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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
34.2.a.a 34.a 1.a $1$ $0.271$ \(\Q\) None 34.2.a.a \(1\) \(-2\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-4q^{7}+q^{8}+\cdots\)
34.2.b.a 34.b 17.b $2$ $0.271$ \(\Q(\sqrt{-2}) \) None 34.2.b.a \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots\)
34.2.c.a 34.c 17.c $2$ $0.271$ \(\Q(\sqrt{-1}) \) None 34.2.c.a \(0\) \(-2\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-iq^{2}+(-1-i)q^{3}-q^{4}+(2+2i)q^{5}+\cdots\)
34.2.c.b 34.c 17.c $2$ $0.271$ \(\Q(\sqrt{-1}) \) None 34.2.c.b \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots\)
34.2.d.a 34.d 17.d $4$ $0.271$ \(\Q(\zeta_{8})\) None 34.2.d.a \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
34.3.e.a 34.e 17.e $8$ $0.926$ \(\Q(\zeta_{16})\) None 34.3.e.a \(0\) \(8\) \(0\) \(8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(\zeta_{16}-\zeta_{16}^{5})q^{2}+(1+\zeta_{16}-\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
34.3.e.b 34.e 17.e $16$ $0.926$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 34.3.e.b \(0\) \(-8\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-\beta _{4}-\beta _{9})q^{2}+(-\beta _{3}+\beta _{7}+\beta _{10}+\cdots)q^{3}+\cdots\)
34.4.a.a 34.a 1.a $1$ $2.006$ \(\Q\) None 34.4.a.a \(-2\) \(-2\) \(-18\) \(-10\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+4q^{4}-18q^{5}+4q^{6}+\cdots\)
34.4.a.b 34.a 1.a $1$ $2.006$ \(\Q\) None 34.4.a.b \(-2\) \(-2\) \(16\) \(24\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+4q^{4}+2^{4}q^{5}+4q^{6}+\cdots\)
34.4.a.c 34.a 1.a $2$ $2.006$ \(\Q(\sqrt{13}) \) None 34.4.a.c \(4\) \(6\) \(-4\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(3+\beta )q^{3}+4q^{4}+(-2-4\beta )q^{5}+\cdots\)
34.4.b.a 34.b 17.b $2$ $2.006$ \(\Q(\sqrt{-1}) \) None 34.4.b.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{2}+iq^{3}+4q^{4}+4iq^{5}-2iq^{6}+\cdots\)
34.4.b.b 34.b 17.b $2$ $2.006$ \(\Q(\sqrt{-2}) \) None 34.4.b.b \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{2}+2\beta q^{3}+4q^{4}+\beta q^{5}+4\beta q^{6}+\cdots\)
34.4.c.a 34.c 17.c $2$ $2.006$ \(\Q(\sqrt{-1}) \) None 34.4.c.a \(0\) \(-6\) \(-14\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q-2iq^{2}+(-3-3i)q^{3}-4q^{4}+(-7+\cdots)q^{5}+\cdots\)
34.4.c.b 34.c 17.c $6$ $2.006$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 34.4.c.b \(0\) \(4\) \(-12\) \(-14\) $\mathrm{SU}(2)[C_{4}]$ \(q+2\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2})q^{3}-4q^{4}+\cdots\)
34.4.d.a 34.d 17.d $8$ $2.006$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 34.4.d.a \(0\) \(0\) \(44\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+2\beta _{5}q^{2}+(-\beta _{2}-2\beta _{5}+\beta _{7})q^{3}+\cdots\)
34.4.d.b 34.d 17.d $12$ $2.006$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 34.4.d.b \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+2\beta _{7}q^{2}+(\beta _{1}+\beta _{2}-\beta _{7})q^{3}+4\beta _{1}q^{4}+\cdots\)
34.5.e.a 34.e 17.e $24$ $3.515$ None 34.5.e.a \(0\) \(-16\) \(0\) \(96\) $\mathrm{SU}(2)[C_{16}]$
34.5.e.b 34.e 17.e $24$ $3.515$ None 34.5.e.b \(0\) \(16\) \(0\) \(-96\) $\mathrm{SU}(2)[C_{16}]$
