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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
2-2e4-1.1-c21-0-0 $6.68$ $44.7$ $2$ $2^{4}$ 1.1 $21.0$ $21$ ✓ ✓ ✓ ✓ $0$ $0$ $0.412216$ Modular form 16.22.a.a Modular form 16.22.a.a.1.1
2-2e4-1.1-c21-0-1 $6.68$ $44.7$ $2$ $2^{4}$ 1.1 $21.0$ $21$ ✓ ✓ ✓ ✓ $0$ $0$ $0.503210$ Modular form 16.22.a.b Modular form 16.22.a.b.1.1
2-2e4-1.1-c21-0-2 $6.68$ $44.7$ $2$ $2^{4}$ 1.1 $21.0$ $21$ ✓ ✓ ✓ $0$ $0$ $0.794886$ Modular form 16.22.a.d.1.2
2-2e4-1.1-c21-0-3 $6.68$ $44.7$ $2$ $2^{4}$ 1.1 $21.0$ $21$ ✓ ✓ ✓ $0$ $0$ $0.903483$ Modular form 16.22.a.d.1.1
2-2e4-1.1-c21-0-4 $6.68$ $44.7$ $2$ $2^{4}$ 1.1 $21.0$ $21$ ✓ ✓ ✓ $0.5$ $1$ $0.979064$ Modular form 16.22.a.f.1.1
2-2e4-1.1-c21-0-5 $6.68$ $44.7$ $2$ $2^{4}$ 1.1 $21.0$ $21$ ✓ ✓ ✓ ✓ $0$ $0$ $1.38570$ Modular form 16.22.a.c Modular form 16.22.a.c.1.1
2-2e4-1.1-c21-0-6 $6.68$ $44.7$ $2$ $2^{4}$ 1.1 $21.0$ $21$ ✓ ✓ ✓ $0.5$ $1$ $1.47663$ Modular form 16.22.a.e.1.1
2-2e4-1.1-c21-0-7 $6.68$ $44.7$ $2$ $2^{4}$ 1.1 $21.0$ $21$ ✓ ✓ ✓ $0.5$ $1$ $1.75987$ Modular form 16.22.a.f.1.3
2-2e4-1.1-c21-0-8 $6.68$ $44.7$ $2$ $2^{4}$ 1.1 $21.0$ $21$ ✓ ✓ ✓ $0.5$ $1$ $1.85832$ Modular form 16.22.a.f.1.2
2-2e4-1.1-c21-0-9 $6.68$ $44.7$ $2$ $2^{4}$ 1.1 $21.0$ $21$ ✓ ✓ ✓ $0.5$ $1$ $2.24563$ Modular form 16.22.a.e.1.2
2-2e4-16.13-c21-0-0 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.476$ $0$ $0.00846853$ Modular form 16.22.e.a.13.23
2-2e4-16.13-c21-0-1 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.421$ $0$ $0.0556895$ Modular form 16.22.e.a.13.21
2-2e4-16.13-c21-0-10 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.0945$ $0$ $0.452232$ Modular form 16.22.e.a.13.12
2-2e4-16.13-c21-0-11 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.0593$ $0$ $0.528331$ Modular form 16.22.e.a.13.14
2-2e4-16.13-c21-0-12 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.361$ $0$ $0.541516$ Modular form 16.22.e.a.13.18
2-2e4-16.13-c21-0-13 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.0382$ $0$ $0.592107$ Modular form 16.22.e.a.13.32
2-2e4-16.13-c21-0-14 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.226$ $0$ $0.625622$ Modular form 16.22.e.a.13.34
2-2e4-16.13-c21-0-15 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.379$ $0$ $0.659712$ Modular form 16.22.e.a.13.17
2-2e4-16.13-c21-0-16 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.195$ $0$ $0.691400$ Modular form 16.22.e.a.13.37
2-2e4-16.13-c21-0-17 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.161$ $0$ $0.738888$ Modular form 16.22.e.a.13.29
2-2e4-16.13-c21-0-18 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.247$ $0$ $0.817131$ Modular form 16.22.e.a.13.15
2-2e4-16.13-c21-0-19 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.261$ $0$ $0.840434$ Modular form 16.22.e.a.13.4
2-2e4-16.13-c21-0-2 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.134$ $0$ $0.0881822$ Modular form 16.22.e.a.13.26
2-2e4-16.13-c21-0-20 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.0205$ $0$ $0.872583$ Modular form 16.22.e.a.13.11
2-2e4-16.13-c21-0-21 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.418$ $0$ $0.905720$ Modular form 16.22.e.a.13.39
