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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
2-539-1.1-c1-0-0 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.465917$ Modular form 539.2.a.k.1.1
2-539-1.1-c1-0-1 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.470874$ Modular form 539.2.a.l.1.1
2-539-1.1-c1-0-10 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.12730$ Modular form 539.2.a.i.1.2
2-539-1.1-c1-0-11 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.23372$ Modular form 539.2.a.g.1.1
2-539-1.1-c1-0-12 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.30212$ Modular form 539.2.a.k.1.2
2-539-1.1-c1-0-13 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.39207$ Modular form 539.2.a.l.1.2
2-539-1.1-c1-0-14 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.54280$ Modular form 539.2.a.j.1.1
2-539-1.1-c1-0-15 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $1.58751$ Elliptic curve 539.c Modular form 539.2.a.c Modular form 539.2.a.c.1.1
2-539-1.1-c1-0-16 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.69743$ Modular form 539.2.a.e.1.1
2-539-1.1-c1-0-17 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.77516$ Modular form 539.2.a.l.1.6
2-539-1.1-c1-0-18 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.78477$ Modular form 539.2.a.h.1.1
2-539-1.1-c1-0-19 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.80626$ Modular form 539.2.a.k.1.3
2-539-1.1-c1-0-2 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.598179$ Modular form 539.2.a.l.1.5
2-539-1.1-c1-0-20 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.87096$ Modular form 539.2.a.l.1.9
2-539-1.1-c1-0-21 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.88740$ Elliptic curve 539.a Modular form 539.2.a.a Modular form 539.2.a.a.1.1
2-539-1.1-c1-0-22 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.98196$ Modular form 539.2.a.j.1.3
2-539-1.1-c1-0-23 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.05077$ Modular form 539.2.a.i.1.3
2-539-1.1-c1-0-24 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.06315$ Modular form 539.2.a.e.1.2
2-539-1.1-c1-0-25 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.11051$ Modular form 539.2.a.g.1.2
2-539-1.1-c1-0-26 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.20053$ Elliptic curve 539.d Modular form 539.2.a.d Modular form 539.2.a.d.1.1
2-539-1.1-c1-0-27 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.24655$ Modular form 539.2.a.l.1.8
2-539-1.1-c1-0-28 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.25386$ Modular form 539.2.a.l.1.10
2-539-1.1-c1-0-29 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.26615$ Modular form 539.2.a.f.1.2
2-539-1.1-c1-0-3 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $0.708130$ Elliptic curve 539.b Modular form 539.2.a.b Modular form 539.2.a.b.1.1
2-539-1.1-c1-0-30 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.27474$ Modular form 539.2.a.k.1.4
2-539-1.1-c1-0-31 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.47840$ Modular form 539.2.a.h.1.3
2-539-1.1-c1-0-32 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.71504$ Modular form 539.2.a.h.1.2
2-539-1.1-c1-0-33 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.80179$ Modular form 539.2.a.g.1.3
2-539-1.1-c1-0-4 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.779021$ Modular form 539.2.a.f.1.1
2-539-1.1-c1-0-5 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.847057$ Modular form 539.2.a.i.1.1
2-539-1.1-c1-0-6 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.923699$ Modular form 539.2.a.j.1.2
2-539-1.1-c1-0-7 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.934402$ Modular form 539.2.a.l.1.3
2-539-1.1-c1-0-8 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.01383$ Modular form 539.2.a.l.1.4
2-539-1.1-c1-0-9 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.08292$ Modular form 539.2.a.l.1.7
2-539-11.3-c1-0-0 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.241$ $0$ $0.386190$ Modular form 539.2.f.f.344.3
2-539-11.3-c1-0-1 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.178$ $0$ $0.475820$ Modular form 539.2.f.e.344.1
2-539-11.3-c1-0-10 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.128$ $0$ $1.18022$ Modular form 539.2.f.d.344.2
2-539-11.3-c1-0-11 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.185$ $0$ $1.20475$ Modular form 539.2.f.a.344.1
2-539-11.3-c1-0-12 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.305$ $0$ $1.21337$ Modular form 539.2.f.i.344.8
2-539-11.3-c1-0-13 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.101$ $0$ $1.23039$ Modular form 539.2.f.h.344.3
2-539-11.3-c1-0-14 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.0789$ $0$ $1.24229$ Modular form 539.2.f.i.344.3
2-539-11.3-c1-0-15 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.241$ $0$ $1.29238$ Modular form 539.2.f.f.344.4
2-539-11.3-c1-0-16 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.176$ $0$ $1.34078$ Modular form 539.2.f.h.344.1
2-539-11.3-c1-0-17 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.105$ $0$ $1.39586$ Modular form 539.2.f.e.344.3
2-539-11.3-c1-0-18 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.194$ $0$ $1.42682$ Modular form 539.2.f.f.344.1
2-539-11.3-c1-0-19 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.0675$ $0$ $1.44786$ Modular form 539.2.f.i.344.9
2-539-11.3-c1-0-2 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.467$ $0$ $0.534514$ Modular form 539.2.f.i.344.6
2-539-11.3-c1-0-20 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.0675$ $0$ $1.46149$ Modular form 539.2.f.i.344.10
2-539-11.3-c1-0-21 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.263$ $0$ $1.62730$ Modular form 539.2.f.h.344.2
2-539-11.3-c1-0-22 $2.07$ $4.30$ $2$ $7^{2} \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.323$ $0$ $1.70383$ Modular form 539.2.f.g.344.1
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