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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
28.2.d.a 28.d 28.d $2$ $0.224$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(-1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)
28.2.e.a 28.e 7.c $2$ $0.224$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
28.2.f.a 28.f 28.f $4$ $0.224$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots\)
28.3.b.a 28.b 7.b $2$ $0.763$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-\beta q^{5}+(5-\beta )q^{7}-15q^{9}+\cdots\)
28.3.c.a 28.c 4.b $6$ $0.763$ 6.0.1539727.2 None \(-1\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-\beta _{3}q^{3}+(-\beta _{1}-\beta _{4})q^{4}+\cdots\)
28.3.g.a 28.g 28.g $12$ $0.763$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{9}+\cdots)q^{4}+\cdots\)
28.3.h.a 28.h 7.d $2$ $0.763$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(3\) \(-14\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}-7q^{7}-6\zeta_{6}q^{9}+\cdots\)
28.4.a.a 28.a 1.a $1$ $1.652$ \(\Q\) None \(0\) \(-10\) \(-8\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-10q^{3}-8q^{5}-7q^{7}+73q^{9}-40q^{11}+\cdots\)
28.4.a.b 28.a 1.a $1$ $1.652$ \(\Q\) None \(0\) \(4\) \(6\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+4q^{3}+6q^{5}+7q^{7}-11q^{9}-12q^{11}+\cdots\)
28.4.d.a 28.d 28.d $2$ $1.652$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(5\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(3-\beta )q^{2}+(7-5\beta )q^{4}+(-7+14\beta )q^{7}+\cdots\)
28.4.d.b 28.d 28.d $8$ $1.652$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)
28.4.e.a 28.e 7.c $4$ $1.652$ \(\Q(\sqrt{-3}, \sqrt{37})\) None \(0\) \(0\) \(14\) \(24\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{3}+(7-7\beta _{1}-2\beta _{2}-2\beta _{3})q^{5}+\cdots\)
28.4.f.a 28.f 28.f $20$ $1.652$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{10}q^{3}-\beta _{14}q^{4}+\cdots\)
28.5.b.a 28.b 7.b $2$ $2.894$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}-3\zeta_{6}q^{5}+(-7-7\zeta_{6})q^{7}+\cdots\)
28.5.c.a 28.c 4.b $12$ $2.894$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(0\) \(24\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-3+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
28.5.g.a 28.g 28.g $28$ $2.894$ None \(2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
28.5.h.a 28.h 7.d $6$ $2.894$ 6.0.11337408.1 None \(0\) \(9\) \(-27\) \(66\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\beta _{1}+\beta _{3})q^{3}+(-3-3\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
28.6.a.a 28.a 1.a $1$ $4.491$ \(\Q\) None \(0\) \(-2\) \(-96\) \(49\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-96q^{5}+7^{2}q^{7}-239q^{9}+\cdots\)
28.6.a.b 28.a 1.a $1$ $4.491$ \(\Q\) None \(0\) \(26\) \(16\) \(-49\) $-$ $\mathrm{SU}(2)$ \(q+26q^{3}+2^{4}q^{5}-7^{2}q^{7}+433q^{9}+\cdots\)
28.6.d.a 28.d 28.d $2$ $4.491$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(-11\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-5-\beta )q^{2}+(23+11\beta )q^{4}+(7^{2}+\cdots)q^{7}+\cdots\)
28.6.d.b 28.d 28.d $16$ $4.491$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{3})q^{2}-\beta _{2}q^{3}+(-3-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
28.6.e.a 28.e 7.c $2$ $4.491$ \(\Q(\sqrt{-3}) \) None \(0\) \(19\) \(-19\) \(-140\) $\mathrm{SU}(2)[C_{3}]$ \(q+19\zeta_{6}q^{3}+(-19+19\zeta_{6})q^{5}+(-133+\cdots)q^{7}+\cdots\)
28.6.e.b 28.e 7.c $4$ $4.491$ \(\Q(\sqrt{-3}, \sqrt{109})\) None \(0\) \(-28\) \(-42\) \(112\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-14+14\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-21\beta _{1}+\cdots)q^{5}+\cdots\)
28.6.f.a 28.f 28.f $36$ $4.491$ None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$
28.7.b.a 28.b 7.b $4$ $6.442$ 4.0.903168.1 None \(0\) \(0\) \(0\) \(-28\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-7-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
28.7.c.a 28.c 4.b $18$ $6.442$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-5\) \(0\) \(-44\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+(\beta _{3}-\beta _{4})q^{3}+(10-\beta _{1})q^{4}+\cdots\)