34.6.a.a 34.a 1.a $1$ $5.453$ \(\Q\) None 34.6.a.a \(4\) \(-14\) \(-74\) \(-78\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-14q^{3}+2^{4}q^{4}-74q^{5}-56q^{6}+\cdots\)
34.6.a.b 34.a 1.a $2$ $5.453$ \(\Q(\sqrt{69}) \) None 34.6.a.b \(-8\) \(-6\) \(-36\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+(-3-3\beta )q^{3}+2^{4}q^{4}+(-18+\cdots)q^{5}+\cdots\)
34.6.a.c 34.a 1.a $2$ $5.453$ \(\Q(\sqrt{43}) \) None 34.6.a.c \(-8\) \(-6\) \(32\) \(-138\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+(-3+\beta )q^{3}+2^{4}q^{4}+(2^{4}+\cdots)q^{5}+\cdots\)
34.6.a.d 34.a 1.a $3$ $5.453$ 3.3.1505580.1 None 34.6.a.d \(12\) \(4\) \(144\) \(-18\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(1+\beta _{2})q^{3}+2^{4}q^{4}+(7^{2}+\beta _{1}+\cdots)q^{5}+\cdots\)
34.6.b.a 34.b 17.b $4$ $5.453$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None 34.6.b.a \(-16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-4q^{2}+\beta _{2}q^{3}+2^{4}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
34.6.b.b 34.b 17.b $4$ $5.453$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None 34.6.b.b \(16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4q^{2}+\beta _{2}q^{3}+2^{4}q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
34.6.c.a 34.c 17.c $6$ $5.453$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 34.6.c.a \(0\) \(12\) \(-26\) \(140\) $\mathrm{SU}(2)[C_{4}]$ \(q-4\beta _{1}q^{2}+(2-2\beta _{1}-\beta _{2})q^{3}-2^{4}q^{4}+\cdots\)
34.6.c.b 34.c 17.c $10$ $5.453$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 34.6.c.b \(0\) \(10\) \(48\) \(96\) $\mathrm{SU}(2)[C_{4}]$ \(q+4\beta _{4}q^{2}+(1-\beta _{1}-\beta _{4})q^{3}-2^{4}q^{4}+\cdots\)
34.6.d.a 34.d 17.d $12$ $5.453$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 34.6.d.a \(0\) \(0\) \(-128\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+4\beta _{5}q^{2}+(2\beta _{2}-2\beta _{5}-\beta _{11})q^{3}+\cdots\)
34.6.d.b 34.d 17.d $16$ $5.453$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 34.6.d.b \(0\) \(0\) \(40\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+4\beta _{1}q^{2}+(\beta _{1}-\beta _{5}-\beta _{8})q^{3}-2^{4}\beta _{8}q^{4}+\cdots\)
34.7.e.a 34.e 17.e $32$ $7.822$ None 34.7.e.a \(0\) \(40\) \(0\) \(-760\) $\mathrm{SU}(2)[C_{16}]$
34.7.e.b 34.e 17.e $40$ $7.822$ None 34.7.e.b \(0\) \(-40\) \(0\) \(760\) $\mathrm{SU}(2)[C_{16}]$
34.8.a.a 34.a 1.a $1$ $10.621$ \(\Q\) None 34.8.a.a \(-8\) \(-68\) \(270\) \(680\) $-$ $\mathrm{SU}(2)$ \(q-8q^{2}-68q^{3}+2^{6}q^{4}+270q^{5}+\cdots\)
34.8.a.b 34.a 1.a $1$ $10.621$ \(\Q\) None 34.8.a.b \(-8\) \(84\) \(-450\) \(-1408\) $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+84q^{3}+2^{6}q^{4}-450q^{5}+\cdots\)
34.8.a.c 34.a 1.a $1$ $10.621$ \(\Q\) None 34.8.a.c \(8\) \(-42\) \(72\) \(-580\) $-$ $\mathrm{SU}(2)$ \(q+8q^{2}-42q^{3}+2^{6}q^{4}+72q^{5}-336q^{6}+\cdots\)
34.8.a.d 34.a 1.a $2$ $10.621$ \(\Q(\sqrt{577}) \) None 34.8.a.d \(-16\) \(16\) \(296\) \(-1136\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+(8+\beta )q^{3}+2^{6}q^{4}+(148+6\beta )q^{5}+\cdots\)
34.8.a.e 34.a 1.a $3$ $10.621$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 34.8.a.e \(24\) \(12\) \(346\) \(1200\) $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+(4-\beta _{1})q^{3}+2^{6}q^{4}+(115+\cdots)q^{5}+\cdots\)
