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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
2-429-1.1-c1-0-0 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.506824$ Modular form 429.2.a.h.1.1
2-429-1.1-c1-0-1 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.576675$ Modular form 429.2.a.e.1.2
2-429-1.1-c1-0-10 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.84763$ Modular form 429.2.a.e.1.3
2-429-1.1-c1-0-11 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.85487$ Modular form 429.2.a.c.1.1
2-429-1.1-c1-0-12 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.87387$ Modular form 429.2.a.h.1.4
2-429-1.1-c1-0-13 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.00486$ Modular form 429.2.a.g.1.2
2-429-1.1-c1-0-14 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.07793$ Modular form 429.2.a.f.1.3
2-429-1.1-c1-0-15 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.09639$ Elliptic curve 429.b Modular form 429.2.a.b Modular form 429.2.a.b.1.1
2-429-1.1-c1-0-16 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.37502$ Modular form 429.2.a.g.1.3
2-429-1.1-c1-0-17 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.65702$ Modular form 429.2.a.c.1.2
2-429-1.1-c1-0-18 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.87032$ Modular form 429.2.a.d.1.2
2-429-1.1-c1-0-2 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.943426$ Modular form 429.2.a.f.1.1
2-429-1.1-c1-0-3 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.974181$ Modular form 429.2.a.h.1.3
2-429-1.1-c1-0-4 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.00242$ Modular form 429.2.a.e.1.1
2-429-1.1-c1-0-5 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.27714$ Modular form 429.2.a.h.1.2
2-429-1.1-c1-0-6 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.28290$ Modular form 429.2.a.g.1.1
2-429-1.1-c1-0-7 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.53225$ Modular form 429.2.a.f.1.2
2-429-1.1-c1-0-8 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.73227$ Modular form 429.2.a.d.1.1
2-429-1.1-c1-0-9 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.82571$ Elliptic curve 429.a Modular form 429.2.a.a Modular form 429.2.a.a.1.1
2-429-11.3-c1-0-0 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $-0.268$ $0$ $0.334888$ Modular form 429.2.n.c.157.5
2-429-11.3-c1-0-1 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.457$ $0$ $0.383156$ Modular form 429.2.n.a.157.1
2-429-11.3-c1-0-10 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $-0.250$ $0$ $1.20266$ Modular form 429.2.n.a.157.2
2-429-11.3-c1-0-11 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.0278$ $0$ $1.37494$ Modular form 429.2.n.b.157.4
2-429-11.3-c1-0-12 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.199$ $0$ $1.62168$ Modular form 429.2.n.c.157.3
2-429-11.3-c1-0-13 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.0810$ $0$ $1.67777$ Modular form 429.2.n.d.157.1
2-429-11.3-c1-0-14 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.0262$ $0$ $1.70695$ Modular form 429.2.n.d.157.7
2-429-11.3-c1-0-15 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.0857$ $0$ $1.83043$ Modular form 429.2.n.a.157.3
2-429-11.3-c1-0-16 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.350$ $0$ $1.84389$ Modular form 429.2.n.d.157.4
2-429-11.3-c1-0-17 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.300$ $0$ $1.86376$ Modular form 429.2.n.b.157.3
2-429-11.3-c1-0-18 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.451$ $0$ $2.11687$ Modular form 429.2.n.c.157.1
2-429-11.3-c1-0-19 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.162$ $0$ $2.17934$ Modular form 429.2.n.d.157.9
2-429-11.3-c1-0-2 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $-0.195$ $0$ $0.803542$ Modular form 429.2.n.d.157.3
2-429-11.3-c1-0-20 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.295$ $0$ $2.19836$ Modular form 429.2.n.c.157.6
2-429-11.3-c1-0-21 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.306$ $0$ $2.59314$ Modular form 429.2.n.d.157.8
2-429-11.3-c1-0-22 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.330$ $0$ $2.65603$ Modular form 429.2.n.b.157.5
2-429-11.3-c1-0-23 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $0.429$ $0$ $3.21704$ Modular form 429.2.n.c.157.7
2-429-11.3-c1-0-3 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $-0.277$ $0$ $0.814556$ Modular form 429.2.n.c.157.2
2-429-11.3-c1-0-4 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $-0.286$ $0$ $0.916668$ Modular form 429.2.n.d.157.5
2-429-11.3-c1-0-5 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $-0.463$ $0$ $0.934579$ Modular form 429.2.n.d.157.2
2-429-11.3-c1-0-6 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $-0.165$ $0$ $0.943849$ Modular form 429.2.n.d.157.6
2-429-11.3-c1-0-7 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $-0.0457$ $0$ $0.966239$ Modular form 429.2.n.b.157.2
2-429-11.3-c1-0-8 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $-0.213$ $0$ $0.996872$ Modular form 429.2.n.b.157.1
2-429-11.3-c1-0-9 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.3 $1.0$ $1$ ✓ ✓ $-0.121$ $0$ $1.04486$ Modular form 429.2.n.c.157.4
2-429-11.4-c1-0-0 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.4 $1.0$ $1$ ✓ ✓ $-0.350$ $0$ $0.0422803$ Modular form 429.2.n.d.235.4
2-429-11.4-c1-0-1 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.4 $1.0$ $1$ ✓ ✓ $-0.451$ $0$ $0.259239$ Modular form 429.2.n.c.235.1
2-429-11.4-c1-0-10 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.4 $1.0$ $1$ ✓ ✓ $0.213$ $0$ $1.29843$ Modular form 429.2.n.b.235.1
2-429-11.4-c1-0-11 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.4 $1.0$ $1$ ✓ ✓ $-0.330$ $0$ $1.51500$ Modular form 429.2.n.b.235.5
2-429-11.4-c1-0-12 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.4 $1.0$ $1$ ✓ ✓ $0.277$ $0$ $1.55824$ Modular form 429.2.n.c.235.2
2-429-11.4-c1-0-13 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.4 $1.0$ $1$ ✓ ✓ $-0.0262$ $0$ $1.89254$ Modular form 429.2.n.d.235.7
2-429-11.4-c1-0-14 $1.85$ $3.42$ $2$ $3 \cdot 11 \cdot 13$ 11.4 $1.0$ $1$ ✓ ✓ $-0.0857$ $0$ $1.98460$ Modular form 429.2.n.a.235.3
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