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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
2-12-3.2-c2-0-0 $0.571$ $0.326$ $2$ $2^{2} \cdot 3$ 3.2 $2.0$ $2$ ✓ ✓ ✓ ✓ $0$ $0$ $5.13182$ Modular form 12.3.c.a Modular form 12.3.c.a.5.1
2-12-4.3-c2-0-0 $0.571$ $0.326$ $2$ $2^{2} \cdot 3$ 4.3 $2.0$ $2$ ✓ ✓ $-0.0833$ $0$ $4.04688$ Modular form 12.3.d.a.7.2
2-12-4.3-c2-0-1 $0.571$ $0.326$ $2$ $2^{2} \cdot 3$ 4.3 $2.0$ $2$ ✓ ✓ $0.0833$ $0$ $5.81330$ Modular form 12.3.d.a.7.1
2-12-1.1-c3-0-0 $0.841$ $0.708$ $2$ $2^{2} \cdot 3$ 1.1 $3.0$ $3$ ✓ ✓ ✓ ✓ $0$ $0$ $4.02436$ Modular form 12.4.a.a Modular form 12.4.a.a.1.1
2-12-12.11-c3-0-0 $0.841$ $0.708$ $2$ $2^{2} \cdot 3$ 12.11 $3.0$ $3$ ✓ ✓ $-0.156$ $0$ $2.75108$ Modular form 12.4.b.a.11.2
2-12-12.11-c3-0-1 $0.841$ $0.708$ $2$ $2^{2} \cdot 3$ 12.11 $3.0$ $3$ ✓ ✓ $-0.0759$ $0$ $3.96721$ Modular form 12.4.b.a.11.4
2-12-12.11-c3-0-2 $0.841$ $0.708$ $2$ $2^{2} \cdot 3$ 12.11 $3.0$ $3$ ✓ ✓ $0.156$ $0$ $4.99667$ Modular form 12.4.b.a.11.1
2-12-12.11-c3-0-3 $0.841$ $0.708$ $2$ $2^{2} \cdot 3$ 12.11 $3.0$ $3$ ✓ ✓ $0.0759$ $0$ $5.11970$ Modular form 12.4.b.a.11.3
2-12-3.2-c4-0-0 $1.11$ $1.24$ $2$ $2^{2} \cdot 3$ 3.2 $4.0$ $4$ ✓ ✓ ✓ ✓ $0$ $0$ $3.35298$ Modular form 12.5.c.a Modular form 12.5.c.a.5.1
2-12-4.3-c4-0-0 $1.11$ $1.24$ $2$ $2^{2} \cdot 3$ 4.3 $4.0$ $4$ ✓ ✓ $-0.225$ $0$ $2.19838$ Modular form 12.5.d.a.7.2
2-12-4.3-c4-0-1 $1.11$ $1.24$ $2$ $2^{2} \cdot 3$ 4.3 $4.0$ $4$ ✓ ✓ $-0.0592$ $0$ $3.57829$ Modular form 12.5.d.a.7.4
2-12-4.3-c4-0-2 $1.11$ $1.24$ $2$ $2^{2} \cdot 3$ 4.3 $4.0$ $4$ ✓ ✓ $0.0592$ $0$ $4.11501$ Modular form 12.5.d.a.7.3
2-12-4.3-c4-0-3 $1.11$ $1.24$ $2$ $2^{2} \cdot 3$ 4.3 $4.0$ $4$ ✓ ✓ $0.225$ $0$ $4.94391$ Modular form 12.5.d.a.7.1
2-12-12.11-c5-0-0 $1.38$ $1.92$ $2$ $2^{2} \cdot 3$ 12.11 $5.0$ $5$ ✓ ✓ $-0.436$ $0$ $0.797356$ Modular form 12.6.b.a.11.4
2-12-12.11-c5-0-1 $1.38$ $1.92$ $2$ $2^{2} \cdot 3$ 12.11 $5.0$ $5$ ✓ ✓ $-0.199$ $0$ $1.30326$ Modular form 12.6.b.a.11.1
2-12-12.11-c5-0-2 $1.38$ $1.92$ $2$ $2^{2} \cdot 3$ 12.11 $5.0$ $5$ ✓ ✓ $-0.157$ $0$ $2.55273$ Modular form 12.6.b.a.11.6
2-12-12.11-c5-0-3 $1.38$ $1.92$ $2$ $2^{2} \cdot 3$ 12.11 $5.0$ $5$ ✓ ✓ $-0.113$ $0$ $2.65981$ Modular form 12.6.b.a.11.8
