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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1694.2.a.a 1694.a 1.a $1$ $13.527$ \(\Q\) None \(-1\) \(-1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
1694.2.a.b 1694.a 1.a $1$ $13.527$ \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
1694.2.a.c 1694.a 1.a $1$ $13.527$ \(\Q\) None \(-1\) \(0\) \(2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
1694.2.a.d 1694.a 1.a $1$ $13.527$ \(\Q\) None \(-1\) \(3\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}+2q^{5}-3q^{6}-q^{7}+\cdots\)
1694.2.a.e 1694.a 1.a $1$ $13.527$ \(\Q\) None \(1\) \(-2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
1694.2.a.f 1694.a 1.a $1$ $13.527$ \(\Q\) None \(1\) \(-1\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
1694.2.a.g 1694.a 1.a $1$ $13.527$ \(\Q\) None \(1\) \(0\) \(-4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
1694.2.a.h 1694.a 1.a $1$ $13.527$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
1694.2.a.i 1694.a 1.a $1$ $13.527$ \(\Q\) None \(1\) \(2\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}+q^{7}+\cdots\)
1694.2.a.j 1694.a 1.a $1$ $13.527$ \(\Q\) None \(1\) \(3\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}+2q^{5}+3q^{6}+q^{7}+\cdots\)
1694.2.a.k 1694.a 1.a $2$ $13.527$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
1694.2.a.l 1694.a 1.a $2$ $13.527$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots\)
1694.2.a.m 1694.a 1.a $2$ $13.527$ \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(4\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+2q^{5}+\beta q^{6}-q^{7}+\cdots\)
1694.2.a.n 1694.a 1.a $2$ $13.527$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-2\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
1694.2.a.o 1694.a 1.a $2$ $13.527$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-2\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
1694.2.a.p 1694.a 1.a $2$ $13.527$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots\)
1694.2.a.q 1694.a 1.a $2$ $13.527$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-3\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
1694.2.a.r 1694.a 1.a $2$ $13.527$ \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+2q^{5}-\beta q^{6}+q^{7}+\cdots\)
1694.2.a.s 1694.a 1.a $2$ $13.527$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-2\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
1694.2.a.t 1694.a 1.a $2$ $13.527$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-2\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
1694.2.a.u 1694.a 1.a $2$ $13.527$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots\)
1694.2.a.v 1694.a 1.a $3$ $13.527$ 3.3.2024.1 None \(-3\) \(2\) \(-1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{2}q^{5}+(-1+\cdots)q^{6}+\cdots\)
1694.2.a.w 1694.a 1.a $3$ $13.527$ 3.3.2024.1 None \(3\) \(2\) \(-1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{2}q^{5}+(1+\cdots)q^{6}+\cdots\)
1694.2.a.x 1694.a 1.a $4$ $13.527$ 4.4.7625.1 None \(-4\) \(-3\) \(-5\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1694.2.a.y 1694.a 1.a $4$ $13.527$ 4.4.13824.1 None \(-4\) \(4\) \(4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{1})q^{3}+q^{4}+(1+\beta _{2}-\beta _{3})q^{5}+\cdots\)
1694.2.a.z 1694.a 1.a $4$ $13.527$ 4.4.7625.1 None \(4\) \(-3\) \(-5\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1694.2.a.ba 1694.a 1.a $4$ $13.527$ 4.4.13824.1 None \(4\) \(4\) \(4\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(1+\beta _{2}-\beta _{3})q^{5}+\cdots\)
