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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
2-408-408.107-c0-0-0 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.107 $0.0$ 0 ✓ ✓ $0.151$ $0$ $1.77150$ Modular form 408.1.bg.a.107.1
2-408-408.107-c0-0-1 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.107 $0.0$ 0 ✓ ✓ $0.213$ $0$ $2.87835$ Modular form 408.1.bg.b.107.1
2-408-408.11-c0-0-0 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.11 $0.0$ 0 ✓ ✓ $-0.0222$ $0$ $1.56455$ Modular form 408.1.bg.b.11.1
2-408-408.11-c0-0-1 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.11 $0.0$ 0 ✓ ✓ $0.290$ $0$ $2.97040$ Modular form 408.1.bg.a.11.1
2-408-408.131-c0-0-0 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.131 $0.0$ 0 ✓ ✓ $-0.225$ $0$ $1.32595$ Modular form 408.1.bg.b.131.1
2-408-408.131-c0-0-1 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.131 $0.0$ 0 ✓ ✓ $0.211$ $0$ $2.68242$ Modular form 408.1.bg.a.131.1
2-408-408.227-c0-0-0 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.227 $0.0$ 0 ✓ ✓ $-0.0328$ $0$ $2.00810$ Modular form 408.1.bg.a.227.1
2-408-408.227-c0-0-1 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.227 $0.0$ 0 ✓ ✓ $0.154$ $0$ $2.38491$ Modular form 408.1.bg.b.227.1
2-408-408.275-c0-0-0 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.275 $0.0$ 0 ✓ ✓ $0.0328$ $0$ $1.59432$ Modular form 408.1.bg.a.275.1
2-408-408.275-c0-0-1 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.275 $0.0$ 0 ✓ ✓ $-0.154$ $0$ $2.05391$ Modular form 408.1.bg.b.275.1
2-408-408.299-c0-0-0 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.299 $0.0$ 0 ✓ ✓ $-0.211$ $0$ $1.61258$ Modular form 408.1.bg.a.299.1
2-408-408.299-c0-0-1 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.299 $0.0$ 0 ✓ ✓ $0.225$ $0$ $2.07214$ Modular form 408.1.bg.b.299.1
2-408-408.347-c0-0-0 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.347 $0.0$ 0 ✓ ✓ $-0.151$ $0$ $0.995234$ Modular form 408.1.bg.a.347.1
2-408-408.347-c0-0-1 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.347 $0.0$ 0 ✓ ✓ $-0.213$ $0$ $1.77022$ Modular form 408.1.bg.b.347.1
2-408-408.371-c0-0-0 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.371 $0.0$ 0 ✓ ✓ $0.0222$ $0$ $1.11338$ Modular form 408.1.bg.b.371.1
2-408-408.371-c0-0-1 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 408.371 $0.0$ 0 ✓ ✓ $-0.290$ $0$ $1.75239$ Modular form 408.1.bg.a.371.1
2-408-51.38-c0-0-0 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 51.38 $0.0$ 0 ✓ ✓ $-0.105$ $0$ $1.87772$ Modular form 408.1.u.a.89.2
2-408-51.38-c0-0-1 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 51.38 $0.0$ 0 ✓ ✓ $0.394$ $0$ $2.93815$ Modular form 408.1.u.a.89.1
2-408-51.47-c0-0-0 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 51.47 $0.0$ 0 ✓ ✓ $-0.394$ $0$ $0.575542$ Modular form 408.1.u.a.353.1
2-408-51.47-c0-0-1 $0.451$ $0.203$ $2$ $2^{3} \cdot 3 \cdot 17$ 51.47 $0.0$ 0 ✓ ✓ $0.105$ $0$ $2.40503$ Modular form 408.1.u.a.353.2
2-408-1.1-c1-0-0 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.35633$ Modular form 408.2.a.f.1.1
2-408-1.1-c1-0-1 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $1.39385$ Elliptic curve 408.a Modular form 408.2.a.a Modular form 408.2.a.a.1.1
2-408-1.1-c1-0-2 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $1.55655$ Elliptic curve 408.d Modular form 408.2.a.d Modular form 408.2.a.d.1.1
2-408-1.1-c1-0-3 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0$ $0$ $1.56214$ Elliptic curve 408.c Modular form 408.2.a.c Modular form 408.2.a.c.1.1