34.8.b.a 34.b 17.b $4$ $10.621$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None 34.8.b.a \(-32\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-8q^{2}+\beta _{1}q^{3}+2^{6}q^{4}+(-\beta _{1}+7\beta _{2}+\cdots)q^{5}+\cdots\)
34.8.b.b 34.b 17.b $6$ $10.621$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 34.8.b.b \(48\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+8q^{2}+\beta _{1}q^{3}+2^{6}q^{4}+(3\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
34.8.c.a 34.c 17.c $10$ $10.621$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 34.8.c.a \(0\) \(-56\) \(-414\) \(-168\) $\mathrm{SU}(2)[C_{4}]$ \(q+8\beta _{4}q^{2}+(-6+\beta _{1}-6\beta _{4})q^{3}-2^{6}q^{4}+\cdots\)
34.8.c.b 34.c 17.c $10$ $10.621$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 34.8.c.b \(0\) \(30\) \(308\) \(-620\) $\mathrm{SU}(2)[C_{4}]$ \(q-8\beta _{3}q^{2}+(3+\beta _{1}+3\beta _{3})q^{3}-2^{6}q^{4}+\cdots\)
34.8.d.a 34.d 17.d $20$ $10.621$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None 34.8.d.a \(0\) \(0\) \(-112\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+8\beta _{4}q^{2}+(3\beta _{2}+3\beta _{4}-\beta _{9})q^{3}+2^{6}\beta _{2}q^{4}+\cdots\)
34.8.d.b 34.d 17.d $24$ $10.621$ None 34.8.d.b \(0\) \(0\) \(104\) \(0\) $\mathrm{SU}(2)[C_{8}]$
34.9.e.a 34.e 17.e $48$ $13.851$ None 34.9.e.a \(0\) \(-224\) \(0\) \(-4416\) $\mathrm{SU}(2)[C_{16}]$
34.9.e.b 34.e 17.e $48$ $13.851$ None 34.9.e.b \(0\) \(224\) \(0\) \(4416\) $\mathrm{SU}(2)[C_{16}]$
34.10.a.a 34.a 1.a $2$ $17.511$ \(\Q(\sqrt{43}) \) None 34.10.a.a \(32\) \(64\) \(-2788\) \(-728\) $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+(2^{5}+\beta )q^{3}+2^{8}q^{4}+(-1394+\cdots)q^{5}+\cdots\)
34.10.a.b 34.a 1.a $3$ $17.511$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 34.10.a.b \(-48\) \(84\) \(-1304\) \(690\) $+$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+(28-\beta _{1})q^{3}+2^{8}q^{4}+(-435+\cdots)q^{5}+\cdots\)
34.10.a.c 34.a 1.a $3$ $17.511$ 3.3.3262740.1 None 34.10.a.c \(-48\) \(84\) \(1314\) \(6912\) $-$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+(28-\beta _{2})q^{3}+2^{8}q^{4}+(438+\cdots)q^{5}+\cdots\)
34.10.a.d 34.a 1.a $4$ $17.511$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 34.10.a.d \(64\) \(226\) \(-1656\) \(2654\) $-$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+(57+\beta _{1})q^{3}+2^{8}q^{4}+(-412+\cdots)q^{5}+\cdots\)
34.10.b.a 34.b 17.b $6$ $17.511$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 34.10.b.a \(96\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2^{4}q^{2}-\beta _{1}q^{3}+2^{8}q^{4}+(5\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
34.10.b.b 34.b 17.b $8$ $17.511$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 34.10.b.b \(-128\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2^{4}q^{2}+\beta _{1}q^{3}+2^{8}q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
34.10.c.a 34.c 17.c $14$ $17.511$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 34.10.c.a \(0\) \(-168\) \(1568\) \(-7602\) $\mathrm{SU}(2)[C_{4}]$ \(q+2^{4}\beta _{5}q^{2}+(-12+\beta _{1}-12\beta _{5})q^{3}+\cdots\)
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