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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
2-338-1.1-c1-0-0 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.753363$ Modular form 338.2.a.g.1.1
2-338-1.1-c1-0-1 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $1.36232$ Elliptic curve 338.b Modular form 338.2.a.b Modular form 338.2.a.b.1.1
2-338-1.1-c1-0-10 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.42154$ Elliptic curve 338.c Modular form 338.2.a.c Modular form 338.2.a.c.1.1
2-338-1.1-c1-0-11 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.87766$ Elliptic curve 338.d Modular form 338.2.a.d Modular form 338.2.a.d.1.1
2-338-1.1-c1-0-2 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.56691$ Modular form 338.2.a.h.1.1
2-338-1.1-c1-0-3 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.68280$ Modular form 338.2.a.g.1.2
2-338-1.1-c1-0-4 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $1.72818$ Elliptic curve 338.e Modular form 338.2.a.e Modular form 338.2.a.e.1.1
2-338-1.1-c1-0-5 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.82604$ Elliptic curve 338.a Modular form 338.2.a.a Modular form 338.2.a.a.1.1
2-338-1.1-c1-0-6 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.86995$ Modular form 338.2.a.g.1.3
2-338-1.1-c1-0-7 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.13123$ Modular form 338.2.a.h.1.3
2-338-1.1-c1-0-8 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.16895$ Modular form 338.2.a.h.1.2
2-338-1.1-c1-0-9 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $2.19431$ Elliptic curve 338.f Modular form 338.2.a.f Modular form 338.2.a.f.1.1
2-338-13.10-c1-0-0 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $-0.236$ $0$ $0.426362$ Modular form 338.2.e.e.23.1
2-338-13.10-c1-0-1 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $-0.404$ $0$ $0.922712$ Modular form 338.2.e.d.23.1
2-338-13.10-c1-0-10 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $0.408$ $0$ $2.46671$ Modular form 338.2.e.a.23.1
2-338-13.10-c1-0-11 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $0.207$ $0$ $2.55002$ Modular form 338.2.e.c.23.2
2-338-13.10-c1-0-12 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $0.424$ $0$ $2.82487$ Modular form 338.2.e.e.23.4
2-338-13.10-c1-0-13 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $0.481$ $0$ $2.99180$ Modular form 338.2.e.e.23.5
2-338-13.10-c1-0-2 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $-0.292$ $0$ $1.07741$ Modular form 338.2.e.c.23.1
2-338-13.10-c1-0-3 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $-0.166$ $0$ $1.36392$ Modular form 338.2.e.e.23.6
2-338-13.10-c1-0-4 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $0.196$ $0$ $1.61525$ Modular form 338.2.e.e.23.2
2-338-13.10-c1-0-5 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $0.123$ $0$ $1.66040$ Modular form 338.2.e.b.23.1
2-338-13.10-c1-0-6 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $0.0956$ $0$ $1.66997$ Modular form 338.2.e.a.23.2
2-338-13.10-c1-0-7 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $-0.0333$ $0$ $1.69760$ Modular form 338.2.e.e.23.3
2-338-13.10-c1-0-8 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $-0.0915$ $0$ $1.74981$ Modular form 338.2.e.d.23.2
2-338-13.10-c1-0-9 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.10 $1.0$ $1$ ✓ ✓ $0.123$ $0$ $1.96331$ Modular form 338.2.e.b.23.2
