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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
4-1-1.1-r0e4-m0.82m8.13m14.59p23.54-0 $1.01$ $1.07$ $4$ $1$ 1.1 $-0.822i, -8.12i, -14.5i, 23.5i$ $$ $0$ $0$ $17.8330$
3-1-1.1-r0e3-m4.76m13.60p18.36-0 $1.68$ $4.78$ $3$ $1$ 1.1 $-4.76i, -13.5i, 18.3i$ $$ $0$ $0$ $17.3513$
4-1-1.1-r0e4-p2.27m6.04m13.14p16.90-0 $1.17$ $1.92$ $4$ $1$ 1.1 $2.27i, -6.03i, -13.1i, 16.8i$ $$ $0$ $0$ $16.1890$
4-1-1.1-r0e4-c4.72c12.47-0 $1.21$ $2.21$ $4$ $1$ 1.1 $-4.72i, 4.72i, -12.4i, 12.4i$ $$ $0$ $0$ $14.4960$
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 \(\Q\)
3-2e2-1.1-r0e3-m2.64m8.24p10.88-0 $1.55$ $3.78$ $3$ $2^{2}$ 1.1 $-2.64i, -8.23i, 10.8i$ $$ $0$ $0$ $12.2526$
3-2e2-1.1-r0e3-m2.94m8.95p11.89-0 $1.71$ $5.01$ $3$ $2^{2}$ 1.1 $-2.93i, -8.95i, 11.8i$ $$ $0.333$ $0$ $11.7088$
4-1-1.1-r0e4-p0.41m6.42m15.50p21.50-0 $0.674$ $0.206$ $4$ $1$ 1.1 $0.411i, -6.41i, -15.4i, 21.5i$ $$ $0$ $0$ $11.6744$
4-1-1.1-r0e4-p0.26m5.89m16.92p22.55-0 $0.560$ $0.0983$ $4$ $1$ 1.1 $0.257i, -5.88i, -16.9i, 22.5i$ $$ $0$ $0$ $10.8298$
4-1-1.1-r0e4-m0.06m7.93m16.63p24.63-0 $0.504$ $0.0646$ $4$ $1$ 1.1 $-0.0621i, -7.93i, -16.6i, 24.6i$ $$ $0$ $0$ $10.6322$
3-1-1.1-r0e3-m4.19m15.32p19.51-0 $1.71$ $5.03$ $3$ $1$ 1.1 $-4.19i, -15.3i, 19.5i$ $$ $0$ $0$ $10.5504$
4-1-1.1-r0e4-p0.79m6.50m16.37p22.07-0 $0.959$ $0.847$ $4$ $1$ 1.1 $0.793i, -6.49i, -16.3i, 22.0i$ $$ $0$ $0$ $9.93676$
4-1-1.1-r0e4-p1.69m4.66m16.94p19.92-0 $1.13$ $1.64$ $4$ $1$ 1.1 $1.68i, -4.66i, -16.9i, 19.9i$ $$ $0$ $0$ $9.69629$
4-1-1.1-r0e4-m4.37p6.73p13.05m15.41-0 $1.39$ $3.77$ $4$ $1$ 1.1 $-4.36i, 6.72i, 13.0i, -15.4i$ $$ $0$ $0$ $9.59674$
4-1-1.1-r0e4-p1.97m5.10m15.91p19.04-0 $1.17$ $1.91$ $4$ $1$ 1.1 $1.97i, -5.10i, -15.9i, 19.0i$ $$ $0$ $0$ $9.56782$
3-1-1.1-r0e3-m2.38m14.14p16.52-0 $1.30$ $2.22$ $3$ $1$ 1.1 $-2.38i, -14.1i, 16.5i$ $$ $0$ $0$ $9.38174$
