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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
2-669-1.1-c1-0-0 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.592332$ Modular form 669.2.a.h.1.1
2-669-1.1-c1-0-1 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.620162$ Modular form 669.2.a.h.1.4
2-669-1.1-c1-0-10 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.20550$ Modular form 669.2.a.i.1.8
2-669-1.1-c1-0-11 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.23715$ Modular form 669.2.a.i.1.1
2-669-1.1-c1-0-12 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.24627$ Modular form 669.2.a.b.1.1
2-669-1.1-c1-0-13 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.32661$ Modular form 669.2.a.i.1.10
2-669-1.1-c1-0-14 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.44991$ Modular form 669.2.a.d.1.1
2-669-1.1-c1-0-15 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.48191$ Modular form 669.2.a.i.1.5
2-669-1.1-c1-0-16 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.53455$ Modular form 669.2.a.i.1.9
2-669-1.1-c1-0-17 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.54051$ Modular form 669.2.a.h.1.6
2-669-1.1-c1-0-18 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.60208$ Modular form 669.2.a.e.1.2
2-669-1.1-c1-0-19 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.63874$ Modular form 669.2.a.e.1.1
2-669-1.1-c1-0-2 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.671384$ Modular form 669.2.a.i.1.6
2-669-1.1-c1-0-20 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.70802$ Modular form 669.2.a.f.1.2
2-669-1.1-c1-0-21 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.73746$ Modular form 669.2.a.h.1.7
2-669-1.1-c1-0-22 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.79298$ Modular form 669.2.a.g.1.1
2-669-1.1-c1-0-23 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.79741$ Modular form 669.2.a.f.1.1
2-669-1.1-c1-0-24 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.82476$ Modular form 669.2.a.i.1.11
2-669-1.1-c1-0-25 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.89946$ Modular form 669.2.a.b.1.2
2-669-1.1-c1-0-26 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.90719$ Modular form 669.2.a.i.1.14
2-669-1.1-c1-0-27 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $1.96180$ Modular form 669.2.a.c.1.1
2-669-1.1-c1-0-28 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.01270$ Modular form 669.2.a.g.1.2
2-669-1.1-c1-0-29 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.03464$ Modular form 669.2.a.i.1.12
2-669-1.1-c1-0-3 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $0.867375$ Modular form 669.2.a.i.1.2
2-669-1.1-c1-0-30 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $2.05461$ Modular form 669.2.a.i.1.13
2-669-1.1-c1-0-31 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.29298$ Elliptic curve 669.a Modular form 669.2.a.a Modular form 669.2.a.a.1.1
2-669-1.1-c1-0-32 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.38833$ Modular form 669.2.a.e.1.3
2-669-1.1-c1-0-33 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.44135$ Modular form 669.2.a.c.1.2
2-669-1.1-c1-0-34 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.47327$ Modular form 669.2.a.f.1.3
2-669-1.1-c1-0-35 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.79705$ Modular form 669.2.a.g.1.3
2-669-1.1-c1-0-36 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.80254$ Modular form 669.2.a.d.1.2
2-669-1.1-c1-0-4 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.08315$ Modular form 669.2.a.h.1.3
2-669-1.1-c1-0-5 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.09323$ Modular form 669.2.a.i.1.3
2-669-1.1-c1-0-6 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.10326$ Modular form 669.2.a.h.1.2
2-669-1.1-c1-0-7 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.11627$ Modular form 669.2.a.i.1.7
2-669-1.1-c1-0-8 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.12950$ Modular form 669.2.a.h.1.5
2-669-1.1-c1-0-9 $2.31$ $5.34$ $2$ $3 \cdot 223$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.19085$ Modular form 669.2.a.i.1.4
2-669-223.100-c1-0-0 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $-0.490$ $0$ $0.0820097$ Modular form 669.2.m.a.100.7
2-669-223.100-c1-0-1 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $-0.244$ $0$ $0.124219$ Modular form 669.2.m.b.100.6
2-669-223.100-c1-0-10 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $-0.150$ $0$ $0.837088$ Modular form 669.2.m.a.100.9
2-669-223.100-c1-0-11 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $-1.14e-5$ $0$ $0.840106$ Modular form 669.2.m.b.100.9
2-669-223.100-c1-0-12 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $0.000620$ $0$ $0.902760$ Modular form 669.2.m.a.100.4
2-669-223.100-c1-0-13 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $-0.410$ $0$ $0.933924$ Modular form 669.2.m.b.100.19
2-669-223.100-c1-0-14 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $0.0801$ $0$ $0.984983$ Modular form 669.2.m.a.100.6
2-669-223.100-c1-0-15 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $0.461$ $0$ $1.10433$ Modular form 669.2.m.b.100.2
2-669-223.100-c1-0-16 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $-0.314$ $0$ $1.11841$ Modular form 669.2.m.a.100.13
2-669-223.100-c1-0-17 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $0.405$ $0$ $1.11942$ Modular form 669.2.m.a.100.2
2-669-223.100-c1-0-18 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $-0.458$ $0$ $1.17963$ Modular form 669.2.m.a.100.18
2-669-223.100-c1-0-19 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $0.175$ $0$ $1.18147$ Modular form 669.2.m.a.100.5
2-669-223.100-c1-0-2 $2.31$ $5.34$ $2$ $3 \cdot 223$ 223.100 $1.0$ $1$ ✓ ✓ $-0.244$ $0$ $0.182288$ Modular form 669.2.m.b.100.10
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