28.7.g.a 28.g 28.g $44$ $6.442$ None \(-6\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
28.7.h.a 28.h 7.d $8$ $6.442$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(168\) \(-452\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{3}+(28-14\beta _{1}-\beta _{5})q^{5}+(-11^{2}+\cdots)q^{7}+\cdots\)
28.8.a.a 28.a 1.a $2$ $8.747$ \(\Q(\sqrt{3529}) \) None \(0\) \(-14\) \(42\) \(686\) $+$ $\mathrm{SU}(2)$ \(q+(-7-\beta )q^{3}+(21-3\beta )q^{5}+7^{3}q^{7}+\cdots\)
28.8.a.b 28.a 1.a $2$ $8.747$ \(\Q(\sqrt{1009}) \) None \(0\) \(14\) \(-294\) \(-686\) $-$ $\mathrm{SU}(2)$ \(q+(7-\beta )q^{3}+(-147+11\beta )q^{5}-7^{3}q^{7}+\cdots\)
28.8.d.a 28.d 28.d $2$ $8.747$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(13\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(7+\beta )q^{2}+(-37+13\beta )q^{4}+(7^{2}+\cdots)q^{7}+\cdots\)
28.8.d.b 28.d 28.d $24$ $8.747$ None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
28.8.e.a 28.e 7.c $10$ $8.747$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(27\) \(249\) \(332\) $\mathrm{SU}(2)[C_{3}]$ \(q+(5-5\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(7^{2}\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
28.8.f.a 28.f 28.f $52$ $8.747$ None \(-8\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$
28.9.b.a 28.b 7.b $6$ $11.407$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(2166\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-3\beta _{1}-\beta _{2})q^{5}+(19^{2}-\beta _{1}+\cdots)q^{7}+\cdots\)
28.9.c.a 28.c 4.b $24$ $11.407$ None \(3\) \(0\) \(-336\) \(0\) $\mathrm{SU}(2)[C_{2}]$
28.9.g.a 28.g 28.g $60$ $11.407$ None \(2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
28.9.h.a 28.h 7.d $10$ $11.407$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-81\) \(-837\) \(1526\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-11+5\beta _{1}+\beta _{3})q^{3}+(-57-55\beta _{1}+\cdots)q^{5}+\cdots\)
28.10.a.a 28.a 1.a $2$ $14.421$ \(\Q(\sqrt{4561}) \) None \(0\) \(-224\) \(1596\) \(4802\) $+$ $\mathrm{SU}(2)$ \(q+(-112-\beta )q^{3}+(798+9\beta )q^{5}+7^{4}q^{7}+\cdots\)
28.10.a.b 28.a 1.a $2$ $14.421$ \(\Q(\sqrt{11209}) \) None \(0\) \(-70\) \(1554\) \(-4802\) $-$ $\mathrm{SU}(2)$ \(q+(-35-\beta )q^{3}+(777-19\beta )q^{5}-7^{4}q^{7}+\cdots\)
28.10.d.a 28.d 28.d $2$ $14.421$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(5\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-6+17\beta )q^{2}+(-542+85\beta )q^{4}+\cdots\)
28.10.d.b 28.d 28.d $32$ $14.421$ None \(-24\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
28.10.e.a 28.e 7.c $12$ $14.421$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-966\) \(7696\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{3}+\beta _{4})q^{3}+(-161+161\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
28.10.f.a 28.f 28.f $68$ $14.421$ None \(16\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$
28.11.b.a 28.b 7.b $6$ $17.790$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(-15666\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-5\beta _{1}-\beta _{2})q^{5}+(-2611+\cdots)q^{7}+\cdots\)
28.11.c.a 28.c 4.b $30$ $17.790$ None \(11\) \(0\) \(3116\) \(0\) $\mathrm{SU}(2)[C_{2}]$
28.11.g.a 28.g 28.g $76$ $17.790$ None \(10\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
28.11.h.a 28.h 7.d $14$ $17.790$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-243\) \(3333\) \(-8810\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-23+12\beta _{1}-\beta _{2})q^{3}+(160+158\beta _{1}+\cdots)q^{5}+\cdots\)
28.12.a.a 28.a 1.a $3$ $21.514$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-100\) \(4762\) \(-50421\) $-$ $\mathrm{SU}(2)$ \(q+(-33-\beta _{1})q^{3}+(1585+7\beta _{1}-\beta _{2})q^{5}+\cdots\)
28.12.a.b 28.a 1.a $3$ $21.514$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(1132\) \(4986\) \(50421\) $+$ $\mathrm{SU}(2)$ \(q+(377-\beta _{1})q^{3}+(1662+\beta _{2})q^{5}+7^{5}q^{7}+\cdots\)
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