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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7 19
5586.2.a.a 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(-4\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.b 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.c 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.d 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.e 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.f 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.g 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.h 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.i 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.j 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.k 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.l 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(-3\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.m 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.n 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.o 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.p 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.q 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.r 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.s 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.t 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.u 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
5586.2.a.v 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.w 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.x 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(-1\) \(4\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.y 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.z 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.ba 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.bb 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.bc 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{7}) \) None \(-2\) \(-2\) \(-2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.bd 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.be 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bf 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{7}) \) None \(-2\) \(2\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bg 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-6\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-3+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bh 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bi 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bj 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
5586.2.a.bk 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{7}) \) None \(2\) \(-2\) \(2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bl 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(4\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bm 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(-4\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.bn 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{7}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.bo 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
5586.2.a.bp 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.bq 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.br 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(6\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(3+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.bs 5586.a 1.a $3$ $44.604$ 3.3.404.1 None \(-3\) \(-3\) \(1\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.bt 5586.a 1.a $3$ $44.604$ 3.3.404.1 None \(-3\) \(3\) \(-1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.bu 5586.a 1.a $3$ $44.604$ 3.3.404.1 None \(3\) \(-3\) \(5\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(2-\beta _{1})q^{5}-q^{6}+\cdots\)
5586.2.a.bv 5586.a 1.a $3$ $44.604$ 3.3.404.1 None \(3\) \(3\) \(-5\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-2+\beta _{1})q^{5}+q^{6}+\cdots\)
5586.2.a.bw 5586.a 1.a $4$ $44.604$ 4.4.29268.1 None \(-4\) \(-4\) \(0\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.bx 5586.a 1.a $4$ $44.604$ 4.4.4352.1 None \(-4\) \(-4\) \(4\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta _{3})q^{5}+q^{6}+\cdots\)
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