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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2400.1.l.a 2400.l 3.b $4$ $1.198$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+(-\zeta_{8}+\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
2400.1.n.a 2400.n 24.h $1$ $1.198$ \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{9}-q^{27}+2q^{31}-q^{49}+\cdots\)
2400.1.n.b 2400.n 24.h $1$ $1.198$ \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}+q^{27}+2q^{31}-q^{49}+\cdots\)
2400.1.u.a 2400.u 120.q $4$ $1.198$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{30}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}+\zeta_{8}^{3}q^{17}+\zeta_{8}^{2}q^{19}+\cdots\)
2400.1.u.b 2400.u 120.q $8$ $1.198$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{11}q^{3}-\zeta_{24}^{10}q^{9}+(\zeta_{24}^{4}+\zeta_{24}^{8}+\cdots)q^{11}+\cdots\)
2400.1.br.a 2400.br 480.aq $8$ $1.198$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{3}q^{3}+\zeta_{16}^{6}q^{4}+\cdots\)
2400.1.ca.a 2400.ca 96.p $8$ $1.198$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{2}+\zeta_{16}q^{3}-\zeta_{16}^{2}q^{4}+\zeta_{16}^{6}q^{6}+\cdots\)
2400.1.cb.a 2400.cb 480.ba $8$ $1.198$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{7}q^{2}-\zeta_{16}^{7}q^{3}-\zeta_{16}^{6}q^{4}+\cdots\)
2400.1.cf.a 2400.cf 600.z $8$ $1.198$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{9}q^{3}+\zeta_{20}^{7}q^{5}+(-\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{7}+\cdots\)
2400.1.cp.a 2400.cp 600.aj $4$ $1.198$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-6}) \) None \(0\) \(-1\) \(1\) \(2\) \(q+\zeta_{10}^{2}q^{3}+\zeta_{10}q^{5}+(-\zeta_{10}^{2}+\zeta_{10}^{3}+\cdots)q^{7}+\cdots\)
2400.1.cp.b 2400.cp 600.aj $4$ $1.198$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-6}) \) None \(0\) \(1\) \(-1\) \(2\) \(q-\zeta_{10}^{2}q^{3}-\zeta_{10}q^{5}+(-\zeta_{10}^{2}+\zeta_{10}^{3}+\cdots)q^{7}+\cdots\)
2400.2.a.a 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
2400.2.a.b 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}+2q^{13}+6q^{17}+\cdots\)
2400.2.a.c 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
2400.2.a.d 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
2400.2.a.e 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}-4q^{11}+3q^{13}+\cdots\)
2400.2.a.f 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}-q^{13}+3q^{19}+q^{21}+\cdots\)
2400.2.a.g 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}+q^{13}-3q^{19}+q^{21}+\cdots\)
2400.2.a.h 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}+4q^{11}-3q^{13}+\cdots\)
2400.2.a.i 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
2400.2.a.j 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+4q^{11}-2q^{13}+2q^{17}+\cdots\)
2400.2.a.k 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}+q^{9}-4q^{11}-7q^{13}+\cdots\)
2400.2.a.l 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}+q^{9}-5q^{13}-5q^{19}+\cdots\)
2400.2.a.m 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}+q^{9}+5q^{13}+5q^{19}+\cdots\)
2400.2.a.n 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}+q^{9}+4q^{11}+7q^{13}+\cdots\)
2400.2.a.o 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}-4q^{13}-8q^{19}+\cdots\)
2400.2.a.p 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}+4q^{13}+8q^{19}+\cdots\)
2400.2.a.q 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(-1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
2400.2.a.r 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
2400.2.a.s 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}-4q^{13}+8q^{19}+\cdots\)
2400.2.a.t 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}+4q^{13}-8q^{19}+\cdots\)
2400.2.a.u 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{7}+q^{9}-4q^{11}+7q^{13}+\cdots\)
2400.2.a.v 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{7}+q^{9}-5q^{13}+5q^{19}+\cdots\)
2400.2.a.w 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{7}+q^{9}+5q^{13}-5q^{19}+\cdots\)
2400.2.a.x 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{7}+q^{9}+4q^{11}-7q^{13}+\cdots\)
2400.2.a.y 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-4q^{11}-2q^{13}+2q^{17}+\cdots\)
2400.2.a.z 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
2400.2.a.ba 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}-4q^{11}-3q^{13}+\cdots\)
2400.2.a.bb 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}-q^{13}-3q^{19}+q^{21}+\cdots\)
2400.2.a.bc 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}+q^{13}+3q^{19}+q^{21}+\cdots\)
2400.2.a.bd 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}+4q^{11}+3q^{13}+\cdots\)
2400.2.a.be 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
2400.2.a.bf 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots\)
2400.2.a.bg 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}+2q^{13}+6q^{17}+\cdots\)
2400.2.a.bh 2400.a 1.a $1$ $19.164$ \(\Q\) None None \(0\) \(1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
2400.2.a.bi 2400.a 1.a $2$ $19.164$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}-\beta q^{11}+\beta q^{13}+\cdots\)
2400.2.a.bj 2400.a 1.a $2$ $19.164$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}-\beta q^{11}-\beta q^{13}+\cdots\)
2400.2.b.a 2400.b 24.f $2$ $19.164$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1+\beta )q^{3}+(-1-2\beta )q^{9}+2\beta q^{11}+\cdots\)
2400.2.b.b 2400.b 24.f $4$ $19.164$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
2400.2.b.c 2400.b 24.f $4$ $19.164$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}-3q^{9}+4\beta _{1}q^{17}+4q^{19}+\cdots\)
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