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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
2-616-616.125-c0-0-0 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.125 $0.0$ 0 ✓ ✓ $-0.103$ $0$ $1.54632$ Modular form 616.1.bh.b.125.1
2-616-616.125-c0-0-1 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.125 $0.0$ 0 ✓ ✓ $0.196$ $0$ $2.40650$ Modular form 616.1.bh.a.125.1
2-616-616.131-c0-0-0 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.131 $0.0$ 0 ✓ ✓ $-0.146$ $0$ $0.683981$ Modular form 616.1.z.b.131.1
2-616-616.131-c0-0-1 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.131 $0.0$ 0 ✓ ✓ $-0.146$ $0$ $1.23808$ Modular form 616.1.z.a.131.1
2-616-616.139-c0-0-0 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.139 $0.0$ 0 ✓ ✓ $0.161$ $0$ $2.20558$ Modular form 616.1.bq.b.139.1
2-616-616.139-c0-0-1 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.139 $0.0$ 0 ✓ ✓ $0.361$ $0$ $2.44751$ Modular form 616.1.bq.a.139.1
2-616-616.181-c0-0-0 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.181 $0.0$ 0 ✓ ✓ $-0.142$ $0$ $1.82281$ Modular form 616.1.bh.b.181.1
2-616-616.181-c0-0-1 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.181 $0.0$ 0 ✓ ✓ $-0.0427$ $0$ $1.82847$ Modular form 616.1.bh.a.181.1
2-616-616.195-c0-0-0 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.195 $0.0$ 0 ✓ ✓ $-0.361$ $0$ $1.00907$ Modular form 616.1.bq.a.195.1
2-616-616.195-c0-0-1 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.195 $0.0$ 0 ✓ ✓ $-0.161$ $0$ $1.68567$ Modular form 616.1.bq.b.195.1
2-616-616.307-c0-0-0 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.307 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $1.46870$ Artin representation 2.616.4t3.c Artin representation 2.616.4t3.c.a Modular form 616.1.g.a Modular form 616.1.g.a.307.1
2-616-616.307-c0-0-1 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.307 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $2.04329$ Artin representation 2.616.4t3.d Artin representation 2.616.4t3.d.a Modular form 616.1.g.b Modular form 616.1.g.b.307.1
2-616-616.395-c0-0-0 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.395 $0.0$ 0 ✓ ✓ $0.146$ $0$ $0.978397$ Modular form 616.1.z.a.395.1
2-616-616.395-c0-0-1 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.395 $0.0$ 0 ✓ ✓ $0.146$ $0$ $1.86582$ Modular form 616.1.z.b.395.1
2-616-616.405-c0-0-0 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.405 $0.0$ 0 ✓ ✓ $0.0427$ $0$ $1.18076$ Modular form 616.1.bh.a.405.1
2-616-616.405-c0-0-1 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.405 $0.0$ 0 ✓ ✓ $0.142$ $0$ $2.13991$ Modular form 616.1.bh.b.405.1
2-616-616.475-c0-0-0 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.475 $0.0$ 0 ✓ ✓ $-0.0465$ $0$ $1.55694$ Modular form 616.1.bq.a.475.1
2-616-616.475-c0-0-1 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.475 $0.0$ 0 ✓ ✓ $0.353$ $0$ $2.03572$ Modular form 616.1.bq.b.475.1
2-616-616.69-c0-0-0 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.69 $0.0$ 0 ✓ ✓ $0.103$ $0$ $1.32209$ Modular form 616.1.bh.b.69.1
2-616-616.69-c0-0-1 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.69 $0.0$ 0 ✓ ✓ $-0.196$ $0$ $1.57566$ Modular form 616.1.bh.a.69.1
2-616-616.83-c0-0-0 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.83 $0.0$ 0 ✓ ✓ $-0.353$ $0$ $0.849792$ Modular form 616.1.bq.b.83.1
2-616-616.83-c0-0-1 $0.554$ $0.307$ $2$ $2^{3} \cdot 7 \cdot 11$ 616.83 $0.0$ 0 ✓ ✓ $0.0465$ $0$ $1.33211$ Modular form 616.1.bq.a.83.1
2-616-1.1-c1-0-0 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.749121$ Modular form 616.2.a.g.1.1
2-616-1.1-c1-0-1 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.905390$ Modular form 616.2.a.h.1.2
2-616-1.1-c1-0-10 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.00157$ Elliptic curve 616.b Modular form 616.2.a.b Modular form 616.2.a.b.1.1
2-616-1.1-c1-0-11 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.14777$ Elliptic curve 616.c Modular form 616.2.a.c Modular form 616.2.a.c.1.1
2-616-1.1-c1-0-12 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.27748$ Elliptic curve 616.d Modular form 616.2.a.d Modular form 616.2.a.d.1.1
2-616-1.1-c1-0-13 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.39887$ Modular form 616.2.a.f.1.2
2-616-1.1-c1-0-2 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.03047$ Modular form 616.2.a.h.1.1
2-616-1.1-c1-0-3 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $1.08576$ Elliptic curve 616.a Modular form 616.2.a.a Modular form 616.2.a.a.1.1
2-616-1.1-c1-0-4 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.34198$ Modular form 616.2.a.g.1.2
2-616-1.1-c1-0-5 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.65268$ Modular form 616.2.a.h.1.3
2-616-1.1-c1-0-6 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $1.66644$ Elliptic curve 616.e Modular form 616.2.a.e Modular form 616.2.a.e.1.1
2-616-1.1-c1-0-7 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.72647$ Modular form 616.2.a.h.1.4
2-616-1.1-c1-0-8 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.77691$ Modular form 616.2.a.f.1.1
2-616-1.1-c1-0-9 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.96478$ Modular form 616.2.a.g.1.3
2-616-11.3-c1-0-0 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.238$ $0$ $0.0838820$ Modular form 616.2.r.f.113.1
2-616-11.3-c1-0-1 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.471$ $0$ $0.306706$ Modular form 616.2.r.e.113.4
2-616-11.3-c1-0-10 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.175$ $0$ $1.47964$ Modular form 616.2.r.e.113.2
2-616-11.3-c1-0-11 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.204$ $0$ $1.53160$ Modular form 616.2.r.f.113.2
2-616-11.3-c1-0-12 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.127$ $0$ $1.58394$ Modular form 616.2.r.d.113.3
2-616-11.3-c1-0-13 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.281$ $0$ $1.70195$ Modular form 616.2.r.c.113.2
2-616-11.3-c1-0-14 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.393$ $0$ $1.98162$ Modular form 616.2.r.f.113.3
2-616-11.3-c1-0-15 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $0.429$ $0$ $2.02930$ Modular form 616.2.r.d.113.1
2-616-11.3-c1-0-16 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.402$ $0$ $2.57474$ Modular form 616.2.r.c.113.1
2-616-11.3-c1-0-17 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.292$ $0$ $2.94140$ Modular form 616.2.r.e.113.1
2-616-11.3-c1-0-2 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.132$ $0$ $0.913451$ Modular form 616.2.r.f.113.4
2-616-11.3-c1-0-3 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.361$ $0$ $0.918575$ Modular form 616.2.r.a.113.1
2-616-11.3-c1-0-4 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.294$ $0$ $1.06918$ Modular form 616.2.r.d.113.4
2-616-11.3-c1-0-5 $2.21$ $4.91$ $2$ $2^{3} \cdot 7 \cdot 11$ 11.3 $1.0$ $1$ ✓ ✓ $-0.273$ $0$ $1.19365$ Modular form 616.2.r.f.113.5
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