2-338-13.12-c1-0-0 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.12 $1.0$ $1$ ✓ ✓ $0.378$ $0$ $0.261331$ Modular form 338.2.b.d.337.4
2-338-13.12-c1-0-1 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.12 $1.0$ $1$ ✓ ✓ $-0.156$ $0$ $0.694985$ Modular form 338.2.b.b.337.1
2-338-13.12-c1-0-10 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.12 $1.0$ $1$ ✓ ✓ $0.245$ $0$ $2.44457$ Modular form 338.2.b.d.337.2
2-338-13.12-c1-0-11 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.12 $1.0$ $1$ ✓ ✓ $-0.378$ $0$ $2.72181$ Modular form 338.2.b.d.337.1
2-338-13.12-c1-0-2 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.12 $1.0$ $1$ ✓ ✓ $-0.156$ $0$ $0.859577$ Modular form 338.2.b.a.337.2
2-338-13.12-c1-0-3 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.12 $1.0$ $1$ ✓ ✓ $-0.343$ $0$ $0.955561$ Modular form 338.2.b.c.337.2
2-338-13.12-c1-0-4 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.12 $1.0$ $1$ ✓ ✓ $0.156$ $0$ $1.06052$ Modular form 338.2.b.a.337.1
2-338-13.12-c1-0-5 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.12 $1.0$ $1$ ✓ ✓ $-0.245$ $0$ $1.36532$ Modular form 338.2.b.d.337.5
2-338-13.12-c1-0-6 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.12 $1.0$ $1$ ✓ ✓ $0.0397$ $0$ $1.62083$ Modular form 338.2.b.d.337.3
2-338-13.12-c1-0-7 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.12 $1.0$ $1$ ✓ ✓ $-0.0397$ $0$ $2.10525$ Modular form 338.2.b.d.337.6
2-338-13.12-c1-0-8 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.12 $1.0$ $1$ ✓ ✓ $0.156$ $0$ $2.19789$ Modular form 338.2.b.b.337.2
2-338-13.12-c1-0-9 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.12 $1.0$ $1$ ✓ ✓ $0.343$ $0$ $2.42549$ Modular form 338.2.b.c.337.1
2-338-13.3-c1-0-0 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.3 $1.0$ $1$ ✓ ✓ $-0.133$ $0$ $0.199284$ Modular form 338.2.c.h.315.1
2-338-13.3-c1-0-1 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.3 $1.0$ $1$ ✓ ✓ $-0.345$ $0$ $0.443171$ Modular form 338.2.c.i.315.2
2-338-13.3-c1-0-10 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.3 $1.0$ $1$ ✓ ✓ $0.145$ $0$ $1.95907$ Modular form 338.2.c.i.315.1
2-338-13.3-c1-0-11 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.3 $1.0$ $1$ ✓ ✓ $0.252$ $0$ $2.16491$ Modular form 338.2.c.d.315.1
2-338-13.3-c1-0-12 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.3 $1.0$ $1$ ✓ ✓ $0.478$ $0$ $2.27473$ Modular form 338.2.c.h.315.2
2-338-13.3-c1-0-2 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.3 $1.0$ $1$ ✓ ✓ $-0.466$ $0$ $0.739495$ Modular form 338.2.c.i.315.3
2-338-13.3-c1-0-3 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.3 $1.0$ $1$ ✓ ✓ $-0.247$ $0$ $0.903123$ Modular form 338.2.c.c.315.1
2-338-13.3-c1-0-4 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.3 $1.0$ $1$ ✓ ✓ $-0.247$ $0$ $1.46212$ Modular form 338.2.c.f.315.1
2-338-13.3-c1-0-5 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.3 $1.0$ $1$ ✓ ✓ $-0.337$ $0$ $1.50951$ Modular form 338.2.c.g.315.1
2-338-13.3-c1-0-6 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.3 $1.0$ $1$ ✓ ✓ $0.162$ $0$ $1.51527$ Modular form 338.2.c.a.315.1
2-338-13.3-c1-0-7 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.3 $1.0$ $1$ ✓ ✓ $-0.0118$ $0$ $1.68535$ Modular form 338.2.c.h.315.3
2-338-13.3-c1-0-8 $1.64$ $2.69$ $2$ $2 \cdot 13^{2}$ 13.3 $1.0$ $1$ ✓ ✓ $-0.0812$ $0$ $1.73608$ Modular form 338.2.c.e.315.1
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