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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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Results (1-50 of 7824627 matches)

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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
1-1-1.1-r0-0-0 $0.00464$ $0.00464$ $1$ $1$ 1.1 $$ $$ $0$ ✓ ✓ ✓ ✓ $0$ $0$ $14.1347$ Artin representation 1.1.1t1.a Artin representation 1.1.1t1.a.a Dirichlet character \(\chi_{1} (1, \cdot) \) Number field \(\Q\)
1-5-5.4-r0-0-0 $0.0232$ $0.0232$ $1$ $5$ 5.4 $0$ $$ $0$ ✓ ✓ ✓ ✓ $0$ $0$ $6.64845$ Dirichlet character \(\chi_{5} (4, \cdot) \)
1-7-7.2-r0-0-0 $0.0325$ $0.0325$ $1$ $7$ 7.2 $0$ $$ $0$ ✓ ✓ $-0.0732$ $0$ $4.35640$ Dirichlet character \(\chi_{7} (2, \cdot) \)
1-7-7.4-r0-0-0 $0.0325$ $0.0325$ $1$ $7$ 7.4 $0$ $$ $0$ ✓ ✓ $0.0732$ $0$ $6.20123$ Dirichlet character \(\chi_{7} (4, \cdot) \)
1-2e3-8.5-r0-0-0 $0.0371$ $0.0371$ $1$ $2^{3}$ 8.5 $0$ $$ $0$ ✓ ✓ ✓ ✓ $0$ $0$ $4.89997$ Dirichlet character \(\chi_{8} (5, \cdot) \)
1-3e2-9.4-r0-0-0 $0.0417$ $0.0417$ $1$ $3^{2}$ 9.4 $0$ $$ $0$ ✓ ✓ $0.111$ $0$ $5.31957$ Dirichlet character \(\chi_{9} (4, \cdot) \)
1-3e2-9.7-r0-0-0 $0.0417$ $0.0417$ $1$ $3^{2}$ 9.7 $0$ $$ $0$ ✓ ✓ $-0.111$ $0$ $3.44409$ Dirichlet character \(\chi_{9} (7, \cdot) \)
1-11-11.3-r0-0-0 $0.0510$ $0.0510$ $1$ $11$ 11.3 $0$ $$ $0$ ✓ ✓ $-0.103$ $0$ $3.61004$ Dirichlet character \(\chi_{11} (3, \cdot) \)
1-11-11.4-r0-0-0 $0.0510$ $0.0510$ $1$ $11$ 11.4 $0$ $$ $0$ ✓ ✓ $0.103$ $0$ $5.13369$ Dirichlet character \(\chi_{11} (4, \cdot) \)
1-11-11.5-r0-0-0 $0.0510$ $0.0510$ $1$ $11$ 11.5 $0$ $$ $0$ ✓ ✓ $0.142$ $0$ $4.62935$ Dirichlet character \(\chi_{11} (5, \cdot) \)
1-11-11.9-r0-0-0 $0.0510$ $0.0510$ $1$ $11$ 11.9 $0$ $$ $0$ ✓ ✓ $-0.142$ $0$ $2.69600$ Dirichlet character \(\chi_{11} (9, \cdot) \)
1-12-12.11-r0-0-0 $0.0557$ $0.0557$ $1$ $2^{2} \cdot 3$ 12.11 $0$ $$ $0$ ✓ ✓ ✓ ✓ $0$ $0$ $3.80462$ Dirichlet character \(\chi_{12} (11, \cdot) \)
1-13-13.10-r0-0-0 $0.0603$ $0.0603$ $1$ $13$ 13.10 $0$ $$ $0$ ✓ ✓ $-0.0853$ $0$ $3.66097$ Dirichlet character \(\chi_{13} (10, \cdot) \)
1-13-13.12-r0-0-0 $0.0603$ $0.0603$ $1$ $13$ 13.12 $0$ $$ $0$ ✓ ✓ ✓ ✓ $0$ $0$ $3.11934$ Dirichlet character \(\chi_{13} (12, \cdot) \)
1-13-13.3-r0-0-0 $0.0603$ $0.0603$ $1$ $13$ 13.3 $0$ $$ $0$ ✓ ✓ $0.209$ $0$ $4.93859$ Dirichlet character \(\chi_{13} (3, \cdot) \)
