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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
2-799-799.140-c0-0-0 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.140 $0.0$ 0 ✓ ✓ $0.444$ $0$ $1.06632$ Modular form 799.1.e.b.140.3
2-799-799.140-c0-0-1 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.140 $0.0$ 0 ✓ ✓ $0.0444$ $0$ $1.50021$ Modular form 799.1.e.b.140.2
2-799-799.140-c0-0-2 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.140 $0.0$ 0 ✓ ✓ $0.244$ $0$ $1.81084$ Modular form 799.1.e.b.140.1
2-799-799.140-c0-0-3 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.140 $0.0$ 0 ✓ ✓ $-0.155$ $0$ $1.83704$ Modular form 799.1.e.b.140.4
2-799-799.140-c0-0-4 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.140 $0.0$ 0 ✓ ✓ $-0.355$ $0$ $3.19389$ Modular form 799.1.e.a.140.1
2-799-799.234-c0-0-0 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.234 $0.0$ 0 ✓ ✓ $-0.244$ $0$ $0.608004$ Modular form 799.1.e.b.234.3
2-799-799.234-c0-0-1 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.234 $0.0$ 0 ✓ ✓ $0.355$ $0$ $0.974320$ Modular form 799.1.e.a.234.1
2-799-799.234-c0-0-2 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.234 $0.0$ 0 ✓ ✓ $0.155$ $0$ $1.74748$ Modular form 799.1.e.b.234.2
2-799-799.234-c0-0-3 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.234 $0.0$ 0 ✓ ✓ $-0.0444$ $0$ $1.81603$ Modular form 799.1.e.b.234.4
2-799-799.234-c0-0-4 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.234 $0.0$ 0 ✓ ✓ $-0.444$ $0$ $2.33726$ Modular form 799.1.e.b.234.1
2-799-799.281-c0-0-0 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.281 $0.0$ 0 ✓ ✓ $-0.332$ $0$ $1.22427$ Modular form 799.1.h.b.281.2
2-799-799.281-c0-0-1 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.281 $0.0$ 0 ✓ ✓ $0.267$ $0$ $1.48238$ Modular form 799.1.h.b.281.1
2-799-799.281-c0-0-2 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.281 $0.0$ 0 ✓ ✓ $0.0675$ $0$ $1.55137$ Modular form 799.1.h.b.281.3
2-799-799.281-c0-0-3 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.281 $0.0$ 0 ✓ ✓ $-0.132$ $0$ $1.84847$ Modular form 799.1.h.a.281.1
2-799-799.281-c0-0-4 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.281 $0.0$ 0 ✓ ✓ $0.467$ $0$ $2.88335$ Modular form 799.1.h.b.281.4
2-799-799.563-c0-0-0 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.563 $0.0$ 0 ✓ ✓ $-0.267$ $0$ $0.338365$ Modular form 799.1.h.b.563.1
2-799-799.563-c0-0-1 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.563 $0.0$ 0 ✓ ✓ $-0.467$ $0$ $1.12032$ Modular form 799.1.h.b.563.4
2-799-799.563-c0-0-2 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.563 $0.0$ 0 ✓ ✓ $-0.0675$ $0$ $2.03377$ Modular form 799.1.h.b.563.3
2-799-799.563-c0-0-3 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.563 $0.0$ 0 ✓ ✓ $0.332$ $0$ $2.15295$ Modular form 799.1.h.b.563.2
2-799-799.563-c0-0-4 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.563 $0.0$ 0 ✓ ✓ $0.132$ $0$ $2.27441$ Modular form 799.1.h.a.563.1
2-799-799.610-c0-0-0 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.610 $0.0$ 0 ✓ ✓ $-0.187$ $0$ $0.983077$ Modular form 799.1.h.b.610.2
2-799-799.610-c0-0-1 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.610 $0.0$ 0 ✓ ✓ $0.412$ $0$ $1.33350$ Modular form 799.1.h.b.610.1
2-799-799.610-c0-0-2 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.610 $0.0$ 0 ✓ ✓ $-0.387$ $0$ $1.49259$ Modular form 799.1.h.b.610.4
2-799-799.610-c0-0-3 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.610 $0.0$ 0 ✓ ✓ $0.0120$ $0$ $1.74253$ Modular form 799.1.h.a.610.1
2-799-799.610-c0-0-4 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.610 $0.0$ 0 ✓ ✓ $0.212$ $0$ $2.46756$ Modular form 799.1.h.b.610.3
2-799-799.798-c0-0-0 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.798 $0.0$ 0 ✓ ✓ $-0.400$ $0$ $0.731933$ Modular form 799.1.c.d.798.2