2-12-12.11-c5-0-4 $1.38$ $1.92$ $2$ $2^{2} \cdot 3$ 12.11 $5.0$ $5$ ✓ ✓ $0.199$ $0$ $3.26438$ Modular form 12.6.b.a.11.2
2-12-12.11-c5-0-5 $1.38$ $1.92$ $2$ $2^{2} \cdot 3$ 12.11 $5.0$ $5$ ✓ ✓ $0.157$ $0$ $3.82697$ Modular form 12.6.b.a.11.5
2-12-12.11-c5-0-6 $1.38$ $1.92$ $2$ $2^{2} \cdot 3$ 12.11 $5.0$ $5$ ✓ ✓ $0.113$ $0$ $4.17191$ Modular form 12.6.b.a.11.7
2-12-12.11-c5-0-7 $1.38$ $1.92$ $2$ $2^{2} \cdot 3$ 12.11 $5.0$ $5$ ✓ ✓ $0.436$ $0$ $5.29014$ Modular form 12.6.b.a.11.3
2-12-3.2-c6-0-0 $1.66$ $2.76$ $2$ $2^{2} \cdot 3$ 3.2 $6.0$ $6$ ✓ ✓ $-0.232$ $0$ $1.34556$ Modular form 12.7.c.a.5.2
2-12-3.2-c6-0-1 $1.66$ $2.76$ $2$ $2^{2} \cdot 3$ 3.2 $6.0$ $6$ ✓ ✓ $0.232$ $0$ $3.51724$ Modular form 12.7.c.a.5.1
2-12-4.3-c6-0-0 $1.66$ $2.76$ $2$ $2^{2} \cdot 3$ 4.3 $6.0$ $6$ ✓ ✓ $0.482$ $0$ $0.406534$ Modular form 12.7.d.a.7.4
2-12-4.3-c6-0-1 $1.66$ $2.76$ $2$ $2^{2} \cdot 3$ 4.3 $6.0$ $6$ ✓ ✓ $-0.0997$ $0$ $1.38582$ Modular form 12.7.d.a.7.1
2-12-4.3-c6-0-2 $1.66$ $2.76$ $2$ $2^{2} \cdot 3$ 4.3 $6.0$ $6$ ✓ ✓ $-0.132$ $0$ $2.31456$ Modular form 12.7.d.a.7.6
2-12-4.3-c6-0-3 $1.66$ $2.76$ $2$ $2^{2} \cdot 3$ 4.3 $6.0$ $6$ ✓ ✓ $0.0997$ $0$ $2.39020$ Modular form 12.7.d.a.7.2
2-12-4.3-c6-0-4 $1.66$ $2.76$ $2$ $2^{2} \cdot 3$ 4.3 $6.0$ $6$ ✓ ✓ $0.132$ $0$ $3.63164$ Modular form 12.7.d.a.7.5
2-12-4.3-c6-0-5 $1.66$ $2.76$ $2$ $2^{2} \cdot 3$ 4.3 $6.0$ $6$ ✓ ✓ $-0.482$ $0$ $4.56029$ Modular form 12.7.d.a.7.3
2-12-1.1-c7-0-0 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 1.1 $7.0$ $7$ ✓ ✓ ✓ ✓ $0$ $0$ $2.17027$ Modular form 12.8.a.b Modular form 12.8.a.b.1.1
2-12-1.1-c7-0-1 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 1.1 $7.0$ $7$ ✓ ✓ ✓ ✓ $0.5$ $1$ $3.92006$ Modular form 12.8.a.a Modular form 12.8.a.a.1.1
2-12-12.11-c7-0-0 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 12.11 $7.0$ $7$ ✓ ✓ $-0.236$ $0$ $0.464456$ Modular form 12.8.b.a.11.1
2-12-12.11-c7-0-1 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 12.11 $7.0$ $7$ ✓ ✓ $-0.254$ $0$ $0.572684$ Modular form 12.8.b.b.11.3
2-12-12.11-c7-0-10 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 12.11 $7.0$ $7$ ✓ ✓ $0.317$ $0$ $3.82154$ Modular form 12.8.b.b.11.7
