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Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7 19
8379.2.a.a 8379.a 1.a $1$ $66.907$ \(\Q\) None 133.2.f.a \(-2\) \(0\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-3q^{5}+6q^{10}-4q^{11}+\cdots\)
8379.2.a.b 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.j.a \(-2\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+2q^{10}-4q^{11}+\cdots\)
8379.2.a.c 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.j.a \(-2\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-2q^{10}-4q^{11}+\cdots\)
8379.2.a.d 8379.a 1.a $1$ $66.907$ \(\Q\) None 133.2.f.a \(-2\) \(0\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+3q^{5}-6q^{10}-4q^{11}+\cdots\)
8379.2.a.e 8379.a 1.a $1$ $66.907$ \(\Q\) None 57.2.a.c \(-1\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
8379.2.a.f 8379.a 1.a $1$ $66.907$ \(\Q\) None 1197.2.a.b \(-1\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}-2q^{11}+6q^{13}+\cdots\)
8379.2.a.g 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.a.c \(-1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+2q^{11}+4q^{13}+\cdots\)
8379.2.a.h 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.j.b \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-2q^{5}+3q^{11}+2q^{13}+4q^{16}+\cdots\)
8379.2.a.i 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.j.b \(0\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+2q^{5}+3q^{11}-2q^{13}+4q^{16}+\cdots\)
8379.2.a.j 8379.a 1.a $1$ $66.907$ \(\Q\) None 19.2.a.a \(0\) \(0\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}-3q^{11}+4q^{13}+4q^{16}+\cdots\)
8379.2.a.k 8379.a 1.a $1$ $66.907$ \(\Q\) None 2793.2.a.d \(1\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots\)
8379.2.a.l 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.a.a \(1\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{8}+2q^{11}-q^{16}+\cdots\)
8379.2.a.m 8379.a 1.a $1$ $66.907$ \(\Q\) None 1197.2.a.b \(1\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{8}+2q^{11}+6q^{13}+\cdots\)
8379.2.a.n 8379.a 1.a $1$ $66.907$ \(\Q\) None 2793.2.a.d \(1\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots\)
8379.2.a.o 8379.a 1.a $1$ $66.907$ \(\Q\) None 399.2.a.b \(1\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots\)
8379.2.a.p 8379.a 1.a $1$ $66.907$ \(\Q\) None 57.2.a.a \(2\) \(0\) \(-3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-3q^{5}-6q^{10}-q^{11}+\cdots\)
8379.2.a.q 8379.a 1.a $1$ $66.907$ \(\Q\) None 57.2.a.b \(2\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}+2q^{10}+3q^{11}+\cdots\)
8379.2.a.r 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 2793.2.a.s \(-2\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
8379.2.a.s 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 2793.2.a.s \(-2\) \(0\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-2q^{10}+\cdots\)
8379.2.a.t 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 2793.2.a.t \(-2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots\)
8379.2.a.u 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 2793.2.a.t \(-2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots\)
8379.2.a.v 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 1197.2.a.f \(-2\) \(0\) \(4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2q^{5}+\cdots\)
8379.2.a.w 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{5}) \) None 133.2.a.c \(-1\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1+2\beta )q^{8}+\cdots\)
8379.2.a.x 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{3}) \) None 1197.2.j.h \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+\beta q^{11}-2q^{13}+4q^{16}+\beta q^{17}+\cdots\)
8379.2.a.y 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{3}) \) None 1197.2.j.h \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-\beta q^{11}+2q^{13}+4q^{16}+\beta q^{17}+\cdots\)
8379.2.a.z 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 133.2.f.b \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-2\beta q^{5}-2\beta q^{8}-4q^{10}+(3+\cdots)q^{11}+\cdots\)
8379.2.a.ba 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 133.2.f.b \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+2\beta q^{5}-2\beta q^{8}+4q^{10}+(3+\cdots)q^{11}+\cdots\)
8379.2.a.bb 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{3}) \) None 1197.2.j.f \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-\beta q^{5}-\beta q^{8}-3q^{10}+\cdots\)
8379.2.a.bc 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{3}) \) None 2793.2.a.q \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-\beta q^{8}-2\beta q^{11}-2\beta q^{13}+\cdots\)
8379.2.a.bd 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{3}) \) None 2793.2.a.q \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-\beta q^{8}-2\beta q^{11}+2\beta q^{13}+\cdots\)
8379.2.a.be 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{3}) \) None 1197.2.j.f \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+\beta q^{5}-\beta q^{8}+3q^{10}+\cdots\)
8379.2.a.bf 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{13}) \) None 133.2.a.b \(1\) \(0\) \(-6\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}-3q^{5}+3q^{8}-3\beta q^{10}+\cdots\)
8379.2.a.bg 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 1197.2.a.f \(2\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2q^{5}+(3+\cdots)q^{8}+\cdots\)
8379.2.a.bh 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 399.2.j.c \(2\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
8379.2.a.bi 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 133.2.f.c \(2\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(3+\beta )q^{8}+\cdots\)
8379.2.a.bj 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 2793.2.a.m \(2\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
8379.2.a.bk 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 2793.2.a.m \(2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
8379.2.a.bl 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 133.2.f.c \(2\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+(3+\beta )q^{8}+\cdots\)
8379.2.a.bm 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{2}) \) None 399.2.j.c \(2\) \(0\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(1+2\beta )q^{5}+\cdots\)
8379.2.a.bn 8379.a 1.a $2$ $66.907$ \(\Q(\sqrt{5}) \) None 133.2.a.a \(3\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
8379.2.a.bo 8379.a 1.a $3$ $66.907$ 3.3.229.1 None 133.2.a.d \(-2\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
8379.2.a.bp 8379.a 1.a $3$ $66.907$ 3.3.148.1 None 399.2.a.d \(-1\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
8379.2.a.bq 8379.a 1.a $3$ $66.907$ 3.3.404.1 None 399.2.a.e \(-1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.br 8379.a 1.a $4$ $66.907$ 4.4.1957.1 None 399.2.j.d \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
8379.2.a.bs 8379.a 1.a $4$ $66.907$ \(\Q(\zeta_{24})^+\) None 1197.2.a.n \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\beta _{3}q^{8}+\cdots\)
8379.2.a.bt 8379.a 1.a $4$ $66.907$ 4.4.1957.1 None 399.2.j.d \(0\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.bu 8379.a 1.a $4$ $66.907$ 4.4.5744.1 None 931.2.a.l \(0\) \(0\) \(-8\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(-2+\cdots)q^{5}+\cdots\)
8379.2.a.bv 8379.a 1.a $4$ $66.907$ 4.4.5744.1 None 931.2.a.l \(0\) \(0\) \(8\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(2+\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.bw 8379.a 1.a $4$ $66.907$ 4.4.13068.1 None 171.2.a.e \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
8379.2.a.bx 8379.a 1.a $4$ $66.907$ 4.4.725.1 None 399.2.j.f \(2\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{4}+(-1+2\beta _{1}+\cdots)q^{5}+\cdots\)
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