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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1150.2.a.a 1150.a 1.a $1$ $9.183$ \(\Q\) None \(-1\) \(-2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots\)
1150.2.a.b 1150.a 1.a $1$ $9.183$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-3q^{11}+\cdots\)
1150.2.a.c 1150.a 1.a $1$ $9.183$ \(\Q\) None \(-1\) \(2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}+q^{7}-q^{8}+\cdots\)
1150.2.a.d 1150.a 1.a $1$ $9.183$ \(\Q\) None \(-1\) \(3\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{6}+4q^{7}-q^{8}+\cdots\)
1150.2.a.e 1150.a 1.a $1$ $9.183$ \(\Q\) None \(1\) \(-3\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}-3q^{6}-4q^{7}+q^{8}+\cdots\)
1150.2.a.f 1150.a 1.a $1$ $9.183$ \(\Q\) None \(1\) \(-2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
1150.2.a.g 1150.a 1.a $1$ $9.183$ \(\Q\) None \(1\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}-3q^{11}+\cdots\)
1150.2.a.h 1150.a 1.a $1$ $9.183$ \(\Q\) None \(1\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{7}+q^{8}-3q^{9}+2q^{11}+\cdots\)
1150.2.a.i 1150.a 1.a $1$ $9.183$ \(\Q\) None \(1\) \(2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
1150.2.a.j 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+(-1+\beta )q^{7}+\cdots\)
1150.2.a.k 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{17}) \) None \(-2\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+(-1+\beta )q^{7}+\cdots\)
1150.2.a.l 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{5}) \) None \(-2\) \(1\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+(3-3\beta )q^{7}+\cdots\)
1150.2.a.m 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{13}) \) None \(2\) \(-3\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
1150.2.a.n 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+(-3+3\beta )q^{7}+\cdots\)
1150.2.a.o 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{21}) \) None \(2\) \(1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+(-1+\beta )q^{7}+\cdots\)
1150.2.a.p 1150.a 1.a $2$ $9.183$ \(\Q(\sqrt{17}) \) None \(2\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+(1-\beta )q^{7}+\cdots\)
1150.2.a.q 1150.a 1.a $3$ $9.183$ 3.3.1101.1 None \(-3\) \(-1\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
1150.2.a.r 1150.a 1.a $4$ $9.183$ 4.4.13448.1 None \(-4\) \(-3\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(1+\beta _{3})q^{6}+\cdots\)
1150.2.a.s 1150.a 1.a $4$ $9.183$ 4.4.13448.1 None \(4\) \(3\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)
1150.2.b.a 1150.b 5.b $2$ $9.183$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-4iq^{7}+\cdots\)
1150.2.b.b 1150.b 5.b $2$ $9.183$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{7}+\cdots\)
1150.2.b.c 1150.b 5.b $2$ $9.183$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+3q^{9}+\cdots\)
1150.2.b.d 1150.b 5.b $2$ $9.183$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-4iq^{7}+iq^{8}+3q^{9}+\cdots\)
1150.2.b.e 1150.b 5.b $2$ $9.183$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots\)
1150.2.b.f 1150.b 5.b $4$ $9.183$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots\)
1150.2.b.g 1150.b 5.b $4$ $9.183$ \(\Q(i, \sqrt{21})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots\)
1150.2.b.h 1150.b 5.b $4$ $9.183$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots\)
1150.2.b.i 1150.b 5.b $4$ $9.183$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1150.2.b.j 1150.b 5.b $6$ $9.183$ 6.0.77580864.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{3}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1150.2.e.a 1150.e 115.e $8$ $9.183$ \(\Q(\zeta_{16})\) None \(0\) \(-16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{16}q^{2}+(-2+2\zeta_{16}^{3})q^{3}+\zeta_{16}^{3}q^{4}+\cdots\)
1150.2.e.b 1150.e 115.e $8$ $9.183$ 8.0.110166016.2 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+(1+\beta _{5})q^{3}+\beta _{7}q^{4}+(1-\beta _{4}+\cdots)q^{6}+\cdots\)
1150.2.e.c 1150.e 115.e $8$ $9.183$ 8.0.110166016.2 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+(1+\beta _{5})q^{3}+\beta _{7}q^{4}+(1-\beta _{4}+\cdots)q^{6}+\cdots\)
1150.2.e.d 1150.e 115.e $16$ $9.183$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{3}-\beta _{4}q^{4}+(-1+\cdots)q^{6}+\cdots\)
1150.2.e.e 1150.e 115.e $16$ $9.183$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}+(\beta _{10}-\beta _{12})q^{3}-\beta _{9}q^{4}+\cdots\)
1150.2.e.f 1150.e 115.e $16$ $9.183$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{2}+(-\beta _{5}+\beta _{7}+\beta _{11})q^{3}-\beta _{8}q^{4}+\cdots\)
1150.3.c.a 1150.c 115.c $8$ $31.335$ 8.0.\(\cdots\).5 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+(-\beta _{3}-\beta _{4})q^{3}-2q^{4}+(2+\cdots)q^{6}+\cdots\)
1150.3.c.b 1150.c 115.c $32$ $31.335$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1150.3.c.c 1150.c 115.c $32$ $31.335$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1150.3.d.a 1150.d 23.b $4$ $31.335$ 4.0.613376.1 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(1-\beta _{2})q^{3}+2q^{4}+(2-\beta _{2}+\cdots)q^{6}+\cdots\)
1150.3.d.b 1150.d 23.b $16$ $31.335$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{4}q^{3}+2q^{4}-\beta _{9}q^{6}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1150.3.d.c 1150.d 23.b $16$ $31.335$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{5}q^{3}+2q^{4}-\beta _{8}q^{6}+\beta _{1}q^{7}+\cdots\)
1150.3.d.d 1150.d 23.b $16$ $31.335$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{5}q^{3}+2q^{4}-\beta _{8}q^{6}+\beta _{1}q^{7}+\cdots\)
1150.3.d.e 1150.d 23.b $24$ $31.335$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1150.4.a.a 1150.a 1.a $1$ $67.852$ \(\Q\) None \(-2\) \(-2\) \(0\) \(-21\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-21q^{7}+\cdots\)
1150.4.a.b 1150.a 1.a $1$ $67.852$ \(\Q\) None \(-2\) \(-1\) \(0\) \(18\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+4q^{4}+2q^{6}+18q^{7}+\cdots\)
1150.4.a.c 1150.a 1.a $1$ $67.852$ \(\Q\) None \(-2\) \(1\) \(0\) \(32\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+4q^{4}-2q^{6}+2^{5}q^{7}+\cdots\)
1150.4.a.d 1150.a 1.a $1$ $67.852$ \(\Q\) None \(-2\) \(9\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+9q^{3}+4q^{4}-18q^{6}-2q^{7}+\cdots\)
1150.4.a.e 1150.a 1.a $1$ $67.852$ \(\Q\) None \(2\) \(-7\) \(0\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-7q^{3}+4q^{4}-14q^{6}-20q^{7}+\cdots\)
1150.4.a.f 1150.a 1.a $1$ $67.852$ \(\Q\) None \(2\) \(-4\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-4q^{3}+4q^{4}-8q^{6}-3q^{7}+\cdots\)
1150.4.a.g 1150.a 1.a $1$ $67.852$ \(\Q\) None \(2\) \(1\) \(0\) \(12\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+4q^{4}+2q^{6}+12q^{7}+\cdots\)
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