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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
29.2.a.a 29.a 1.a $2$ $0.232$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
29.2.b.a 29.b 29.b $2$ $0.232$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(-6\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots\)
29.2.d.a 29.d 29.d $6$ $0.232$ \(\Q(\zeta_{14})\) None \(-2\) \(-5\) \(1\) \(1\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
29.2.e.a 29.e 29.e $12$ $0.232$ 12.0.\(\cdots\).1 None \(-7\) \(-7\) \(-1\) \(-11\) $\mathrm{SU}(2)[C_{14}]$ \(q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots\)
29.3.c.a 29.c 29.c $8$ $0.790$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(2\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{2}+(\beta _{2}+\beta _{6})q^{3}+(\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
29.3.f.a 29.f 29.f $48$ $0.790$ None \(-16\) \(-12\) \(-14\) \(-10\) $\mathrm{SU}(2)[C_{28}]$
29.4.a.a 29.a 1.a $2$ $1.711$ \(\Q(\sqrt{2}) \) None \(-2\) \(-10\) \(-10\) \(-16\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(-5-3\beta )q^{3}+(-5+\cdots)q^{4}+\cdots\)
29.4.a.b 29.a 1.a $5$ $1.711$ 5.5.13458092.1 None \(0\) \(8\) \(10\) \(40\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(6+\cdots)q^{4}+\cdots\)
29.4.b.a 29.b 29.b $6$ $1.711$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(22\) \(-28\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-5+\beta _{4}+\beta _{5})q^{4}+\cdots\)
29.4.d.a 29.d 29.d $42$ $1.711$ None \(-5\) \(-5\) \(-7\) \(-31\) $\mathrm{SU}(2)[C_{7}]$
29.4.e.a 29.e 29.e $36$ $1.711$ None \(-7\) \(-7\) \(-29\) \(21\) $\mathrm{SU}(2)[C_{14}]$
29.5.c.a 29.c 29.c $18$ $2.998$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-8\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}-\beta _{2}+6\beta _{4}+\cdots)q^{4}+\cdots\)
29.5.f.a 29.f 29.f $108$ $2.998$ None \(-6\) \(-12\) \(-14\) \(-10\) $\mathrm{SU}(2)[C_{28}]$
29.6.a.a 29.a 1.a $4$ $4.651$ 4.4.3257317.1 None \(0\) \(-28\) \(-68\) \(-208\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(-7+\beta _{1}+\beta _{2})q^{3}+(2-3\beta _{1}+\cdots)q^{4}+\cdots\)
29.6.a.b 29.a 1.a $7$ $4.651$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4\) \(26\) \(32\) \(184\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(4+\beta _{5})q^{3}+(23-3\beta _{1}+\cdots)q^{4}+\cdots\)
29.6.b.a 29.b 29.b $12$ $4.651$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(46\) \(20\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-14+\beta _{2})q^{4}+\cdots\)
29.6.d.a 29.d 29.d $66$ $4.651$ None \(-11\) \(-5\) \(29\) \(17\) $\mathrm{SU}(2)[C_{7}]$
29.6.e.a 29.e 29.e $72$ $4.651$ None \(-7\) \(-7\) \(-53\) \(-27\) $\mathrm{SU}(2)[C_{14}]$
29.7.c.a 29.c 29.c $28$ $6.672$ None \(0\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
29.7.f.a 29.f 29.f $168$ $6.672$ None \(-14\) \(-12\) \(-14\) \(-10\) $\mathrm{SU}(2)[C_{28}]$
29.8.a.a 29.a 1.a $7$ $9.059$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-8\) \(-82\) \(-320\) \(-1704\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-12+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
29.8.a.b 29.a 1.a $10$ $9.059$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(80\) \(180\) \(1040\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(8+\beta _{2})q^{3}+(92+2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
29.8.b.a 29.b 29.b $16$ $9.059$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-198\) \(660\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{6})q^{3}+(-45+\beta _{2}+\cdots)q^{4}+\cdots\)
29.8.d.a 29.d 29.d $102$ $9.059$ None \(1\) \(-5\) \(133\) \(657\) $\mathrm{SU}(2)[C_{7}]$