2-408-1.1-c1-0-4 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0$ $0$ $1.89013$ Modular form 408.2.a.f.1.2
2-408-1.1-c1-0-5 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.22645$ Modular form 408.2.a.e.1.1
2-408-1.1-c1-0-6 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 1.1 $1.0$ $1$ ✓ ✓ ✓ $0.5$ $1$ $2.37575$ Modular form 408.2.a.e.1.2
2-408-1.1-c1-0-7 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 1.1 $1.0$ $1$ ✓ ✓ ✓ ✓ $0.5$ $1$ $2.63752$ Elliptic curve 408.b Modular form 408.2.a.b Modular form 408.2.a.b.1.1
2-408-136.101-c1-0-0 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $-0.420$ $0$ $0.0964583$ Modular form 408.2.l.a.373.2
2-408-136.101-c1-0-1 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $-0.249$ $0$ $0.211436$ Modular form 408.2.l.b.373.9
2-408-136.101-c1-0-10 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $-0.285$ $0$ $1.12281$ Modular form 408.2.l.a.373.10
2-408-136.101-c1-0-11 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $-0.211$ $0$ $1.13031$ Modular form 408.2.l.b.373.8
2-408-136.101-c1-0-12 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $-0.0980$ $0$ $1.14015$ Modular form 408.2.l.a.373.4
2-408-136.101-c1-0-13 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $-0.206$ $0$ $1.23657$ Modular form 408.2.l.b.373.16
2-408-136.101-c1-0-14 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $-0.158$ $0$ $1.24902$ Modular form 408.2.l.a.373.18
2-408-136.101-c1-0-15 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $0.0980$ $0$ $1.31758$ Modular form 408.2.l.a.373.3
2-408-136.101-c1-0-16 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $0.211$ $0$ $1.49043$ Modular form 408.2.l.b.373.7
2-408-136.101-c1-0-17 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $-0.120$ $0$ $1.58774$ Modular form 408.2.l.b.373.6
2-408-136.101-c1-0-18 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $0.120$ $0$ $1.63038$ Modular form 408.2.l.b.373.5
2-408-136.101-c1-0-19 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $0.00555$ $0$ $1.63268$ Modular form 408.2.l.a.373.15
2-408-136.101-c1-0-2 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $0.487$ $0$ $0.435122$ Modular form 408.2.l.a.373.14
2-408-136.101-c1-0-20 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $0.420$ $0$ $1.64483$ Modular form 408.2.l.a.373.1
2-408-136.101-c1-0-21 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $0.0631$ $0$ $1.66460$ Modular form 408.2.l.a.373.12
2-408-136.101-c1-0-22 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $-0.185$ $0$ $1.67321$ Modular form 408.2.l.b.373.14
2-408-136.101-c1-0-23 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $0.285$ $0$ $1.68458$ Modular form 408.2.l.a.373.9
2-408-136.101-c1-0-24 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $0.197$ $0$ $1.70676$ Modular form 408.2.l.b.373.4
2-408-136.101-c1-0-25 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $0.457$ $0$ $1.85472$ Modular form 408.2.l.a.373.7
2-408-136.101-c1-0-26 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $-0.0760$ $0$ $1.89541$ Modular form 408.2.l.b.373.18
2-408-136.101-c1-0-27 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $0.159$ $0$ $1.90241$ Modular form 408.2.l.b.373.1
2-408-136.101-c1-0-28 $1.80$ $3.25$ $2$ $2^{3} \cdot 3 \cdot 17$ 136.101 $1.0$ $1$ ✓ ✓ $0.158$ $0$ $1.94298$ Modular form 408.2.l.a.373.17
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