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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
2-13e2-1.1-c3-0-0 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.400809$ Modular form 169.4.a.l.1.5
2-13e2-1.1-c3-0-1 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.526269$ Modular form 169.4.a.g.1.1
2-13e2-1.1-c3-0-10 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.37696$ Modular form 169.4.a.k.1.4
2-13e2-1.1-c3-0-11 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.38775$ Modular form 169.4.a.f.1.1
2-13e2-1.1-c3-0-12 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.53405$ Modular form 169.4.a.l.1.3
2-13e2-1.1-c3-0-13 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0$ $0$ $1.61421$ Modular form 169.4.a.e Modular form 169.4.a.e.1.1
2-13e2-1.1-c3-0-14 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.72006$ Modular form 169.4.a.k.1.1
2-13e2-1.1-c3-0-15 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.76609$ Modular form 169.4.a.b Modular form 169.4.a.b.1.1
2-13e2-1.1-c3-0-16 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.78182$ Modular form 169.4.a.g.1.2
2-13e2-1.1-c3-0-17 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.82955$ Modular form 169.4.a.k.1.5
2-13e2-1.1-c3-0-18 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.00053$ Modular form 169.4.a.i.1.1
2-13e2-1.1-c3-0-19 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $2.02081$ Modular form 169.4.a.l.1.7
2-13e2-1.1-c3-0-2 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.526918$ Modular form 169.4.a.f.1.2
2-13e2-1.1-c3-0-20 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0$ $0$ $2.03820$ Modular form 169.4.a.d Modular form 169.4.a.d.1.1
2-13e2-1.1-c3-0-21 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $2.06083$ Modular form 169.4.a.l.1.8
2-13e2-1.1-c3-0-22 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.08378$ Modular form 169.4.a.k.1.3
2-13e2-1.1-c3-0-23 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.08729$ Modular form 169.4.a.k.1.2
2-13e2-1.1-c3-0-24 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $2.26268$ Modular form 169.4.a.l.1.9
2-13e2-1.1-c3-0-25 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $2.39164$ Modular form 169.4.a.j.1.2
2-13e2-1.1-c3-0-26 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.53093$ Modular form 169.4.a.k.1.6
2-13e2-1.1-c3-0-27 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.54707$ Modular form 169.4.a.h.1.2
2-13e2-1.1-c3-0-28 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.69016$ Modular form 169.4.a.i.1.2
2-13e2-1.1-c3-0-29 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.73321$ Modular form 169.4.a.c Modular form 169.4.a.c.1.1
2-13e2-1.1-c3-0-3 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0$ $0$ $0.610785$ Modular form 169.4.a.a Modular form 169.4.a.a.1.1
2-13e2-1.1-c3-0-30 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.88312$ Modular form 169.4.a.k.1.9
2-13e2-1.1-c3-0-31 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $2.93564$ Modular form 169.4.a.k.1.7
2-13e2-1.1-c3-0-32 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $3.32605$ Modular form 169.4.a.k.1.8
2-13e2-1.1-c3-0-4 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.737025$ Modular form 169.4.a.l.1.6
2-13e2-1.1-c3-0-5 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $0.866254$ Modular form 169.4.a.l.1.1
2-13e2-1.1-c3-0-6 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.05122$ Modular form 169.4.a.j.1.1
2-13e2-1.1-c3-0-7 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.10824$ Modular form 169.4.a.l.1.2
2-13e2-1.1-c3-0-8 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0$ $0$ $1.12804$ Modular form 169.4.a.l.1.4
2-13e2-1.1-c3-0-9 $3.15$ $9.97$ $2$ $13^{2}$ 1.1 $3.0$ $3$ ✓ ✓ ✓ $0.5$ $1$ $1.29137$ Modular form 169.4.a.h.1.1
2-13e2-13.10-c3-0-0 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $0.398$ $0$ $0.0236021$ Modular form 169.4.e.h.23.7
2-13e2-13.10-c3-0-1 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $0.398$ $0$ $0.0498098$ Modular form 169.4.e.h.23.10
2-13e2-13.10-c3-0-10 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $0.0122$ $0$ $0.880282$ Modular form 169.4.e.f.23.3
2-13e2-13.10-c3-0-11 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $-0.174$ $0$ $1.01523$ Modular form 169.4.e.f.23.4
2-13e2-13.10-c3-0-12 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $-0.249$ $0$ $1.04748$ Modular form 169.4.e.h.23.4
2-13e2-13.10-c3-0-13 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $-0.209$ $0$ $1.05950$ Modular form 169.4.e.b.23.1
2-13e2-13.10-c3-0-14 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $-0.386$ $0$ $1.07740$ Modular form 169.4.e.h.23.9
2-13e2-13.10-c3-0-15 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $-0.174$ $0$ $1.10564$ Modular form 169.4.e.e.23.1
2-13e2-13.10-c3-0-16 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $-0.249$ $0$ $1.11119$ Modular form 169.4.e.h.23.13
2-13e2-13.10-c3-0-17 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $0.123$ $0$ $1.30707$ Modular form 169.4.e.d.23.1
2-13e2-13.10-c3-0-18 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $0.0122$ $0$ $1.34090$ Modular form 169.4.e.f.23.1
2-13e2-13.10-c3-0-19 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $0.180$ $0$ $1.35626$ Modular form 169.4.e.h.23.11
2-13e2-13.10-c3-0-2 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $-0.174$ $0$ $0.197009$ Modular form 169.4.e.f.23.2
2-13e2-13.10-c3-0-20 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $0.0406$ $0$ $1.37234$ Modular form 169.4.e.c.23.2
2-13e2-13.10-c3-0-21 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $0.0406$ $0$ $1.45101$ Modular form 169.4.e.g.23.2
2-13e2-13.10-c3-0-22 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $0.180$ $0$ $1.45910$ Modular form 169.4.e.h.23.1
2-13e2-13.10-c3-0-23 $3.15$ $9.97$ $2$ $13^{2}$ 13.10 $3.0$ $3$ ✓ ✓ $0.123$ $0$ $1.69427$ Modular form 169.4.e.d.23.2
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