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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
2-847-1.1-c1-0-0 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.413890$ Modular form 847.2.a.p.1.3
2-847-1.1-c1-0-1 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.430999$ Modular form 847.2.a.f.1.1
2-847-1.1-c1-0-10 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.815093$ Modular form 847.2.a.n.1.1
2-847-1.1-c1-0-11 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.966097$ Modular form 847.2.a.o.1.1
2-847-1.1-c1-0-12 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.966334$ Modular form 847.2.a.n.1.2
2-847-1.1-c1-0-13 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.00105$ Modular form 847.2.a.m.1.3
2-847-1.1-c1-0-14 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.01459$ Modular form 847.2.a.p.1.6
2-847-1.1-c1-0-15 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.08269$ Modular form 847.2.a.p.1.1
2-847-1.1-c1-0-16 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.14335$ Modular form 847.2.a.m.1.1
2-847-1.1-c1-0-17 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.14360$ Modular form 847.2.a.k.1.1
2-847-1.1-c1-0-18 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.18523$ Modular form 847.2.a.n.1.3
2-847-1.1-c1-0-19 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.18570$ Modular form 847.2.a.o.1.2
2-847-1.1-c1-0-2 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.566789$ Modular form 847.2.a.n.1.4
2-847-1.1-c1-0-20 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $1.19698$ Elliptic curve 847.c Modular form 847.2.a.c Modular form 847.2.a.c.1.1
2-847-1.1-c1-0-21 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.32889$ Elliptic curve 847.b Modular form 847.2.a.b Modular form 847.2.a.b.1.1
2-847-1.1-c1-0-22 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.36241$ Modular form 847.2.a.l.1.1
2-847-1.1-c1-0-23 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.39703$ Modular form 847.2.a.n.1.6
2-847-1.1-c1-0-24 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.41954$ Modular form 847.2.a.o.1.4
2-847-1.1-c1-0-25 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.47045$ Modular form 847.2.a.g.1.2
2-847-1.1-c1-0-26 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.47212$ Modular form 847.2.a.j.1.2
2-847-1.1-c1-0-27 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.52521$ Modular form 847.2.a.p.1.2
2-847-1.1-c1-0-28 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.52999$ Modular form 847.2.a.k.1.2
2-847-1.1-c1-0-29 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.54941$ Modular form 847.2.a.e.1.1
2-847-1.1-c1-0-3 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.599131$ Modular form 847.2.a.o.1.5
2-847-1.1-c1-0-30 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.55579$ Modular form 847.2.a.d.1.2
2-847-1.1-c1-0-31 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.64693$ Modular form 847.2.a.i.1.1
2-847-1.1-c1-0-32 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.73173$ Modular form 847.2.a.p.1.5
2-847-1.1-c1-0-33 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.74639$ Modular form 847.2.a.l.1.2
2-847-1.1-c1-0-34 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.85083$ Modular form 847.2.a.d.1.1
2-847-1.1-c1-0-35 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.88590$ Modular form 847.2.a.n.1.5
2-847-1.1-c1-0-36 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.90596$ Modular form 847.2.a.i.1.2
2-847-1.1-c1-0-37 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.91939$ Elliptic curve 847.a Modular form 847.2.a.a Modular form 847.2.a.a.1.1
2-847-1.1-c1-0-38 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.93084$ Modular form 847.2.a.m.1.2
2-847-1.1-c1-0-39 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.93773$ Modular form 847.2.a.h.1.2
2-847-1.1-c1-0-4 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.700425$ Modular form 847.2.a.g.1.1
2-847-1.1-c1-0-40 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.01583$ Modular form 847.2.a.p.1.7
2-847-1.1-c1-0-41 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.02658$ Modular form 847.2.a.p.1.8
2-847-1.1-c1-0-42 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.05499$ Modular form 847.2.a.o.1.8
2-847-1.1-c1-0-43 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.06776$ Modular form 847.2.a.o.1.7
2-847-1.1-c1-0-44 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.07343$ Modular form 847.2.a.f.1.2
2-847-1.1-c1-0-45 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.10000$ Modular form 847.2.a.m.1.5
2-847-1.1-c1-0-46 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.11164$ Modular form 847.2.a.j.1.3
2-847-1.1-c1-0-47 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.11971$ Modular form 847.2.a.k.1.4
2-847-1.1-c1-0-48 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.14632$ Modular form 847.2.a.i.1.3
2-847-1.1-c1-0-49 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.19153$ Modular form 847.2.a.m.1.4
2-847-1.1-c1-0-5 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.766703$ Modular form 847.2.a.p.1.4
2-847-1.1-c1-0-50 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.25386$ Modular form 847.2.a.k.1.3
2-847-1.1-c1-0-51 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.35167$ Modular form 847.2.a.m.1.6
2-847-1.1-c1-0-52 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.46110$ Modular form 847.2.a.e.1.2
2-847-1.1-c1-0-53 $2.60$ $6.76$ $2$ $7 \cdot 11^{2}$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.48986$ Modular form 847.2.a.l.1.4
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