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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 13
3822.2.a.a 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(-3\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.b 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.c 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.d 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.e 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.f 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.g 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.h 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.i 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.j 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.k 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.l 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.m 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.n 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.o 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.p 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.q 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.r 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.s 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.t 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.u 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(0\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
3822.2.a.v 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.w 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.x 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.y 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(3\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.z 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(4\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.ba 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(-4\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bb 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(-3\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bc 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(-3\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bd 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.be 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bf 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(0\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
3822.2.a.bg 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(3\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bh 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(3\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bi 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{7}) \) None \(-2\) \(-2\) \(2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
3822.2.a.bj 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.bk 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{7}) \) None \(-2\) \(2\) \(-2\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
3822.2.a.bl 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.bm 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{57}) \) None \(-2\) \(2\) \(1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.bn 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-4\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots\)
3822.2.a.bo 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
3822.2.a.bp 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.bq 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.br 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bs 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bt 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{41}) \) None \(2\) \(2\) \(1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bu 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(4\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots\)
3822.2.a.bv 3822.a 1.a $3$ $30.519$ 3.3.2700.1 None \(-3\) \(-3\) \(3\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)
3822.2.a.bw 3822.a 1.a $3$ $30.519$ 3.3.2700.1 None \(-3\) \(3\) \(-3\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
3822.2.a.bx 3822.a 1.a $4$ $30.519$ 4.4.10304.1 None \(-4\) \(-4\) \(-6\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-2+\beta _{1})q^{5}+q^{6}+\cdots\)
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