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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
2-861-1.1-c1-0-0 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.520123$ Modular form 861.2.a.k.1.1
2-861-1.1-c1-0-1 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.556711$ Modular form 861.2.a.j.1.2
2-861-1.1-c1-0-10 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.05828$ Modular form 861.2.a.m.1.1
2-861-1.1-c1-0-11 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.07387$ Modular form 861.2.a.f.1.1
2-861-1.1-c1-0-12 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.07592$ Modular form 861.2.a.m.1.2
2-861-1.1-c1-0-13 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.09198$ Modular form 861.2.a.l.1.1
2-861-1.1-c1-0-14 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.24213$ Modular form 861.2.a.m.1.3
2-861-1.1-c1-0-15 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.32483$ Modular form 861.2.a.f.1.2
2-861-1.1-c1-0-16 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.32549$ Modular form 861.2.a.i.1.1
2-861-1.1-c1-0-17 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.36268$ Modular form 861.2.a.l.1.3
2-861-1.1-c1-0-18 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.45549$ Modular form 861.2.a.j.1.5
2-861-1.1-c1-0-19 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.46817$ Modular form 861.2.a.k.1.4
2-861-1.1-c1-0-2 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.581243$ Modular form 861.2.a.j.1.1
2-861-1.1-c1-0-20 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.51672$ Modular form 861.2.a.h.1.2
2-861-1.1-c1-0-21 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.59709$ Modular form 861.2.a.i.1.2
2-861-1.1-c1-0-22 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.62510$ Modular form 861.2.a.l.1.4
2-861-1.1-c1-0-23 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.66361$ Elliptic curve 861.b Modular form 861.2.a.b Modular form 861.2.a.b.1.1
2-861-1.1-c1-0-24 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.69083$ Modular form 861.2.a.h.1.1
2-861-1.1-c1-0-25 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.73227$ Modular form 861.2.a.e.1.1
2-861-1.1-c1-0-26 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.80592$ Modular form 861.2.a.g.1.1
2-861-1.1-c1-0-27 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.82379$ Modular form 861.2.a.m.1.5
2-861-1.1-c1-0-28 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.86254$ Modular form 861.2.a.m.1.6
2-861-1.1-c1-0-29 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.94752$ Modular form 861.2.a.m.1.7
2-861-1.1-c1-0-3 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.610933$ Modular form 861.2.a.k.1.2
2-861-1.1-c1-0-30 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.95490$ Modular form 861.2.a.k.1.5
2-861-1.1-c1-0-31 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.05180$ Modular form 861.2.a.l.1.5
2-861-1.1-c1-0-32 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.11738$ Elliptic curve 861.c Modular form 861.2.a.c Modular form 861.2.a.c.1.1
2-861-1.1-c1-0-33 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.12257$ Modular form 861.2.a.i.1.3
2-861-1.1-c1-0-34 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.13308$ Modular form 861.2.a.e.1.2
2-861-1.1-c1-0-35 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.26186$ Modular form 861.2.a.h.1.3
2-861-1.1-c1-0-36 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.35873$ Elliptic curve 861.d Modular form 861.2.a.d Modular form 861.2.a.d.1.1
2-861-1.1-c1-0-37 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.52462$ Modular form 861.2.a.g.1.2
2-861-1.1-c1-0-38 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.54224$ Modular form 861.2.a.i.1.4
2-861-1.1-c1-0-4 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.743428$ Modular form 861.2.a.k.1.3
2-861-1.1-c1-0-5 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.782381$ Modular form 861.2.a.j.1.4
2-861-1.1-c1-0-6 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.882968$ Modular form 861.2.a.l.1.2
2-861-1.1-c1-0-7 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $0.943610$ Elliptic curve 861.a Modular form 861.2.a.a Modular form 861.2.a.a.1.1
2-861-1.1-c1-0-8 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.00787$ Modular form 861.2.a.j.1.3
2-861-1.1-c1-0-9 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.01701$ Modular form 861.2.a.m.1.4
2-861-123.101-c1-0-0 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 123.101 $1.0$ $1$ ✓ ✓ $-0.415$ $0$ $0.0398116$ Modular form 861.2.ca.a.470.38
2-861-123.101-c1-0-1 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 123.101 $1.0$ $1$ ✓ ✓ $-0.255$ $0$ $0.0738768$ Modular form 861.2.ca.a.470.3
2-861-123.101-c1-0-10 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 123.101 $1.0$ $1$ ✓ ✓ $0.189$ $0$ $0.753822$ Modular form 861.2.ca.a.470.4
2-861-123.101-c1-0-11 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 123.101 $1.0$ $1$ ✓ ✓ $-0.340$ $0$ $0.757264$ Modular form 861.2.ca.a.470.76
2-861-123.101-c1-0-12 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 123.101 $1.0$ $1$ ✓ ✓ $-0.0473$ $0$ $0.775247$ Modular form 861.2.ca.a.470.16
2-861-123.101-c1-0-13 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 123.101 $1.0$ $1$ ✓ ✓ $0.0542$ $0$ $0.820582$ Modular form 861.2.ca.a.470.18
2-861-123.101-c1-0-14 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 123.101 $1.0$ $1$ ✓ ✓ $-0.184$ $0$ $0.839138$ Modular form 861.2.ca.a.470.32
2-861-123.101-c1-0-15 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 123.101 $1.0$ $1$ ✓ ✓ $-0.498$ $0$ $0.913966$ Modular form 861.2.ca.a.470.67
2-861-123.101-c1-0-16 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 123.101 $1.0$ $1$ ✓ ✓ $-0.379$ $0$ $0.931740$ Modular form 861.2.ca.a.470.71
2-861-123.101-c1-0-17 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 123.101 $1.0$ $1$ ✓ ✓ $0.344$ $0$ $0.945198$ Modular form 861.2.ca.a.470.10
2-861-123.101-c1-0-18 $2.62$ $6.87$ $2$ $3 \cdot 7 \cdot 41$ 123.101 $1.0$ $1$ ✓ ✓ $-0.250$ $0$ $0.957207$ Modular form 861.2.ca.a.470.41
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