4-1-1.1-r0e4-p1.49m4.26m18.43p21.20-0 $1.10$ $1.51$ $4$ $1$ 1.1 $1.49i, -4.26i, -18.4i, 21.2i$ $$ $0$ $0$ $9.30431$
2-1-1.1-c11-0-0 $0.876$ $0.768$ $2$ $1$ 1.1 $$ $11.0$ $11$ $0$ $0$ $9.22237$ Modular form 1.12.a.a Modular form 1.12.a.a.1.1
3-1-1.1-r0e3-m5.87m17.43p23.29-0 $2.12$ $9.58$ $3$ $1$ 1.1 $-5.86i, -17.4i, 23.2i$ $$ $0$ $0$ $9.08011$
4-1-1.1-r0e4-p1.20m3.82m19.88p22.50-0 $1.04$ $1.18$ $4$ $1$ 1.1 $1.20i, -3.81i, -19.8i, 22.4i$ $$ $0$ $0$ $9.03017$
4-1-1.1-r0e4-c4.03c14.73-0 $1.22$ $2.24$ $4$ $1$ 1.1 $-4.02i, 4.02i, -14.7i, 14.7i$ $$ $0$ $0$ $9.01112$
4-1-1.1-r0e4-p3.68m5.52m17.16p19.00-0 $1.43$ $4.22$ $4$ $1$ 1.1 $3.67i, -5.51i, -17.1i, 19.0i$ $$ $0$ $0$ $8.78956$
4-1-1.1-r0e4-p3.20m4.73m20.54p22.06-0 $1.44$ $4.37$ $4$ $1$ 1.1 $3.20i, -4.72i, -20.5i, 22.0i$ $$ $0$ $0$ $8.58812$
4-1-1.1-r0e4-m4.45p8.45p13.75m17.76-0 $1.55$ $5.87$ $4$ $1$ 1.1 $-4.44i, 8.45i, 13.7i, -17.7i$ $$ $0$ $0$ $8.56691$
3-1-1.1-r0e3-m4.04m16.76p20.80-0 $1.78$ $5.66$ $3$ $1$ 1.1 $-4.03i, -16.7i, 20.7i$ $$ $0$ $0$ $8.46899$
4-1-1.1-r0e4-p1.63m4.25m19.47p22.09-0 $1.16$ $1.83$ $4$ $1$ 1.1 $1.62i, -4.25i, -19.4i, 22.0i$ $$ $0$ $0$ $8.46570$
4-1-1.1-r0e4-c3.20c17.88-0 $1.20$ $2.07$ $4$ $1$ 1.1 $-3.19i, 3.19i, -17.8i, 17.8i$ $$ $0$ $0$ $8.40243$
2-2-1.1-c7-0-0 $0.790$ $0.624$ $2$ $2$ 1.1 $$ $7.0$ $7$ $0$ $0$ $8.27204$ Modular form 2.8.a.a Modular form 2.8.a.a.1.1
2-3-1.1-c5-0-0 $0.693$ $0.481$ $2$ $3$ 1.1 $$ $5.0$ $5$ $0$ $0$ $8.20343$ Modular form 3.6.a.a Modular form 3.6.a.a.1.1
3-1-1.1-r0e3-m1.98m16.05p18.04-0 $1.31$ $2.27$ $3$ $1$ 1.1 $-1.98i, -16.0i, 18.0i$ $$ $0$ $0$ $8.19881$
2-1-1.1-c17-0-0 $1.35$ $1.83$ $2$ $1$ 1.1 $$ $17.0$ $17$ $0.5$ $1$ $8.14161$ Modular form 1.18.a.a Modular form 1.18.a.a.1.1
4-1-1.1-r0e4-c3.71c16.17-0 $1.23$ $2.29$ $4$ $1$ 1.1 $-3.71i, 3.71i, -16.1i, 16.1i$ $$ $0$ $0$ $8.08759$
4-1-1.1-r0e4-c2.71c20.02-0 $1.16$ $1.86$ $4$ $1$ 1.1 $-2.71i, 2.71i, -20.0i, 20.0i$ $$ $0$ $0$ $8.06923$