1694.2.c.a 1694.c 77.b $8$ $13.527$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{3}-q^{4}+\zeta_{16}^{2}q^{5}+\cdots\)
1694.2.c.b 1694.c 77.b $32$ $13.527$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1694.2.c.c 1694.c 77.b $32$ $13.527$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1694.4.a.a 1694.a 1.a $1$ $99.949$ \(\Q\) None \(-2\) \(-10\) \(-14\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-10q^{3}+4q^{4}-14q^{5}+20q^{6}+\cdots\)
1694.4.a.b 1694.a 1.a $1$ $99.949$ \(\Q\) None \(-2\) \(-2\) \(-12\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+4q^{4}-12q^{5}+4q^{6}+\cdots\)
1694.4.a.c 1694.a 1.a $1$ $99.949$ \(\Q\) None \(-2\) \(-2\) \(18\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+4q^{4}+18q^{5}+4q^{6}+\cdots\)
1694.4.a.d 1694.a 1.a $1$ $99.949$ \(\Q\) None \(-2\) \(7\) \(3\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+7q^{3}+4q^{4}+3q^{5}-14q^{6}+\cdots\)
1694.4.a.e 1694.a 1.a $1$ $99.949$ \(\Q\) None \(2\) \(-5\) \(-1\) \(7\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-5q^{3}+4q^{4}-q^{5}-10q^{6}+\cdots\)
1694.4.a.f 1694.a 1.a $1$ $99.949$ \(\Q\) None \(2\) \(0\) \(2\) \(7\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+2q^{5}+7q^{7}+8q^{8}+\cdots\)
1694.4.a.g 1694.a 1.a $1$ $99.949$ \(\Q\) None \(2\) \(8\) \(-14\) \(7\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+8q^{3}+4q^{4}-14q^{5}+2^{4}q^{6}+\cdots\)
1694.4.a.h 1694.a 1.a $2$ $99.949$ \(\Q(\sqrt{57}) \) None \(-4\) \(-5\) \(-17\) \(14\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-10+\cdots)q^{5}+\cdots\)
1694.4.a.i 1694.a 1.a $2$ $99.949$ \(\Q(\sqrt{133}) \) None \(-4\) \(-5\) \(-2\) \(-14\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-2-\beta )q^{3}+4q^{4}-q^{5}+\cdots\)
1694.4.a.j 1694.a 1.a $2$ $99.949$ \(\Q(\sqrt{5}) \) None \(-4\) \(-4\) \(-13\) \(-14\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1-6\beta )q^{3}+4q^{4}+(-12+\cdots)q^{5}+\cdots\)
1694.4.a.k 1694.a 1.a $2$ $99.949$ \(\Q(\sqrt{5}) \) None \(-4\) \(6\) \(2\) \(-14\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(2+2\beta )q^{3}+4q^{4}+(6-10\beta )q^{5}+\cdots\)
1694.4.a.l 1694.a 1.a $2$ $99.949$ \(\Q(\sqrt{137}) \) None \(4\) \(-5\) \(-7\) \(-14\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
1694.4.a.m 1694.a 1.a $2$ $99.949$ \(\Q(\sqrt{133}) \) None \(4\) \(-5\) \(-2\) \(14\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-2-\beta )q^{3}+4q^{4}-q^{5}+\cdots\)
1694.4.a.n 1694.a 1.a $2$ $99.949$ \(\Q(\sqrt{5}) \) None \(4\) \(-4\) \(-13\) \(14\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1-6\beta )q^{3}+4q^{4}+(-12+\cdots)q^{5}+\cdots\)
1694.4.a.o 1694.a 1.a $2$ $99.949$ \(\Q(\sqrt{5}) \) None \(4\) \(6\) \(2\) \(14\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(2+2\beta )q^{3}+4q^{4}+(6-10\beta )q^{5}+\cdots\)
1694.4.a.p 1694.a 1.a $2$ $99.949$ \(\Q(\sqrt{37}) \) None \(4\) \(6\) \(26\) \(-14\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(3+\beta )q^{3}+4q^{4}+(13-\beta )q^{5}+\cdots\)
1694.4.a.q 1694.a 1.a $3$ $99.949$ 3.3.27093.1 None \(-6\) \(-5\) \(-5\) \(-21\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-1+\cdots)q^{5}+\cdots\)
1694.4.a.r 1694.a 1.a $3$ $99.949$ 3.3.46700.1 None \(-6\) \(-5\) \(5\) \(21\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
1694.4.a.s 1694.a 1.a $3$ $99.949$ 3.3.7636.1 None \(-6\) \(6\) \(26\) \(21\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+(9-\beta _{2})q^{5}+\cdots\)
1694.4.a.t 1694.a 1.a $3$ $99.949$ 3.3.27093.1 None \(6\) \(-5\) \(-5\) \(21\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-1+\cdots)q^{5}+\cdots\)
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