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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
22.2.c.a 22.c 11.c $4$ $0.176$ \(\Q(\zeta_{10})\) None \(-1\) \(-4\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
22.3.b.a 22.b 11.b $2$ $0.599$ \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+q^{3}-2q^{4}-q^{5}+\beta q^{6}-6\beta q^{7}+\cdots\)
22.3.d.a 22.d 11.d $8$ $0.599$ 8.0.64000000.1 None \(0\) \(-2\) \(2\) \(-30\) $\mathrm{SU}(2)[C_{10}]$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-2\beta _{2}+\beta _{3}+2\beta _{4}+\cdots)q^{3}+\cdots\)
22.4.a.a 22.a 1.a $1$ $1.298$ \(\Q\) None \(-2\) \(-7\) \(-19\) \(14\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-7q^{3}+4q^{4}-19q^{5}+14q^{6}+\cdots\)
22.4.a.b 22.a 1.a $1$ $1.298$ \(\Q\) None \(-2\) \(4\) \(14\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{3}+4q^{4}+14q^{5}-8q^{6}+\cdots\)
22.4.a.c 22.a 1.a $1$ $1.298$ \(\Q\) None \(2\) \(1\) \(-3\) \(-10\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+4q^{4}-3q^{5}+2q^{6}+\cdots\)
22.4.c.a 22.c 11.c $4$ $1.298$ \(\Q(\zeta_{10})\) None \(-2\) \(-1\) \(3\) \(25\) $\mathrm{SU}(2)[C_{5}]$ \(q-2\zeta_{10}q^{2}+(-3+3\zeta_{10}+8\zeta_{10}^{3})q^{3}+\cdots\)
22.4.c.b 22.c 11.c $8$ $1.298$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(3\) \(5\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q-2\beta _{3}q^{2}+(1+\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
22.5.b.a 22.b 11.b $4$ $2.274$ \(\Q(\sqrt{-2}, \sqrt{553})\) None \(0\) \(2\) \(-30\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-8q^{4}+(-8-\beta _{1}+\cdots)q^{5}+\cdots\)
22.5.d.a 22.d 11.d $16$ $2.274$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-2\) \(30\) \(150\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{4}q^{2}+(1+\beta _{2}+3\beta _{3}-\beta _{10}-\beta _{13}+\cdots)q^{3}+\cdots\)
22.6.a.a 22.a 1.a $1$ $3.528$ \(\Q\) None \(-4\) \(-21\) \(81\) \(98\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-21q^{3}+2^{4}q^{4}+3^{4}q^{5}+84q^{6}+\cdots\)
22.6.a.b 22.a 1.a $1$ $3.528$ \(\Q\) None \(-4\) \(1\) \(-51\) \(-166\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+q^{3}+2^{4}q^{4}-51q^{5}-4q^{6}+\cdots\)
22.6.a.c 22.a 1.a $1$ $3.528$ \(\Q\) None \(4\) \(-29\) \(-31\) \(-230\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-29q^{3}+2^{4}q^{4}-31q^{5}-116q^{6}+\cdots\)
22.6.a.d 22.a 1.a $2$ $3.528$ \(\Q(\sqrt{793}) \) None \(8\) \(29\) \(-13\) \(-14\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(15-\beta )q^{3}+2^{4}q^{4}+(-9+\cdots)q^{5}+\cdots\)
22.6.c.a 22.c 11.c $8$ $3.528$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(20\) \(-30\) \(48\) $\mathrm{SU}(2)[C_{5}]$ \(q-4\beta _{3}q^{2}+(3+3\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
22.6.c.b 22.c 11.c $12$ $3.528$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(0\) \(44\) \(-326\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-4+4\beta _{1}+4\beta _{2}-4\beta _{3})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots\)
