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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 5 23
5520.2.a.a 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
5520.2.a.b 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
5520.2.a.c 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-3q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
5520.2.a.d 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-2q^{11}+q^{15}+6q^{17}+\cdots\)
5520.2.a.e 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-2q^{13}+q^{15}-6q^{17}+\cdots\)
5520.2.a.f 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
5520.2.a.g 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
5520.2.a.h 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(-1\) \(3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+3q^{7}+q^{9}+4q^{11}+q^{15}+\cdots\)
5520.2.a.i 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
5520.2.a.j 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
5520.2.a.k 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-2q^{11}-q^{15}+6q^{17}+\cdots\)
5520.2.a.l 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
5520.2.a.m 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(1\) \(3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+3q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
5520.2.a.n 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(1\) \(3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+3q^{7}+q^{9}+4q^{11}-q^{15}+\cdots\)
5520.2.a.o 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(1\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
5520.2.a.p 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(-1\) \(1\) \(5\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+5q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
5520.2.a.q 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(-1\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
5520.2.a.r 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(-1\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}+q^{9}+2q^{11}-q^{15}+\cdots\)
5520.2.a.s 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(-1\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
5520.2.a.t 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(-1\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-3q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
5520.2.a.u 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}-q^{15}+\cdots\)
5520.2.a.v 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
5520.2.a.w 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-6q^{13}-q^{15}+2q^{17}+\cdots\)
5520.2.a.x 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}+6q^{13}-q^{15}+2q^{17}+\cdots\)
5520.2.a.y 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
5520.2.a.z 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
5520.2.a.ba 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(-1\) \(5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+5q^{7}+q^{9}+4q^{13}-q^{15}+\cdots\)
5520.2.a.bb 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(1\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
5520.2.a.bc 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(1\) \(-3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
5520.2.a.bd 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
5520.2.a.be 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
5520.2.a.bf 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
5520.2.a.bg 5520.a 1.a $1$ $44.077$ \(\Q\) None \(0\) \(1\) \(1\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
5520.2.a.bh 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-2\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+2\beta q^{11}+\cdots\)
5520.2.a.bi 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(-2\) \(2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
5520.2.a.bj 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{15}) \) None \(0\) \(-2\) \(2\) \(-6\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-3q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
5520.2.a.bk 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+(2+3\beta )q^{11}+\cdots\)
5520.2.a.bl 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(-2\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
5520.2.a.bm 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(1+2\beta )q^{7}+q^{9}+(4+\beta )q^{11}+\cdots\)
5520.2.a.bn 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-2\) \(3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}-2q^{11}+\cdots\)
5520.2.a.bo 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{11}) \) None \(0\) \(2\) \(-2\) \(6\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+3q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
5520.2.a.bp 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-1+2\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
5520.2.a.bq 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(2\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-\beta q^{7}+q^{9}-4q^{11}+(-2+\cdots)q^{13}+\cdots\)
5520.2.a.br 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(2\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-\beta q^{7}+q^{9}-2\beta q^{11}+\cdots\)
5520.2.a.bs 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5520.2.a.bt 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(1+2\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
5520.2.a.bu 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(6\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+3q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
5520.2.a.bv 5520.a 1.a $3$ $44.077$ 3.3.3144.1 None \(0\) \(-3\) \(-3\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(-1+\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5520.2.a.bw 5520.a 1.a $3$ $44.077$ 3.3.1436.1 None \(0\) \(-3\) \(-3\) \(2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(1-\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5520.2.a.bx 5520.a 1.a $3$ $44.077$ 3.3.316.1 None \(0\) \(-3\) \(-3\) \(6\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(2-\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
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