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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
2-583-583.10-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.10 $0.0$ 0 ✓ ✓ $0.0677$ $0$ $1.91939$ Modular form 583.1.o.a.10.1
2-583-583.131-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.131 $0.0$ 0 ✓ ✓ $-0.0508$ $0$ $1.66263$ Modular form 583.1.n.a.131.1
2-583-583.142-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.142 $0.0$ 0 ✓ ✓ $-0.143$ $0$ $1.07322$ Modular form 583.1.o.a.142.1
2-583-583.153-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.153 $0.0$ 0 ✓ ✓ $-0.0720$ $0$ $2.09573$ Modular form 583.1.o.a.153.1
2-583-583.175-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.175 $0.0$ 0 ✓ ✓ $-0.0677$ $0$ $1.37228$ Modular form 583.1.o.a.175.1
2-583-583.197-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.197 $0.0$ 0 ✓ ✓ $0.264$ $0$ $2.29988$ Modular form 583.1.n.a.197.1
2-583-583.208-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.208 $0.0$ 0 ✓ ✓ $-0.145$ $0$ $1.52847$ Modular form 583.1.o.a.208.1
2-583-583.219-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.219 $0.0$ 0 ✓ ✓ $-0.264$ $0$ $1.14035$ Modular form 583.1.n.a.219.1
2-583-583.241-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.241 $0.0$ 0 ✓ ✓ $-0.0957$ $0$ $1.50840$ Modular form 583.1.n.a.241.1
2-583-583.252-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.252 $0.0$ 0 ✓ ✓ $-0.154$ $0$ $1.67877$ Modular form 583.1.n.a.252.1
2-583-583.274-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.274 $0.0$ 0 ✓ ✓ $0.379$ $0$ $2.49774$ Modular form 583.1.n.a.274.1
2-583-583.307-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.307 $0.0$ 0 ✓ ✓ $0.477$ $0$ $3.08297$ Modular form 583.1.o.a.307.1
2-583-583.329-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.329 $0.0$ 0 ✓ ✓ $0.0957$ $0$ $2.30879$ Modular form 583.1.n.a.329.1
2-583-583.362-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.362 $0.0$ 0 ✓ ✓ $0.0720$ $0$ $1.99977$ Modular form 583.1.o.a.362.1
2-583-583.384-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.384 $0.0$ 0 ✓ ✓ $0.145$ $0$ $2.36237$ Modular form 583.1.o.a.384.1
2-583-583.395-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.395 $0.0$ 0 ✓ ✓ $-0.477$ $0$ $0.755362$ Modular form 583.1.o.a.395.1
2-583-583.417-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.417 $0.0$ 0 ✓ ✓ $-0.342$ $0$ $3.19978$ Modular form 583.1.o.a.417.1
2-583-583.428-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.428 $0.0$ 0 ✓ ✓ $0.154$ $0$ $2.32461$ Modular form 583.1.n.a.428.1
2-583-583.43-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.43 $0.0$ 0 ✓ ✓ $-0.293$ $0$ $1.11075$ Modular form 583.1.n.a.43.1
2-583-583.439-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.439 $0.0$ 0 ✓ ✓ $0.342$ $0$ $0.0897669$ Modular form 583.1.o.a.439.1
2-583-583.461-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.461 $0.0$ 0 ✓ ✓ $0.293$ $0$ $2.91217$ Modular form 583.1.n.a.461.1
2-583-583.483-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.483 $0.0$ 0 ✓ ✓ $-0.379$ $0$ $0.795735$ Modular form 583.1.n.a.483.1
2-583-583.494-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.494 $0.0$ 0 ✓ ✓ $0.0508$ $0$ $1.41835$ Modular form 583.1.n.a.494.1
2-583-583.505-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.505 $0.0$ 0 ✓ ✓ $0.143$ $0$ $1.92480$ Modular form 583.1.o.a.505.1
2-583-583.582-c0-0-0 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.582 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.24145$ Artin representation 2.583.8t6.b.b Modular form 583.1.d.b.582.1
2-583-583.582-c0-0-1 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.582 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $1.43660$ Artin representation 2.583.4t3.b Artin representation 2.583.4t3.b.a Modular form 583.1.d.a Modular form 583.1.d.a.582.1
2-583-583.582-c0-0-2 $0.539$ $0.290$ $2$ $11 \cdot 53$ 583.582 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $2.18552$ Artin representation 2.583.8t6.b.a Modular form 583.1.d.b.582.2
2-583-1.1-c1-0-0 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.487393$ Modular form 583.2.a.i.1.6
2-583-1.1-c1-0-1 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.566990$ Modular form 583.2.a.h.1.1
2-583-1.1-c1-0-10 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.31875$ Modular form 583.2.a.e.1.1
2-583-1.1-c1-0-11 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.33989$ Modular form 583.2.a.i.1.8
2-583-1.1-c1-0-12 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.40858$ Modular form 583.2.a.i.1.2
2-583-1.1-c1-0-13 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.43319$ Modular form 583.2.a.h.1.8
2-583-1.1-c1-0-14 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $1.43685$ Elliptic curve 583.a Modular form 583.2.a.a Modular form 583.2.a.a.1.1
2-583-1.1-c1-0-15 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.45401$ Modular form 583.2.a.i.1.1
2-583-1.1-c1-0-16 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.45511$ Modular form 583.2.a.h.1.2
2-583-1.1-c1-0-17 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.49544$ Modular form 583.2.a.g.1.3
2-583-1.1-c1-0-18 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.56840$ Modular form 583.2.a.i.1.5
2-583-1.1-c1-0-19 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.57504$ Modular form 583.2.a.d.1.1
2-583-1.1-c1-0-2 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.701238$ Modular form 583.2.a.h.1.7
2-583-1.1-c1-0-20 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.68544$ Modular form 583.2.a.i.1.11
2-583-1.1-c1-0-21 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.69720$ Modular form 583.2.a.g.1.5
2-583-1.1-c1-0-22 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.78369$ Modular form 583.2.a.g.1.2
2-583-1.1-c1-0-23 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.87589$ Modular form 583.2.a.h.1.6
2-583-1.1-c1-0-24 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.89697$ Modular form 583.2.a.g.1.4
2-583-1.1-c1-0-25 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.90855$ Modular form 583.2.a.f.1.3
2-583-1.1-c1-0-26 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.94407$ Modular form 583.2.a.f.1.1
2-583-1.1-c1-0-27 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.96142$ Modular form 583.2.a.h.1.10
2-583-1.1-c1-0-28 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.03850$ Modular form 583.2.a.i.1.9
2-583-1.1-c1-0-29 $2.15$ $4.65$ $2$ $11 \cdot 53$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $2.04504$ Elliptic curve 583.b Modular form 583.2.a.b Modular form 583.2.a.b.1.1
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