1-13-13.4-r0-0-0 $0.0603$ $0.0603$ $1$ $13$ 13.4 $0$ $$ $0$ ✓ ✓ $0.0853$ $0$ $4.45485$ Dirichlet character \(\chi_{13} (4, \cdot) \)
1-13-13.9-r0-0-0 $0.0603$ $0.0603$ $1$ $13$ 13.9 $0$ $$ $0$ ✓ ✓ $-0.209$ $0$ $2.27313$ Dirichlet character \(\chi_{13} (9, \cdot) \)
1-15-15.2-r0-0-0 $0.0696$ $0.0696$ $1$ $3 \cdot 5$ 15.2 $0$ $$ $0$ ✓ ✓ $-0.161$ $0$ $2.73460$ Dirichlet character \(\chi_{15} (2, \cdot) \)
1-15-15.8-r0-0-0 $0.0696$ $0.0696$ $1$ $3 \cdot 5$ 15.8 $0$ $$ $0$ ✓ ✓ $0.161$ $0$ $4.40670$ Dirichlet character \(\chi_{15} (8, \cdot) \)
1-2e4-16.13-r0-0-0 $0.0743$ $0.0743$ $1$ $2^{4}$ 16.13 $0$ $$ $0$ ✓ ✓ $0.0625$ $0$ $3.77219$ Dirichlet character \(\chi_{16} (13, \cdot) \)
1-2e4-16.5-r0-0-0 $0.0743$ $0.0743$ $1$ $2^{4}$ 16.5 $0$ $$ $0$ ✓ ✓ $-0.0625$ $0$ $2.84244$ Dirichlet character \(\chi_{16} (5, \cdot) \)
1-17-17.13-r0-0-0 $0.0789$ $0.0789$ $1$ $17$ 17.13 $0$ $$ $0$ ✓ ✓ $0.144$ $0$ $3.38764$ Dirichlet character \(\chi_{17} (13, \cdot) \)
1-17-17.15-r0-0-0 $0.0789$ $0.0789$ $1$ $17$ 17.15 $0$ $$ $0$ ✓ ✓ $0.237$ $0$ $4.85147$ Dirichlet character \(\chi_{17} (15, \cdot) \)
1-17-17.16-r0-0-0 $0.0789$ $0.0789$ $1$ $17$ 17.16 $0$ $$ $0$ ✓ ✓ ✓ ✓ $0$ $0$ $3.72814$ Dirichlet character \(\chi_{17} (16, \cdot) \)
1-17-17.2-r0-0-0 $0.0789$ $0.0789$ $1$ $17$ 17.2 $0$ $$ $0$ ✓ ✓ $0.117$ $0$ $3.73234$ Dirichlet character \(\chi_{17} (2, \cdot) \)
1-17-17.4-r0-0-0 $0.0789$ $0.0789$ $1$ $17$ 17.4 $0$ $$ $0$ ✓ ✓ $-0.144$ $0$ $1.89456$ Dirichlet character \(\chi_{17} (4, \cdot) \)
1-17-17.8-r0-0-0 $0.0789$ $0.0789$ $1$ $17$ 17.8 $0$ $$ $0$ ✓ ✓ $-0.237$ $0$ $2.12217$ Dirichlet character \(\chi_{17} (8, \cdot) \)
1-17-17.9-r0-0-0 $0.0789$ $0.0789$ $1$ $17$ 17.9 $0$ $$ $0$ ✓ ✓ $-0.117$ $0$ $3.03085$ Dirichlet character \(\chi_{17} (9, \cdot) \)
1-19-19.11-r0-0-0 $0.0882$ $0.0882$ $1$ $19$ 19.11 $0$ $$ $0$ ✓ ✓ $-0.299$ $0$ $1.57320$ Dirichlet character \(\chi_{19} (11, \cdot) \)
1-19-19.16-r0-0-0 $0.0882$ $0.0882$ $1$ $19$ 19.16 $0$ $$ $0$ ✓ ✓ $0.113$ $0$ $3.63715$ Dirichlet character \(\chi_{19} (16, \cdot) \)
1-19-19.17-r0-0-0 $0.0882$ $0.0882$ $1$ $19$ 19.17 $0$ $$ $0$ ✓ ✓ $0.0530$ $0$ $2.87454$ Dirichlet character \(\chi_{19} (17, \cdot) \)
1-19-19.4-r0-0-0 $0.0882$ $0.0882$ $1$ $19$ 19.4 $0$ $$ $0$ ✓ ✓ $0.132$ $0$ $4.27062$ Dirichlet character \(\chi_{19} (4, \cdot) \)
1-19-19.5-r0-0-0 $0.0882$ $0.0882$ $1$ $19$ 19.5 $0$ $$ $0$ ✓ ✓ $-0.132$ $0$ $2.73327$ Dirichlet character \(\chi_{19} (5, \cdot) \)
