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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
2-506-1.1-c1-0-0 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.462705$ Modular form 506.2.a.g.1.1
2-506-1.1-c1-0-1 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.704118$ Modular form 506.2.a.h.1.1
2-506-1.1-c1-0-10 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.62001$ Modular form 506.2.a.h.1.3
2-506-1.1-c1-0-11 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.75759$ Modular form 506.2.a.j.1.3
2-506-1.1-c1-0-12 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.77492$ Elliptic curve 506.a Modular form 506.2.a.a Modular form 506.2.a.a.1.1
2-506-1.1-c1-0-13 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.78037$ Modular form 506.2.a.i.1.3
2-506-1.1-c1-0-14 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.85787$ Modular form 506.2.a.h.1.2
2-506-1.1-c1-0-15 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.87282$ Modular form 506.2.a.j.1.5
2-506-1.1-c1-0-16 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.90712$ Modular form 506.2.a.i.1.4
2-506-1.1-c1-0-17 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.07583$ Elliptic curve 506.d Modular form 506.2.a.d Modular form 506.2.a.d.1.1
2-506-1.1-c1-0-18 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.23037$ Modular form 506.2.a.j.1.4
2-506-1.1-c1-0-19 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.30646$ Elliptic curve 506.e Modular form 506.2.a.e Modular form 506.2.a.e.1.1
2-506-1.1-c1-0-2 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.954134$ Modular form 506.2.a.j.1.1
2-506-1.1-c1-0-20 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.73272$ Elliptic curve 506.f Modular form 506.2.a.f Modular form 506.2.a.f.1.1
2-506-1.1-c1-0-3 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $0.998610$ Elliptic curve 506.c Modular form 506.2.a.c Modular form 506.2.a.c.1.1
2-506-1.1-c1-0-4 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.18084$ Modular form 506.2.a.i.1.2
2-506-1.1-c1-0-5 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $1.23789$ Elliptic curve 506.b Modular form 506.2.a.b Modular form 506.2.a.b.1.1
2-506-1.1-c1-0-6 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.36234$ Modular form 506.2.a.g.1.2
2-506-1.1-c1-0-7 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.38230$ Modular form 506.2.a.i.1.1
2-506-1.1-c1-0-8 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.49778$ Modular form 506.2.a.g.1.3
2-506-1.1-c1-0-9 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.60048$ Modular form 506.2.a.j.1.2
2-506-11.3-c1-0-0 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $0.326$ $0$ $0.165519$ Modular form 506.2.e.h.47.5
2-506-11.3-c1-0-1 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.276$ $0$ $0.173101$ Modular form 506.2.e.g.47.1
2-506-11.3-c1-0-10 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.171$ $0$ $1.53349$ Modular form 506.2.e.i.47.6
2-506-11.3-c1-0-11 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $0.0389$ $0$ $1.73435$ Modular form 506.2.e.c.47.1
2-506-11.3-c1-0-12 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.0340$ $0$ $1.87348$ Modular form 506.2.e.g.47.3
2-506-11.3-c1-0-13 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $0.238$ $0$ $1.91277$ Modular form 506.2.e.f.47.2
2-506-11.3-c1-0-14 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $0.238$ $0$ $1.92999$ Modular form 506.2.e.f.47.1
2-506-11.3-c1-0-15 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $0.314$ $0$ $2.02735$ Modular form 506.2.e.a.47.1
2-506-11.3-c1-0-16 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $0.334$ $0$ $2.12578$ Modular form 506.2.e.i.47.2
2-506-11.3-c1-0-17 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $0.238$ $0$ $2.14332$ Modular form 506.2.e.e.47.1
2-506-11.3-c1-0-18 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $0.364$ $0$ $2.30149$ Modular form 506.2.e.i.47.3
2-506-11.3-c1-0-19 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.466$ $0$ $2.43847$ Modular form 506.2.e.h.47.1
2-506-11.3-c1-0-2 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.297$ $0$ $0.742658$ Modular form 506.2.e.i.47.5
2-506-11.3-c1-0-20 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.485$ $0$ $2.84256$ Modular form 506.2.e.b.47.1
2-506-11.3-c1-0-21 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.335$ $0$ $3.53618$ Modular form 506.2.e.i.47.1
2-506-11.3-c1-0-3 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.319$ $0$ $0.908390$ Modular form 506.2.e.h.47.3
2-506-11.3-c1-0-4 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.406$ $0$ $1.07030$ Modular form 506.2.e.g.47.4
2-506-11.3-c1-0-5 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.165$ $0$ $1.25576$ Modular form 506.2.e.h.47.4
2-506-11.3-c1-0-6 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.0213$ $0$ $1.28918$ Modular form 506.2.e.h.47.2
2-506-11.3-c1-0-7 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.0267$ $0$ $1.33893$ Modular form 506.2.e.i.47.4
2-506-11.3-c1-0-8 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $-0.131$ $0$ $1.39652$ Modular form 506.2.e.d.47.1
2-506-11.3-c1-0-9 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.3 $1.0$ $1$ ✓ ✓ $0.178$ $0$ $1.46093$ Modular form 506.2.e.g.47.2
2-506-11.4-c1-0-0 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.4 $1.0$ $1$ ✓ ✓ $0.335$ $0$ $0.362858$ Modular form 506.2.e.i.323.1
2-506-11.4-c1-0-1 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.4 $1.0$ $1$ ✓ ✓ $-0.314$ $0$ $0.444177$ Modular form 506.2.e.a.323.1
2-506-11.4-c1-0-10 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.4 $1.0$ $1$ ✓ ✓ $0.165$ $0$ $1.26873$ Modular form 506.2.e.h.323.4
2-506-11.4-c1-0-11 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.4 $1.0$ $1$ ✓ ✓ $0.0213$ $0$ $1.30699$ Modular form 506.2.e.h.323.2
2-506-11.4-c1-0-12 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.4 $1.0$ $1$ ✓ ✓ $-0.238$ $0$ $1.39763$ Modular form 506.2.e.f.323.1
2-506-11.4-c1-0-13 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.4 $1.0$ $1$ ✓ ✓ $-0.0389$ $0$ $1.48893$ Modular form 506.2.e.c.323.1
2-506-11.4-c1-0-14 $2.01$ $4.04$ $2$ $2 \cdot 11 \cdot 23$ 11.4 $1.0$ $1$ ✓ ✓ $0.276$ $0$ $1.53179$ Modular form 506.2.e.g.323.1
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