22.7.b.a 22.b 11.b $6$ $5.061$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-52\) \(368\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-9+\beta _{1})q^{3}-2^{5}q^{4}+(61+\cdots)q^{5}+\cdots\)
22.7.d.a 22.d 11.d $24$ $5.061$ None \(0\) \(52\) \(-368\) \(720\) $\mathrm{SU}(2)[C_{10}]$
22.8.a.a 22.a 1.a $1$ $6.872$ \(\Q\) None \(-8\) \(-19\) \(317\) \(-1030\) $-$ $\mathrm{SU}(2)$ \(q-8q^{2}-19q^{3}+2^{6}q^{4}+317q^{5}+\cdots\)
22.8.a.b 22.a 1.a $1$ $6.872$ \(\Q\) None \(-8\) \(91\) \(185\) \(-722\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+91q^{3}+2^{6}q^{4}+185q^{5}+\cdots\)
22.8.a.c 22.a 1.a $1$ $6.872$ \(\Q\) None \(8\) \(-21\) \(-551\) \(62\) $-$ $\mathrm{SU}(2)$ \(q+8q^{2}-21q^{3}+2^{6}q^{4}-551q^{5}+\cdots\)
22.8.a.d 22.a 1.a $2$ $6.872$ \(\Q(\sqrt{14881}) \) None \(16\) \(-23\) \(331\) \(1794\) $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+(-11-\beta )q^{3}+2^{6}q^{4}+(165+\cdots)q^{5}+\cdots\)
22.8.c.a 22.c 11.c $12$ $6.872$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-24\) \(44\) \(220\) \(534\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-8+8\beta _{1}+8\beta _{2}+8\beta _{3})q^{2}+(5\beta _{1}+\cdots)q^{3}+\cdots\)
22.8.c.b 22.c 11.c $16$ $6.872$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(32\) \(-96\) \(-82\) \(-700\) $\mathrm{SU}(2)[C_{5}]$ \(q-8\beta _{2}q^{2}+(-10-10\beta _{2}+3\beta _{3}+3\beta _{5}+\cdots)q^{3}+\cdots\)
22.9.b.a 22.b 11.b $8$ $8.962$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(182\) \(-1410\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(23+\beta _{1})q^{3}-2^{7}q^{4}+(-176+\cdots)q^{5}+\cdots\)
22.9.d.a 22.d 11.d $32$ $8.962$ None \(0\) \(-182\) \(1410\) \(-10950\) $\mathrm{SU}(2)[C_{10}]$
22.10.a.a 22.a 1.a $1$ $11.331$ \(\Q\) None \(16\) \(-41\) \(-1039\) \(-3482\) $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}-41q^{3}+2^{8}q^{4}-1039q^{5}+\cdots\)
22.10.a.b 22.a 1.a $1$ $11.331$ \(\Q\) None \(16\) \(137\) \(-595\) \(11354\) $-$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+137q^{3}+2^{8}q^{4}-595q^{5}+\cdots\)
22.10.a.c 22.a 1.a $1$ $11.331$ \(\Q\) None \(16\) \(201\) \(2349\) \(-8806\) $-$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+201q^{3}+2^{8}q^{4}+2349q^{5}+\cdots\)
22.10.a.d 22.a 1.a $2$ $11.331$ \(\Q(\sqrt{889}) \) None \(-32\) \(-21\) \(-521\) \(-7490\) $-$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+(-6-9\beta )q^{3}+2^{8}q^{4}+(-212+\cdots)q^{5}+\cdots\)
22.10.a.e 22.a 1.a $2$ $11.331$ \(\Q(\sqrt{463}) \) None \(-32\) \(34\) \(-1478\) \(8196\) $+$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+(17+\beta )q^{3}+2^{8}q^{4}+(-739+\cdots)q^{5}+\cdots\)
22.10.c.a 22.c 11.c $16$ $11.331$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(64\) \(-13\) \(1999\) \(3779\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2^{4}+2^{4}\beta _{1}+2^{4}\beta _{2}-2^{4}\beta _{3})q^{2}+\cdots\)
22.10.c.b 22.c 11.c $20$ $11.331$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-80\) \(15\) \(-2455\) \(17413\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2^{4}+2^{4}\beta _{3}-2^{4}\beta _{4}-2^{4}\beta _{5})q^{2}+\cdots\)