1-3-3.2-r1-0-0 $0.322$ $0.322$ $1$ $3$ 3.2 $1$ $$ $0$ $0$ $0$ $8.03973$ Dirichlet character \(\chi_{3} (2, \cdot) \)
4-1-1.1-r0e4-p3.32m5.98m15.82p18.49-0 $1.38$ $3.70$ $4$ $1$ 1.1 $3.32i, -5.98i, -15.8i, 18.4i$ $$ $0$ $0$ $8.03401$
4-1-1.1-r0e4-c2.26c21.57-0 $1.10$ $1.49$ $4$ $1$ 1.1 $-2.26i, 2.26i, -21.5i, 21.5i$ $$ $0$ $0$ $8.00121$
4-1-1.1-r0e4-p1.95m4.74m18.21p21.00-0 $1.22$ $2.22$ $4$ $1$ 1.1 $1.95i, -4.74i, -18.2i, 21.0i$ $$ $0$ $0$ $7.97811$
2-5-1.1-c3-0-0 $0.543$ $0.295$ $2$ $5$ 1.1 $$ $3.0$ $3$ $0$ $0$ $7.80368$ Modular form 5.4.a.a Modular form 5.4.a.a.1.1
3-1-1.1-r0e3-m5.01m22.23p27.24-0 $2.30$ $12.2$ $3$ $1$ 1.1 $-5.00i, -22.2i, 27.2i$ $$ $0$ $0$ $7.79131$
4-1-1.1-r0e4-p3.32m5.46m18.04p20.17-0 $1.43$ $4.21$ $4$ $1$ 1.1 $3.32i, -5.45i, -18.0i, 20.1i$ $$ $0$ $0$ $7.71924$
3-1-1.1-r0e3-m3.37m21.12p24.49-0 $1.91$ $7.00$ $3$ $1$ 1.1 $-3.37i, -21.1i, 24.4i$ $$ $0$ $0$ $7.67603$
4-1-1.1-r0e4-p1.69m4.20m20.71p23.22-0 $1.20$ $2.11$ $4$ $1$ 1.1 $1.68i, -4.20i, -20.7i, 23.2i$ $$ $0$ $0$ $7.60308$
3-1-1.1-r0e3-m3.48m19.82p23.30-0 $1.86$ $6.46$ $3$ $1$ 1.1 $-3.48i, -19.8i, 23.3i$ $$ $0$ $0$ $7.56577$
2-2e2-4.3-c4-0-0 $0.643$ $0.413$ $2$ $2^{2}$ 4.3 $$ $4.0$ $4$ $0$ $0$ $7.53515$ Modular form 4.5.b.a Modular form 4.5.b.a.3.1
3-2e2-1.1-r0e3-m3.18m10.70p13.88-0 $1.96$ $7.58$ $3$ $2^{2}$ 1.1 $-3.18i, -10.6i, 13.8i$ $$ $-0.333$ $0$ $7.53321$
3-1-1.1-r0e3-m3.77m18.36p22.13-0 $1.83$ $6.15$ $3$ $1$ 1.1 $-3.77i, -18.3i, 22.1i$ $$ $0$ $0$ $7.49667$
4-1-1.1-r0e4-p2.22m4.47m21.65p23.90-0 $1.34$ $3.25$ $4$ $1$ 1.1 $2.22i, -4.46i, -21.6i, 23.8i$ $$ $0$ $0$ $7.49541$
2-3-1.1-c9-0-1 $1.24$ $1.54$ $2$ $3$ 1.1 $$ $9.0$ $9$ $0.5$ $1$ $7.47037$ Modular form 3.10.a.a Modular form 3.10.a.a.1.1
3-1-1.1-r0e3-m2.97m23.96p26.93-0 $1.97$ $7.68$ $3$ $1$ 1.1 $-2.97i, -23.9i, 26.9i$ $$ $0$ $0$ $7.41872$
4-1-1.1-r0e4-c3.08c19.08-0 $1.21$ $2.20$ $4$ $1$ 1.1 $-3.08i, 3.08i, -19.0i, 19.0i$ $$ $0$ $0$ $7.39921$
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