29.8.e.a 29.e 29.e $96$ $9.059$ None \(-7\) \(-7\) \(191\) \(-667\) $\mathrm{SU}(2)[C_{14}]$
29.9.c.a 29.c 29.c $38$ $11.814$ None \(-8\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
29.9.f.a 29.f 29.f $228$ $11.814$ None \(-6\) \(-12\) \(-14\) \(-10\) $\mathrm{SU}(2)[C_{28}]$
29.10.a.a 29.a 1.a $9$ $14.936$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-244\) \(-738\) \(-7128\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-3^{3}-\beta _{4})q^{3}+(133+2\beta _{1}+\cdots)q^{4}+\cdots\)
29.10.a.b 29.a 1.a $12$ $14.936$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(16\) \(242\) \(1762\) \(12080\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(20+\beta _{1}-\beta _{3})q^{3}+(291+\cdots)q^{4}+\cdots\)
29.10.b.a 29.b 29.b $22$ $14.936$ None \(0\) \(0\) \(-1374\) \(-4956\) $\mathrm{SU}(2)[C_{2}]$
29.10.d.a 29.d 29.d $126$ $14.936$ None \(-23\) \(-5\) \(-1031\) \(-4959\) $\mathrm{SU}(2)[C_{7}]$
29.10.e.a 29.e 29.e $132$ $14.936$ None \(-7\) \(-7\) \(1367\) \(4949\) $\mathrm{SU}(2)[C_{14}]$
29.11.c.a 29.c 29.c $48$ $18.425$ None \(8\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
29.11.f.a 29.f 29.f $288$ $18.425$ None \(-22\) \(-12\) \(-14\) \(-10\) $\mathrm{SU}(2)[C_{28}]$
29.12.a.a 29.a 1.a $11$ $22.282$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-32\) \(-982\) \(-2740\) \(-49432\) $-$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{2}+(-89-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
29.12.a.b 29.a 1.a $14$ $22.282$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(476\) \(9760\) \(85024\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(34-\beta _{3})q^{3}+(1312+3\beta _{1}+\cdots)q^{4}+\cdots\)
29.12.b.a 29.b 29.b $26$ $22.282$ None \(0\) \(0\) \(3742\) \(-2108\) $\mathrm{SU}(2)[C_{2}]$
29.12.d.a 29.d 29.d $162$ $22.282$ None \(73\) \(-5\) \(-16687\) \(-2111\) $\mathrm{SU}(2)[C_{7}]$
29.12.e.a 29.e 29.e $156$ $22.282$ None \(-7\) \(-7\) \(-3749\) \(2101\) $\mathrm{SU}(2)[C_{14}]$
29.13.c.a 29.c 29.c $58$ $26.506$ None \(88\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
29.14.a.a 29.a 1.a $14$ $31.097$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-2188\) \(-67808\) \(-669728\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-156-\beta _{1}+\beta _{3})q^{3}+(2912+\cdots)q^{4}+\cdots\)
29.14.a.b 29.a 1.a $17$ $31.097$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(64\) \(2186\) \(-5308\) \(271464\) $-$ $\mathrm{SU}(2)$ \(q+(4-\beta _{1})q^{2}+(129-\beta _{1}+\beta _{3})q^{3}+\cdots\)
29.14.b.a 29.b 29.b $32$ $31.097$ None \(0\) \(0\) \(-90794\) \(398260\) $\mathrm{SU}(2)[C_{2}]$
29.15.c.a 29.c 29.c $68$ $36.055$ None \(-312\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
29.16.a.a 29.a 1.a $16$ $41.381$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-128\) \(-3214\) \(-82010\) \(-3706320\) $-$ $\mathrm{SU}(2)$ \(q+(-8-\beta _{1})q^{2}+(-201+\beta _{2})q^{3}+\cdots\)
29.16.a.b 29.a 1.a $19$ $41.381$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(9908\) \(230490\) \(2882024\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(521+2\beta _{1}+\beta _{2})q^{3}+(20389+\cdots)q^{4}+\cdots\)
29.16.b.a 29.b 29.b $36$ $41.381$ None \(0\) \(0\) \(470082\) \(-4820620\) $\mathrm{SU}(2)[C_{2}]$
29.17.c.a 29.c 29.c $78$ $47.074$ None \(184\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
29.18.a.a 29.a 1.a $18$ $53.134$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-15400\) \(-564228\) \(-43925040\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-856-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
29.18.a.b 29.a 1.a $21$ $53.134$ None \(256\) \(23966\) \(998272\) \(2193368\) $-$ $\mathrm{SU}(2)$
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