22.11.b.a 22.b 11.b $10$ $13.978$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-106\) \(1138\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-11-\beta _{2})q^{3}-2^{9}q^{4}+\cdots\)
22.11.d.a 22.d 11.d $40$ $13.978$ None \(0\) \(106\) \(-1138\) \(19470\) $\mathrm{SU}(2)[C_{10}]$
22.12.a.a 22.a 1.a $2$ $16.904$ \(\Q(\sqrt{331}) \) None \(64\) \(-426\) \(2290\) \(-86324\) $-$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}+(-213+3\beta )q^{3}+2^{10}q^{4}+\cdots\)
22.12.a.b 22.a 1.a $3$ $16.904$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-96\) \(-70\) \(-5624\) \(-30576\) $-$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}+(-23+\beta _{2})q^{3}+2^{10}q^{4}+\cdots\)
22.12.a.c 22.a 1.a $3$ $16.904$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-96\) \(106\) \(17344\) \(13204\) $+$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}+(35+\beta _{1})q^{3}+2^{10}q^{4}+(5771+\cdots)q^{5}+\cdots\)
22.12.a.d 22.a 1.a $3$ $16.904$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(96\) \(370\) \(-1928\) \(58472\) $+$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}+(123-\beta _{1})q^{3}+2^{10}q^{4}+\cdots\)
22.12.c.a 22.c 11.c $20$ $16.904$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-160\) \(56\) \(-362\) \(-167178\) $\mathrm{SU}(2)[C_{5}]$ \(q+2^{5}\beta _{2}q^{2}+(7+\beta _{1}+7\beta _{2}+9\beta _{4}+\cdots)q^{3}+\cdots\)
22.12.c.b 22.c 11.c $24$ $16.904$ None \(192\) \(-36\) \(-11720\) \(20572\) $\mathrm{SU}(2)[C_{5}]$
22.13.b.a 22.b 11.b $12$ $20.108$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-1240\) \(-1440\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-103-\beta _{1})q^{3}-2^{11}q^{4}+\cdots\)
22.13.d.a 22.d 11.d $48$ $20.108$ None \(0\) \(1240\) \(1440\) \(439200\) $\mathrm{SU}(2)[C_{10}]$
22.14.a.a 22.a 1.a $2$ $23.591$ \(\Q(\sqrt{100039}) \) None \(-128\) \(-662\) \(-48566\) \(404508\) $+$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+(-331+\beta )q^{3}+2^{12}q^{4}+\cdots\)
22.14.a.b 22.a 1.a $2$ $23.591$ \(\Q(\sqrt{55441}) \) None \(-128\) \(1626\) \(7666\) \(637048\) $-$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+(813-3\beta )q^{3}+2^{12}q^{4}+\cdots\)
22.14.a.c 22.a 1.a $2$ $23.591$ \(\Q(\sqrt{45769}) \) None \(128\) \(-926\) \(2914\) \(-170560\) $+$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+(-463-\beta )q^{3}+2^{12}q^{4}+\cdots\)
22.14.a.d 22.a 1.a $3$ $23.591$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(192\) \(-298\) \(40432\) \(40452\) $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+(-10^{2}-\beta _{1}-\beta _{2})q^{3}+2^{12}q^{4}+\cdots\)
22.14.c.a 22.c 11.c $24$ $23.591$ None \(384\) \(2708\) \(32920\) \(-509572\) $\mathrm{SU}(2)[C_{5}]$
22.14.c.b 22.c 11.c $28$ $23.591$ None \(-448\) \(-1248\) \(71554\) \(361734\) $\mathrm{SU}(2)[C_{5}]$
22.15.b.a 22.b 11.b $14$ $27.352$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(4394\) \(69758\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(314+\beta _{1})q^{3}-2^{13}q^{4}+\cdots\)
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