1.1
2-2e9-1.1-c1-0-10 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.86215$ Modular form 512.2.a.f.1.2
2-2e9-1.1-c1-0-11 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.00670$ Modular form 512.2.a.b.1.1
2-2e9-1.1-c1-0-12 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.20310$ Modular form 512.2.a.c.1.1
2-2e9-1.1-c1-0-13 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.27097$ Modular form 512.2.a.a.1.2
2-2e9-1.1-c1-0-14 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.51934$ Modular form 512.2.a.c.1.2
2-2e9-1.1-c1-0-15 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.73634$ Modular form 512.2.a.b.1.2
2-2e9-1.1-c1-0-2 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.12736$ Modular form 512.2.a.e.1.1
2-2e9-1.1-c1-0-3 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.21158$ Modular form 512.2.a.g.1.2
2-2e9-1.1-c1-0-4 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.34921$ Modular form 512.2.a.f.1.1
2-2e9-1.1-c1-0-5 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.50430$ Modular form 512.2.a.g.1.3
2-2e9-1.1-c1-0-6 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.68277$ Modular form 512.2.a.e.1.2
2-2e9-1.1-c1-0-7 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.72627$ Modular form 512.2.a.a.1.1
2-2e9-1.1-c1-0-8 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.84922$ Modular form 512.2.a.g.1.4
2-2e9-1.1-c1-0-9 $2.02$ $4.08$ $2$ $2^{9}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.85171$ Modular form 512.2.a.d.1.2
2-2e9-128.101-c1-0-0 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $-0.388$ $0$ $0.219446$ Modular form 512.2.k.a.497.7
2-2e9-128.101-c1-0-1 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $-0.435$ $0$ $0.370249$ Modular form 512.2.k.a.497.6
2-2e9-128.101-c1-0-10 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $0.0876$ $0$ $1.73834$ Modular form 512.2.k.a.497.12
2-2e9-128.101-c1-0-11 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $0.0613$ $0$ $1.90405$ Modular form 512.2.k.a.497.14
2-2e9-128.101-c1-0-12 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $0.195$ $0$ $1.90703$ Modular form 512.2.k.a.497.10
2-2e9-128.101-c1-0-13 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $0.208$ $0$ $2.32110$ Modular form 512.2.k.a.497.15
2-2e9-128.101-c1-0-14 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $0.480$ $0$ $2.80500$ Modular form 512.2.k.a.497.11
2-2e9-128.101-c1-0-2 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $-0.271$ $0$ $0.382373$ Modular form 512.2.k.a.497.2
2-2e9-128.101-c1-0-3 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $-0.265$ $0$ $0.614366$ Modular form 512.2.k.a.497.9
2-2e9-128.101-c1-0-4 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $-0.191$ $0$ $1.02484$ Modular form 512.2.k.a.497.1
2-2e9-128.101-c1-0-5 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $0.0909$ $0$ $1.07370$ Modular form 512.2.k.a.497.4
2-2e9-128.101-c1-0-6 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $-0.155$ $0$ $1.10092$ Modular form 512.2.k.a.497.8
2-2e9-128.101-c1-0-7 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $0.00876$ $0$ $1.29007$ Modular form 512.2.k.a.497.5
2-2e9-128.101-c1-0-8 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $-0.0590$ $0$ $1.36309$ Modular form 512.2.k.a.497.13
2-2e9-128.101-c1-0-9 $2.02$ $4.08$ $2$ $2^{9}$ 128.101 $1.0$ $1$ ✓ ✓ $0.266$ $0$ $1.54364$ Modular form 512.2.k.a.497.3
2-2e9-128.109-c1-0-0 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $-0.480$ $0$ $0.271463$ Modular form 512.2.k.a.273.11
2-2e9-128.109-c1-0-1 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $-0.266$ $0$ $0.317180$ Modular form 512.2.k.a.273.3
2-2e9-128.109-c1-0-10 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $0.155$ $0$ $1.90107$ Modular form 512.2.k.a.273.8
2-2e9-128.109-c1-0-11 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $0.388$ $0$ $1.97415$ Modular form 512.2.k.a.273.7
2-2e9-128.109-c1-0-12 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $0.0590$ $0$ $1.97693$ Modular form 512.2.k.a.273.13
2-2e9-128.109-c1-0-13 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $0.265$ $0$ $2.06530$ Modular form 512.2.k.a.273.9
2-2e9-128.109-c1-0-14 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $0.435$ $0$ $2.49989$ Modular form 512.2.k.a.273.6
2-2e9-128.109-c1-0-2 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $-0.0909$ $0$ $0.623165$ Modular form 512.2.k.a.273.4
2-2e9-128.109-c1-0-3 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $-0.195$ $0$ $1.04073$ Modular form 512.2.k.a.273.10
2-2e9-128.109-c1-0-4 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $-0.00876$ $0$ $1.17570$ Modular form 512.2.k.a.273.5
2-2e9-128.109-c1-0-5 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $0.271$ $0$ $1.24965$ Modular form 512.2.k.a.273.2
2-2e9-128.109-c1-0-6 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $-0.208$ $0$ $1.26953$ Modular form 512.2.k.a.273.15
2-2e9-128.109-c1-0-7 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $0.191$ $0$ $1.33626$ Modular form 512.2.k.a.273.1
2-2e9-128.109-c1-0-8 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $-0.0876$ $0$ $1.48334$ Modular form 512.2.k.a.273.12
2-2e9-128.109-c1-0-9 $2.02$ $4.08$ $2$ $2^{9}$ 128.109 $1.0$ $1$ ✓ ✓ $-0.0613$ $0$ $1.76945$ Modular form 512.2.k.a.273.14
2-2e9-128.117-c1-0-0 $2.02$ $4.08$ $2$ $2^{9}$ 128.117 $1.0$ $1$ ✓ ✓ $0.355$ $0$ $0.149819$ Modular form 512.2.k.a.305.1
2-2e9-128.117-c1-0-1 $2.02$ $4.08$ $2$ $2^{9}$ 128.117 $1.0$ $1$ ✓ ✓ $-0.388$ $0$ $0.359324$ Modular form 512.2.k.a.305.9
2-2e9-128.117-c1-0-10 $2.02$ $4.08$ $2$ $2^{9}$ 128.117 $1.0$ $1$ ✓ ✓ $0.393$ $0$ $1.79297$ Modular form 512.2.k.a.305.6
2-2e9-128.117-c1-0-11 $2.02$ $4.08$ $2$ $2^{9}$ 128.117 $1.0$ $1$ ✓ ✓ $0.135$ $0$ $1.96701$ Modular form 512.2.k.a.305.11
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