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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
2-75-1.1-c9-0-0 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $0.324780$ Modular form 75.10.a.i.1.2
2-75-1.1-c9-0-1 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $0.420937$ Modular form 75.10.a.k.1.3
2-75-1.1-c9-0-10 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $0.934411$ Modular form 75.10.a.i.1.1
2-75-1.1-c9-0-11 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $0.987694$ Modular form 75.10.a.j.1.1
2-75-1.1-c9-0-12 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $1.07803$ Modular form 75.10.a.i.1.4
2-75-1.1-c9-0-13 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.11917$ Modular form 75.10.a.b Modular form 75.10.a.b.1.1
2-75-1.1-c9-0-14 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0.5$ $1$ $1.25774$ Modular form 75.10.a.g.1.1
2-75-1.1-c9-0-15 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0.5$ $1$ $1.36364$ Modular form 75.10.a.h.1.1
2-75-1.1-c9-0-16 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $1.37794$ Modular form 75.10.a.k.1.4
2-75-1.1-c9-0-17 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ ✓ $0.5$ $1$ $1.45182$ Modular form 75.10.a.c Modular form 75.10.a.c.1.1
2-75-1.1-c9-0-18 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0.5$ $1$ $1.45518$ Modular form 75.10.a.l.1.1
2-75-1.1-c9-0-19 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ ✓ $0$ $0$ $1.48847$ Modular form 75.10.a.d Modular form 75.10.a.d.1.1
2-75-1.1-c9-0-2 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $0.496796$ Modular form 75.10.a.f.1.1
2-75-1.1-c9-0-20 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0.5$ $1$ $1.49047$ Modular form 75.10.a.l.1.2
2-75-1.1-c9-0-21 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0.5$ $1$ $1.49452$ Modular form 75.10.a.e.1.1
2-75-1.1-c9-0-22 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $1.60749$ Modular form 75.10.a.j.1.4
2-75-1.1-c9-0-23 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0.5$ $1$ $1.66522$ Modular form 75.10.a.e.1.2
2-75-1.1-c9-0-24 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0.5$ $1$ $1.87181$ Modular form 75.10.a.g.1.2
2-75-1.1-c9-0-25 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0.5$ $1$ $2.15669$ Modular form 75.10.a.l.1.3
2-75-1.1-c9-0-26 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0.5$ $1$ $2.18683$ Modular form 75.10.a.h.1.2
2-75-1.1-c9-0-27 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0.5$ $1$ $2.38487$ Modular form 75.10.a.l.1.4
2-75-1.1-c9-0-3 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $0.581025$ Modular form 75.10.a.k.1.1
2-75-1.1-c9-0-4 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $0.609308$ Modular form 75.10.a.k.1.2
2-75-1.1-c9-0-5 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $0.684723$ Modular form 75.10.a.i.1.3
2-75-1.1-c9-0-6 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $0.855746$ Modular form 75.10.a.f.1.2
2-75-1.1-c9-0-7 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ ✓ $0$ $0$ $0.856631$ Modular form 75.10.a.a Modular form 75.10.a.a.1.1
2-75-1.1-c9-0-8 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $0.895601$ Modular form 75.10.a.j.1.3
2-75-1.1-c9-0-9 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 1.1 $9.0$ $9$ ✓ ✓ ✓ $0$ $0$ $0.907986$ Modular form 75.10.a.j.1.2
2-75-15.2-c9-0-0 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $0.0685$ $0$ $0.0240161$ Modular form 75.10.e.f.32.3
2-75-15.2-c9-0-1 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $0.249$ $0$ $0.154848$ Modular form 75.10.e.g.32.4
2-75-15.2-c9-0-10 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.149$ $0$ $0.474488$ Modular form 75.10.e.g.32.17
2-75-15.2-c9-0-11 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $0.0310$ $0$ $0.495501$ Modular form 75.10.e.g.32.21
2-75-15.2-c9-0-12 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.105$ $0$ $0.563032$ Modular form 75.10.e.a.32.2
2-75-15.2-c9-0-13 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.226$ $0$ $0.564116$ Modular form 75.10.e.f.32.5
2-75-15.2-c9-0-14 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.244$ $0$ $0.612769$ Modular form 75.10.e.g.32.7
2-75-15.2-c9-0-15 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.187$ $0$ $0.614882$ Modular form 75.10.e.e.32.1
2-75-15.2-c9-0-16 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.188$ $0$ $0.640158$ Modular form 75.10.e.g.32.2
2-75-15.2-c9-0-17 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.286$ $0$ $0.668464$ Modular form 75.10.e.c.32.2
2-75-15.2-c9-0-18 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.425$ $0$ $0.699778$ Modular form 75.10.e.g.32.3
2-75-15.2-c9-0-19 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $0.114$ $0$ $0.703520$ Modular form 75.10.e.e.32.3
2-75-15.2-c9-0-2 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $0.277$ $0$ $0.198769$ Modular form 75.10.e.f.32.8
2-75-15.2-c9-0-20 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.0268$ $0$ $0.745493$ Modular form 75.10.e.g.32.18
2-75-15.2-c9-0-21 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.225$ $0$ $0.755673$ Modular form 75.10.e.f.32.1
2-75-15.2-c9-0-22 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.349$ $0$ $0.759430$ Modular form 75.10.e.g.32.15
2-75-15.2-c9-0-23 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.385$ $0$ $0.809296$ Modular form 75.10.e.e.32.2
2-75-15.2-c9-0-24 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.0850$ $0$ $0.834327$ Modular form 75.10.e.f.32.13
2-75-15.2-c9-0-25 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $-0.0445$ $0$ $0.868553$ Modular form 75.10.e.g.32.9
2-75-15.2-c9-0-26 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $0.133$ $0$ $0.879981$ Modular form 75.10.e.g.32.14
2-75-15.2-c9-0-27 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $0.213$ $0$ $0.907401$ Modular form 75.10.e.c.32.1
2-75-15.2-c9-0-28 $6.21$ $38.6$ $2$ $3 \cdot 5^{2}$ 15.2 $9.0$ $9$ ✓ ✓ $0.0322$ $0$ $0.941008$ Modular form 75.10.e.a.32.1
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