2-12-12.11-c7-0-11 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 12.11 $7.0$ $7$ ✓ ✓ $0.376$ $0$ $4.06809$ Modular form 12.8.b.b.11.5
2-12-12.11-c7-0-2 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 12.11 $7.0$ $7$ ✓ ✓ $-0.317$ $0$ $1.17235$ Modular form 12.8.b.b.11.8
2-12-12.11-c7-0-3 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 12.11 $7.0$ $7$ ✓ ✓ $-0.376$ $0$ $1.27298$ Modular form 12.8.b.b.11.6
2-12-12.11-c7-0-4 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 12.11 $7.0$ $7$ ✓ ✓ $-0.228$ $0$ $1.30979$ Modular form 12.8.b.b.11.2
2-12-12.11-c7-0-5 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 12.11 $7.0$ $7$ ✓ ✓ $0.236$ $0$ $2.22195$ Modular form 12.8.b.a.11.2
2-12-12.11-c7-0-6 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 12.11 $7.0$ $7$ ✓ ✓ $0.00450$ $0$ $2.56429$ Modular form 12.8.b.a.11.3
2-12-12.11-c7-0-7 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 12.11 $7.0$ $7$ ✓ ✓ $0.228$ $0$ $2.56911$ Modular form 12.8.b.b.11.1
2-12-12.11-c7-0-8 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 12.11 $7.0$ $7$ ✓ ✓ $-0.00450$ $0$ $2.86836$ Modular form 12.8.b.a.11.4
2-12-12.11-c7-0-9 $1.93$ $3.74$ $2$ $2^{2} \cdot 3$ 12.11 $7.0$ $7$ ✓ ✓ $0.254$ $0$ $3.01022$ Modular form 12.8.b.b.11.4
2-12-3.2-c8-0-0 $2.21$ $4.88$ $2$ $2^{2} \cdot 3$ 3.2 $8.0$ $8$ ✓ ✓ $-0.358$ $0$ $0.348863$ Modular form 12.9.c.b.5.1
2-12-3.2-c8-0-1 $2.21$ $4.88$ $2$ $2^{2} \cdot 3$ 3.2 $8.0$ $8$ ✓ ✓ ✓ ✓ $0$ $0$ $2.05258$ Modular form 12.9.c.a Modular form 12.9.c.a.5.1
2-12-3.2-c8-0-2 $2.21$ $4.88$ $2$ $2^{2} \cdot 3$ 3.2 $8.0$ $8$ ✓ ✓ $0.358$ $0$ $2.83317$ Modular form 12.9.c.b.5.2
2-12-4.3-c8-0-0 $2.21$ $4.88$ $2$ $2^{2} \cdot 3$ 4.3 $8.0$ $8$ ✓ ✓ $-0.295$ $0$ $0.306045$ Modular form 12.9.d.a.7.3
2-12-4.3-c8-0-1 $2.21$ $4.88$ $2$ $2^{2} \cdot 3$ 4.3 $8.0$ $8$ ✓ ✓ $-0.291$ $0$ $0.498903$ Modular form 12.9.d.a.7.2
2-12-4.3-c8-0-2 $2.21$ $4.88$ $2$ $2^{2} \cdot 3$ 4.3 $8.0$ $8$ ✓ ✓ $-0.404$ $0$ $1.01813$ Modular form 12.9.d.a.7.6
2-12-4.3-c8-0-3 $2.21$ $4.88$ $2$ $2^{2} \cdot 3$ 4.3 $8.0$ $8$ ✓ ✓ $-0.0752$ $0$ $2.14170$ Modular form 12.9.d.a.7.8
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