2-799-799.798-c0-0-1 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.798 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $0.889799$ Modular form 799.1.c.c.798.1
2-799-799.798-c0-0-10 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.798 $0.0$ 0 ✓ ✓ $0.200$ $0$ $2.81711$ Modular form 799.1.c.d.798.3
2-799-799.798-c0-0-2 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.798 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.14367$ Artin representation 2.799.8t6.a.a Modular form 799.1.c.b.798.1
2-799-799.798-c0-0-3 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.798 $0.0$ 0 ✓ ✓ ✓ ✓ $0$ $0$ $1.19290$ Artin representation 2.799.4t3.a Artin representation 2.799.4t3.a.a Modular form 799.1.c.a Modular form 799.1.c.a.798.1
2-799-799.798-c0-0-4 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.798 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.48972$ Artin representation 2.799.8t6.a.b Modular form 799.1.c.b.798.2
2-799-799.798-c0-0-5 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.798 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.58425$ Modular form 799.1.c.c.798.2
2-799-799.798-c0-0-6 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.798 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $1.87223$ Modular form 799.1.c.c.798.3
2-799-799.798-c0-0-7 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.798 $0.0$ 0 ✓ ✓ $-0.200$ $0$ $1.89740$ Modular form 799.1.c.d.798.4
2-799-799.798-c0-0-8 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.798 $0.0$ 0 ✓ ✓ ✓ $0$ $0$ $2.14037$ Modular form 799.1.c.c.798.4
2-799-799.798-c0-0-9 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.798 $0.0$ 0 ✓ ✓ $0.400$ $0$ $2.15833$ Modular form 799.1.c.d.798.1
2-799-799.93-c0-0-0 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.93 $0.0$ 0 ✓ ✓ $-0.212$ $0$ $0.894786$ Modular form 799.1.h.b.93.3
2-799-799.93-c0-0-1 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.93 $0.0$ 0 ✓ ✓ $-0.412$ $0$ $1.09419$ Modular form 799.1.h.b.93.1
2-799-799.93-c0-0-2 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.93 $0.0$ 0 ✓ ✓ $-0.0120$ $0$ $1.52141$ Modular form 799.1.h.a.93.1
2-799-799.93-c0-0-3 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.93 $0.0$ 0 ✓ ✓ $0.187$ $0$ $2.09975$ Modular form 799.1.h.b.93.2
2-799-799.93-c0-0-4 $0.631$ $0.398$ $2$ $17 \cdot 47$ 799.93 $0.0$ 0 ✓ ✓ $0.387$ $0$ $3.06285$ Modular form 799.1.h.b.93.4
2-799-1.1-c1-0-0 $2.52$ $6.38$ $2$ $17 \cdot 47$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.0835569$ Modular form 799.2.a.g.1.9
2-799-1.1-c1-0-1 $2.52$ $6.38$ $2$ $17 \cdot 47$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.371380$ Modular form 799.2.a.f.1.1
2-799-1.1-c1-0-10 $2.52$ $6.38$ $2$ $17 \cdot 47$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.769334$ Modular form 799.2.a.g.1.5
2-799-1.1-c1-0-11 $2.52$ $6.38$ $2$ $17 \cdot 47$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.854140$ Modular form 799.2.a.g.1.2
2-799-1.1-c1-0-12 $2.52$ $6.38$ $2$ $17 \cdot 47$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.932484$ Modular form 799.2.a.g.1.10
2-799-1.1-c1-0-13 $2.52$ $6.38$ $2$ $17 \cdot 47$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.01038$ Modular form 799.2.a.d.1.3
2-799-1.1-c1-0-14 $2.52$ $6.38$ $2$ $17 \cdot 47$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.04537$ Modular form 799.2.a.g.1.1
2-799-1.1-c1-0-15 $2.52$ $6.38$ $2$ $17 \cdot 47$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.08693$ Modular form 799.2.a.g.1.15
2-799-1.1-c1-0-16 $2.52$ $6.38$ $2$ $17 \cdot 47$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.10534$ Modular form 799.2.a.f.1.3
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