2-2e4-16.13-c21-0-22 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.425$ $0$ $0.930611$ Modular form 16.22.e.a.13.20
2-2e4-16.13-c21-0-23 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.173$ $0$ $0.961835$ Modular form 16.22.e.a.13.8
2-2e4-16.13-c21-0-24 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.0696$ $0$ $0.992497$ Modular form 16.22.e.a.13.33
2-2e4-16.13-c21-0-25 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.169$ $0$ $1.05499$ Modular form 16.22.e.a.13.16
2-2e4-16.13-c21-0-26 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.255$ $0$ $1.07994$ Modular form 16.22.e.a.13.35
2-2e4-16.13-c21-0-27 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.258$ $0$ $1.34069$ Modular form 16.22.e.a.13.6
2-2e4-16.13-c21-0-28 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.117$ $0$ $1.44346$ Modular form 16.22.e.a.13.27
2-2e4-16.13-c21-0-29 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.0193$ $0$ $1.56757$ Modular form 16.22.e.a.13.30
2-2e4-16.13-c21-0-3 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.493$ $0$ $0.186524$ Modular form 16.22.e.a.13.1
2-2e4-16.13-c21-0-30 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.0337$ $0$ $1.58764$ Modular form 16.22.e.a.13.9
2-2e4-16.13-c21-0-31 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.455$ $0$ $1.71164$ Modular form 16.22.e.a.13.22
2-2e4-16.13-c21-0-32 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.458$ $0$ $1.79500$ Modular form 16.22.e.a.13.2
2-2e4-16.13-c21-0-33 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.342$ $0$ $1.86231$ Modular form 16.22.e.a.13.40
2-2e4-16.13-c21-0-34 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.135$ $0$ $1.88417$ Modular form 16.22.e.a.13.10
2-2e4-16.13-c21-0-35 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.382$ $0$ $1.91381$ Modular form 16.22.e.a.13.41
2-2e4-16.13-c21-0-36 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.191$ $0$ $2.00913$ Modular form 16.22.e.a.13.36
2-2e4-16.13-c21-0-37 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.387$ $0$ $2.04730$ Modular form 16.22.e.a.13.25
2-2e4-16.13-c21-0-38 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.461$ $0$ $2.15335$ Modular form 16.22.e.a.13.19
2-2e4-16.13-c21-0-39 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.217$ $0$ $2.35385$ Modular form 16.22.e.a.13.28
2-2e4-16.13-c21-0-4 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.168$ $0$ $0.223184$ Modular form 16.22.e.a.13.13
2-2e4-16.13-c21-0-40 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.116$ $0$ $2.78953$ Modular form 16.22.e.a.13.31
2-2e4-16.13-c21-0-5 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.383$ $0$ $0.231834$ Modular form 16.22.e.a.13.5
2-2e4-16.13-c21-0-6 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $0.273$ $0$ $0.302402$ Modular form 16.22.e.a.13.3
2-2e4-16.13-c21-0-7 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.183$ $0$ $0.321291$ Modular form 16.22.e.a.13.7
2-2e4-16.13-c21-0-8 $6.68$ $44.7$ $2$ $2^{4}$ 16.13 $21.0$ $21$ ✓ ✓ $-0.400$ $0$ $0.327183$ Modular form 16.22.e.a.13.38
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