1-19-19.6-r0-0-0 $0.0882$ $0.0882$ $1$ $19$ 19.6 $0$ $$ $0$ ✓ ✓ $-0.113$ $0$ $3.09878$ Dirichlet character \(\chi_{19} (6, \cdot) \)
1-19-19.7-r0-0-0 $0.0882$ $0.0882$ $1$ $19$ 19.7 $0$ $$ $0$ ✓ ✓ $0.299$ $0$ $4.40883$ Dirichlet character \(\chi_{19} (7, \cdot) \)
1-19-19.9-r0-0-0 $0.0882$ $0.0882$ $1$ $19$ 19.9 $0$ $$ $0$ ✓ ✓ $-0.0530$ $0$ $2.13818$ Dirichlet character \(\chi_{19} (9, \cdot) \)
1-20-20.3-r0-0-0 $0.0928$ $0.0928$ $1$ $2^{2} \cdot 5$ 20.3 $0$ $$ $0$ ✓ ✓ $-0.0881$ $0$ $2.43970$ Dirichlet character \(\chi_{20} (3, \cdot) \)
1-20-20.7-r0-0-0 $0.0928$ $0.0928$ $1$ $2^{2} \cdot 5$ 20.7 $0$ $$ $0$ ✓ ✓ $0.0881$ $0$ $3.53109$ Dirichlet character \(\chi_{20} (7, \cdot) \)
1-21-21.17-r0-0-0 $0.0975$ $0.0975$ $1$ $3 \cdot 7$ 21.17 $0$ $$ $0$ ✓ ✓ $-0.146$ $0$ $2.71366$ Dirichlet character \(\chi_{21} (17, \cdot) \)
1-21-21.20-r0-0-0 $0.0975$ $0.0975$ $1$ $3 \cdot 7$ 21.20 $0$ $$ $0$ ✓ ✓ ✓ ✓ $0$ $0$ $2.31518$ Dirichlet character \(\chi_{21} (20, \cdot) \)
1-21-21.5-r0-0-0 $0.0975$ $0.0975$ $1$ $3 \cdot 7$ 21.5 $0$ $$ $0$ ✓ ✓ $0.146$ $0$ $3.93679$ Dirichlet character \(\chi_{21} (5, \cdot) \)
1-23-23.12-r0-0-0 $0.106$ $0.106$ $1$ $23$ 23.12 $0$ $$ $0$ ✓ ✓ $-0.233$ $0$ $1.96977$ Dirichlet character \(\chi_{23} (12, \cdot) \)
1-23-23.13-r0-0-0 $0.106$ $0.106$ $1$ $23$ 23.13 $0$ $$ $0$ ✓ ✓ $0.248$ $0$ $4.12168$ Dirichlet character \(\chi_{23} (13, \cdot) \)
1-23-23.16-r0-0-0 $0.106$ $0.106$ $1$ $23$ 23.16 $0$ $$ $0$ ✓ ✓ $-0.248$ $0$ $2.04476$ Dirichlet character \(\chi_{23} (16, \cdot) \)
1-23-23.18-r0-0-0 $0.106$ $0.106$ $1$ $23$ 23.18 $0$ $$ $0$ ✓ ✓ $0.0263$ $0$ $3.18006$ Dirichlet character \(\chi_{23} (18, \cdot) \)
1-23-23.2-r0-0-0 $0.106$ $0.106$ $1$ $23$ 23.2 $0$ $$ $0$ ✓ ✓ $0.233$ $0$ $4.10757$ Dirichlet character \(\chi_{23} (2, \cdot) \)
1-23-23.3-r0-0-0 $0.106$ $0.106$ $1$ $23$ 23.3 $0$ $$ $0$ ✓ ✓ $-0.187$ $0$ $1.27653$ Dirichlet character \(\chi_{23} (3, \cdot) \)
1-23-23.4-r0-0-0 $0.106$ $0.106$ $1$ $23$ 23.4 $0$ $$ $0$ ✓ ✓ $0.0869$ $0$ $2.69506$ Dirichlet character \(\chi_{23} (4, \cdot) \)
1-23-23.6-r0-0-0 $0.106$ $0.106$ $1$ $23$ 23.6 $0$ $$ $0$ ✓ ✓ $-0.0869$ $0$ $2.47039$ Dirichlet character \(\chi_{23} (6, \cdot) \)
1-23-23.8-r0-0-0 $0.106$ $0.106$ $1$ $23$ 23.8 $0$ $$ $0$ ✓ ✓ $0.187$ $0$ $3.01197$ Dirichlet character \(\chi_{23} (8, \cdot) \)
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