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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
700.1.d.a 700.d 7.b $2$ $0.349$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{7}-q^{11}-iq^{13}+iq^{17}+\cdots\)
700.1.j.a 700.j 140.j $4$ $0.349$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{35}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots\)
700.1.j.b 700.j 140.j $8$ $0.349$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{7}+\cdots\)
700.1.u.a 700.u 28.g $4$ $0.349$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}-q^{6}+\cdots\)
700.1.bf.a 700.bf 140.x $8$ $0.349$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{2}+(\zeta_{24}^{5}+\zeta_{24}^{9})q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
700.2.a.a 700.a 1.a $1$ $5.590$ \(\Q\) None None \(0\) \(-3\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{7}+6q^{9}+3q^{11}-q^{13}+\cdots\)
700.2.a.b 700.a 1.a $1$ $5.590$ \(\Q\) None None \(0\) \(-3\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{7}+6q^{9}-5q^{11}+3q^{13}+\cdots\)
700.2.a.c 700.a 1.a $1$ $5.590$ \(\Q\) None None \(0\) \(-2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\)
700.2.a.d 700.a 1.a $1$ $5.590$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
700.2.a.e 700.a 1.a $1$ $5.590$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{9}-5q^{11}+6q^{13}-4q^{17}+\cdots\)
700.2.a.f 700.a 1.a $1$ $5.590$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{9}-4q^{13}-4q^{17}+4q^{19}+\cdots\)
700.2.a.g 700.a 1.a $1$ $5.590$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}-5q^{11}-6q^{13}+4q^{17}+\cdots\)
700.2.a.h 700.a 1.a $1$ $5.590$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}+4q^{13}+4q^{17}+4q^{19}+\cdots\)
700.2.a.i 700.a 1.a $1$ $5.590$ \(\Q\) None None \(0\) \(2\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{7}+q^{9}+3q^{11}+4q^{13}+\cdots\)
700.2.a.j 700.a 1.a $1$ $5.590$ \(\Q\) None None \(0\) \(3\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{7}+6q^{9}+3q^{11}+q^{13}+\cdots\)
700.2.c.a 700.c 140.c $4$ $5.590$ \(\Q(i, \sqrt{6})\) None None \(-4\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}-2\beta _{1}q^{4}+\cdots\)
700.2.c.b 700.c 140.c $4$ $5.590$ \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{12}^{3})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
700.2.c.c 700.c 140.c $4$ $5.590$ \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{12}^{3})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
700.2.c.d 700.c 140.c $4$ $5.590$ \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2\beta _{1}+\beta _{3})q^{7}+\cdots\)
700.2.c.e 700.c 140.c $4$ $5.590$ \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{12}^{3})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
700.2.c.f 700.c 140.c $4$ $5.590$ \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
700.2.c.g 700.c 140.c $4$ $5.590$ \(\Q(i, \sqrt{6})\) None None \(4\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}-2\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
700.2.c.h 700.c 140.c $8$ $5.590$ 8.0.49787136.1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{7})q^{7}+\cdots\)
700.2.c.i 700.c 140.c $8$ $5.590$ 8.0.342102016.5 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(\beta _{3}+\beta _{4})q^{3}+(\beta _{3}+\beta _{4}+\beta _{7})q^{4}+\cdots\)
700.2.c.j 700.c 140.c $8$ $5.590$ 8.0.342102016.5 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
700.2.c.k 700.c 140.c $16$ $5.590$ 16.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}+(-\beta _{5}+\beta _{6}-\beta _{7}+\beta _{8}-\beta _{9}+\cdots)q^{3}+\cdots\)
700.2.e.a 700.e 5.b $2$ $5.590$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+iq^{7}-6q^{9}-5q^{11}-3iq^{13}+\cdots\)
700.2.e.b 700.e 5.b $2$ $5.590$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+iq^{7}-q^{9}+3q^{11}+4iq^{13}+\cdots\)
700.2.e.c 700.e 5.b $2$ $5.590$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{7}+2q^{9}+3q^{11}-iq^{13}+\cdots\)
700.2.e.d 700.e 5.b $2$ $5.590$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}+3q^{9}-5q^{11}-6iq^{13}-4iq^{17}+\cdots\)
700.2.g.a 700.g 28.d $2$ $5.590$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}+(-2+\beta )q^{4}+(1-2\beta )q^{7}+\cdots\)
700.2.g.b 700.g 28.d $4$ $5.590$ \(\Q(i, \sqrt{6})\) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}-2\beta _{1}q^{4}+\cdots\)
700.2.g.c 700.g 28.d $4$ $5.590$ \(\Q(\sqrt{-3}, \sqrt{-7})\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\beta _{1}-\beta _{3})q^{2}+(1+\beta _{2})q^{4}+(1-2\beta _{3})q^{7}+\cdots\)
700.2.g.d 700.g 28.d $4$ $5.590$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(2\beta _{1}-\beta _{2})q^{3}-2q^{4}+2\beta _{3}q^{6}+\cdots\)
700.2.g.e 700.g 28.d $4$ $5.590$ \(\Q(\sqrt{-3}, \sqrt{-7})\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+\beta _{3})q^{2}+(1+\beta _{2})q^{4}+(-1+2\beta _{3})q^{7}+\cdots\)
700.2.g.f 700.g 28.d $4$ $5.590$ \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
700.2.g.g 700.g 28.d $4$ $5.590$ \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
700.2.g.h 700.g 28.d $4$ $5.590$ \(\Q(i, \sqrt{6})\) None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}-2\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
700.2.g.i 700.g 28.d $8$ $5.590$ 8.0.5473632256.3 None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{4})q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{3}+\cdots\)
700.2.g.j 700.g 28.d $8$ $5.590$ 8.0.342102016.5 None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{5}-\beta _{7})q^{3}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
700.2.g.k 700.g 28.d $8$ $5.590$ 8.0.5473632256.3 None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{4})q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots\)
700.2.g.l 700.g 28.d $16$ $5.590$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{10}q^{3}+(1-\beta _{4})q^{4}+\beta _{14}q^{6}+\cdots\)
700.2.i.a 700.i 7.c $2$ $5.590$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}+(1-3\zeta_{6})q^{7}-6\zeta_{6}q^{9}+\cdots\)
700.2.i.b 700.i 7.c $2$ $5.590$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(-3+\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
700.2.i.c 700.i 7.c $2$ $5.590$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(3-2\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
700.2.i.d 700.i 7.c $6$ $5.590$ 6.0.1783323.2 None None \(0\) \(-1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{3}+\beta _{5})q^{3}+(1-\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)
700.2.i.e 700.i 7.c $6$ $5.590$ 6.0.1783323.2 None None \(0\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{3}-\beta _{5})q^{3}+(-1+\beta _{2}+\beta _{3}-\beta _{5})q^{7}+\cdots\)
700.2.i.f 700.i 7.c $8$ $5.590$ 8.0.2702336256.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{4}-\beta _{6})q^{3}+(\beta _{3}-\beta _{4})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
700.2.k.a 700.k 20.e $24$ $5.590$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
700.2.k.b 700.k 20.e $36$ $5.590$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
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