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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
6384.2.a.a 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(-4\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6384.2.a.b 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(-4\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6384.2.a.c 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(-4\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
6384.2.a.d 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
6384.2.a.e 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
6384.2.a.f 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6384.2.a.g 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6384.2.a.h 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6384.2.a.i 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
6384.2.a.j 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}-2q^{13}-8q^{17}+\cdots\)
6384.2.a.k 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
6384.2.a.l 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
6384.2.a.m 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
6384.2.a.n 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(2\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
6384.2.a.o 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(2\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
6384.2.a.p 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(4\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}-q^{7}+q^{9}+2q^{11}-4q^{15}+\cdots\)
6384.2.a.q 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(-1\) \(4\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
6384.2.a.r 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(-4\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}+q^{7}+q^{9}-2q^{13}-4q^{15}+\cdots\)
6384.2.a.s 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
6384.2.a.t 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(-2\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
6384.2.a.u 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(-2\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
6384.2.a.v 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(-2\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6384.2.a.w 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6384.2.a.x 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}+2q^{11}-4q^{17}+\cdots\)
6384.2.a.y 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6384.2.a.z 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6384.2.a.ba 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
6384.2.a.bb 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}-2q^{13}-q^{19}+q^{21}+\cdots\)
6384.2.a.bc 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6384.2.a.bd 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
6384.2.a.be 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(2\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
6384.2.a.bf 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(2\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
6384.2.a.bg 6384.a 1.a $1$ $50.976$ \(\Q\) None \(0\) \(1\) \(2\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
6384.2.a.bh 6384.a 1.a $2$ $50.976$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-4\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-2+\beta )q^{5}+q^{7}+q^{9}-2\beta q^{11}+\cdots\)
6384.2.a.bi 6384.a 1.a $2$ $50.976$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{5}-q^{7}+q^{9}+4q^{11}+\cdots\)
6384.2.a.bj 6384.a 1.a $2$ $50.976$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots\)
6384.2.a.bk 6384.a 1.a $2$ $50.976$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+q^{7}+q^{9}-2q^{13}-\beta q^{15}+\cdots\)
6384.2.a.bl 6384.a 1.a $2$ $50.976$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
6384.2.a.bm 6384.a 1.a $2$ $50.976$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
6384.2.a.bn 6384.a 1.a $2$ $50.976$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
6384.2.a.bo 6384.a 1.a $2$ $50.976$ \(\Q(\sqrt{7}) \) None \(0\) \(2\) \(-2\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots\)
6384.2.a.bp 6384.a 1.a $2$ $50.976$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}+2\beta q^{13}+\cdots\)
6384.2.a.bq 6384.a 1.a $2$ $50.976$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}-\beta q^{13}+\cdots\)
6384.2.a.br 6384.a 1.a $2$ $50.976$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
6384.2.a.bs 6384.a 1.a $2$ $50.976$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{13}+\cdots\)
6384.2.a.bt 6384.a 1.a $3$ $50.976$ 3.3.1016.1 None \(0\) \(-3\) \(0\) \(-3\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
6384.2.a.bu 6384.a 1.a $3$ $50.976$ 3.3.404.1 None \(0\) \(-3\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.bv 6384.a 1.a $3$ $50.976$ 3.3.316.1 None \(0\) \(-3\) \(0\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}+(1-\beta _{1})q^{11}+(-2+\cdots)q^{13}+\cdots\)
6384.2.a.bw 6384.a 1.a $3$ $50.976$ 3.3.568.1 None \(0\) \(3\) \(0\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta _{1}q^{5}+q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.bx 6384.a 1.a $3$ $50.976$ 3.3.148.1 None \(0\) \(3\) \(4\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
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