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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
2-869-869.157-c0-0-0 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.157 $0.0$ 0 ✓ ✓ $0.463$ $0$ $0.0194739$ Modular form 869.1.j.a.157.3
2-869-869.157-c0-0-1 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.157 $0.0$ 0 ✓ ✓ $-0.136$ $0$ $0.889662$ Modular form 869.1.j.a.157.2
2-869-869.157-c0-0-2 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.157 $0.0$ 0 ✓ ✓ $-0.336$ $0$ $1.04080$ Modular form 869.1.j.a.157.1
2-869-869.157-c0-0-3 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.157 $0.0$ 0 ✓ ✓ $0.0637$ $0$ $1.68405$ Modular form 869.1.j.a.157.4
2-869-869.157-c0-0-4 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.157 $0.0$ 0 ✓ ✓ $0.263$ $0$ $2.62749$ Modular form 869.1.j.a.157.5
2-869-869.236-c0-0-0 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.236 $0.0$ 0 ✓ ✓ $0.137$ $0$ $0.802447$ Modular form 869.1.j.a.236.1
2-869-869.236-c0-0-1 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.236 $0.0$ 0 ✓ ✓ $-0.462$ $0$ $1.12987$ Modular form 869.1.j.a.236.4
2-869-869.236-c0-0-2 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.236 $0.0$ 0 ✓ ✓ $-0.0627$ $0$ $1.15179$ Modular form 869.1.j.a.236.3
2-869-869.236-c0-0-3 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.236 $0.0$ 0 ✓ ✓ $-0.262$ $0$ $1.60163$ Modular form 869.1.j.a.236.5
2-869-869.236-c0-0-4 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.236 $0.0$ 0 ✓ ✓ $0.337$ $0$ $2.19890$ Modular form 869.1.j.a.236.2
2-869-869.394-c0-0-0 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.394 $0.0$ 0 ✓ ✓ $-0.337$ $0$ $1.11424$ Modular form 869.1.j.a.394.2
2-869-869.394-c0-0-1 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.394 $0.0$ 0 ✓ ✓ $-0.137$ $0$ $1.59067$ Modular form 869.1.j.a.394.1
2-869-869.394-c0-0-2 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.394 $0.0$ 0 ✓ ✓ $0.262$ $0$ $1.66998$ Modular form 869.1.j.a.394.5
2-869-869.394-c0-0-3 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.394 $0.0$ 0 ✓ ✓ $0.0627$ $0$ $1.98258$ Modular form 869.1.j.a.394.3
2-869-869.394-c0-0-4 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.394 $0.0$ 0 ✓ ✓ $0.462$ $0$ $2.63346$ Modular form 869.1.j.a.394.4
2-869-869.631-c0-0-0 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.631 $0.0$ 0 ✓ ✓ $0.136$ $0$ $1.03889$ Modular form 869.1.j.a.631.2
2-869-869.631-c0-0-1 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.631 $0.0$ 0 ✓ ✓ $-0.263$ $0$ $1.74414$ Modular form 869.1.j.a.631.5
2-869-869.631-c0-0-2 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.631 $0.0$ 0 ✓ ✓ $0.336$ $0$ $1.77787$ Modular form 869.1.j.a.631.1
2-869-869.631-c0-0-3 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.631 $0.0$ 0 ✓ ✓ $-0.0637$ $0$ $2.13345$ Modular form 869.1.j.a.631.4
2-869-869.631-c0-0-4 $0.658$ $0.433$ $2$ $11 \cdot 79$ 869.631 $0.0$ 0 ✓ ✓ $-0.463$ $0$ $2.48902$ Modular form 869.1.j.a.631.3
2-869-1.1-c1-0-0 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.363947$ Modular form 869.2.a.h.1.14
2-869-1.1-c1-0-1 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.384142$ Modular form 869.2.a.g.1.4
2-869-1.1-c1-0-10 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.759203$ Modular form 869.2.a.g.1.9
2-869-1.1-c1-0-11 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.866289$ Modular form 869.2.a.g.1.13
2-869-1.1-c1-0-12 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.895439$ Modular form 869.2.a.g.1.7
2-869-1.1-c1-0-13 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.904135$ Modular form 869.2.a.h.1.6
2-869-1.1-c1-0-14 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.924980$ Modular form 869.2.a.h.1.10
2-869-1.1-c1-0-15 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $0.941338$ Modular form 869.2.a.f.1.2
2-869-1.1-c1-0-16 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $0.947323$ Elliptic curve 869.b Modular form 869.2.a.b Modular form 869.2.a.b.1.1
2-869-1.1-c1-0-17 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.998881$ Modular form 869.2.a.g.1.11
2-869-1.1-c1-0-18 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.06775$ Modular form 869.2.a.e.1.6
2-869-1.1-c1-0-19 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.09914$ Modular form 869.2.a.g.1.6
2-869-1.1-c1-0-2 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.394081$ Modular form 869.2.a.h.1.7
2-869-1.1-c1-0-20 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.11184$ Modular form 869.2.a.h.1.11
2-869-1.1-c1-0-21 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.14253$ Modular form 869.2.a.g.1.3
2-869-1.1-c1-0-22 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.28570$ Modular form 869.2.a.e.1.3
2-869-1.1-c1-0-23 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.30084$ Modular form 869.2.a.g.1.1
2-869-1.1-c1-0-24 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.30831$ Modular form 869.2.a.g.1.16
2-869-1.1-c1-0-25 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.30952$ Modular form 869.2.a.h.1.4
2-869-1.1-c1-0-26 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.34620$ Modular form 869.2.a.h.1.16
2-869-1.1-c1-0-27 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.35301$ Modular form 869.2.a.h.1.1
2-869-1.1-c1-0-28 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.39236$ Modular form 869.2.a.f.1.5
2-869-1.1-c1-0-29 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.44602$ Modular form 869.2.a.g.1.5
2-869-1.1-c1-0-3 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.438752$ Modular form 869.2.a.g.1.8
2-869-1.1-c1-0-30 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.47521$ Modular form 869.2.a.g.1.10
2-869-1.1-c1-0-31 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.49582$ Modular form 869.2.a.f.1.1
2-869-1.1-c1-0-32 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.51925$ Modular form 869.2.a.f.1.7
2-869-1.1-c1-0-33 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.54599$ Modular form 869.2.a.h.1.21
2-869-1.1-c1-0-34 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.55809$ Modular form 869.2.a.h.1.15
2-869-1.1-c1-0-35 $2.63$ $6.93$ $2$ $11 \cdot 79$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.59366$ Modular form 869.2.a.h.1.9
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