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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1800.1.c.a 1800.c 15.d $4$ $0.898$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{7}+(-\zeta_{8}-\zeta_{8}^{3})q^{11}+\zeta_{8}^{2}q^{13}+\cdots\)
1800.1.g.a 1800.g 8.d $1$ $0.898$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{11}+q^{16}+q^{17}+\cdots\)
1800.1.g.b 1800.g 8.d $1$ $0.898$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{11}+q^{16}-q^{17}+\cdots\)
1800.1.g.c 1800.g 8.d $2$ $0.898$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+q^{16}+q^{19}+\cdots\)
1800.1.l.a 1800.l 3.b $2$ $0.898$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}-\beta q^{11}+q^{13}+\beta q^{17}+q^{19}+\cdots\)
1800.1.l.b 1800.l 3.b $2$ $0.898$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(2\) \(q+q^{7}-\beta q^{11}-q^{13}-\beta q^{17}+q^{19}+\cdots\)
1800.1.p.a 1800.p 40.e $2$ $0.898$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+q^{11}+q^{16}+\cdots\)
1800.1.r.a 1800.r 120.q $4$ $0.898$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{2})q^{7}+\cdots\)
1800.1.r.b 1800.r 120.q $4$ $0.898$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{2})q^{7}+\cdots\)
1800.1.u.a 1800.u 40.i $4$ $0.898$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-30}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}-q^{16}+\cdots\)
1800.1.u.b 1800.u 40.i $4$ $0.898$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{2})q^{7}+\cdots\)
1800.1.ba.a 1800.ba 360.z $4$ $0.898$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
1800.1.ba.b 1800.ba 360.z $4$ $0.898$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
1800.1.ba.c 1800.ba 360.z $4$ $0.898$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+q^{6}+\cdots\)
1800.1.bk.a 1800.bk 72.p $2$ $0.898$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+q^{6}+q^{8}+\cdots\)
1800.1.bk.b 1800.bk 72.p $2$ $0.898$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(2\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{6}+\cdots\)
1800.1.bk.c 1800.bk 72.p $2$ $0.898$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(1\) \(-2\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{6}+\cdots\)
1800.1.bk.d 1800.bk 72.p $2$ $0.898$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)
1800.1.bk.e 1800.bk 72.p $2$ $0.898$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+q^{6}-q^{8}+\cdots\)
1800.1.cj.a 1800.cj 360.at $8$ $0.898$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{11}q^{2}-\zeta_{24}^{9}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
1800.1.cj.b 1800.cj 360.at $8$ $0.898$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
1800.1.cj.c 1800.cj 360.at $8$ $0.898$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{11}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
1800.1.cr.a 1800.cr 200.x $16$ $0.898$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{40}^{19}q^{2}-\zeta_{40}^{18}q^{4}+\zeta_{40}^{9}q^{5}+\cdots\)
1800.1.dg.a 1800.dg 1800.cg $16$ $0.898$ \(\Q(\zeta_{60})\) None None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{60}^{29}q^{2}+\zeta_{60}^{18}q^{3}-\zeta_{60}^{28}q^{4}+\cdots\)
1800.2.a.a 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-5q^{7}+6q^{11}-3q^{13}+2q^{17}+q^{19}+\cdots\)
1800.2.a.b 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-4q^{11}+4q^{13}+6q^{17}-4q^{19}+\cdots\)
1800.2.a.c 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{7}+6q^{13}-2q^{17}+4q^{19}-8q^{23}+\cdots\)
1800.2.a.d 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-4q^{7}+4q^{11}+4q^{13}-6q^{17}-4q^{19}+\cdots\)
1800.2.a.e 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-3q^{7}-2q^{11}+3q^{13}+6q^{17}-7q^{19}+\cdots\)
1800.2.a.f 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-2q^{11}-4q^{13}-2q^{17}+4q^{19}+\cdots\)
1800.2.a.g 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-2q^{11}+2q^{13}-6q^{17}+8q^{19}+\cdots\)
1800.2.a.h 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-q^{11}-4q^{13}+5q^{17}+q^{19}+\cdots\)
1800.2.a.i 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+2q^{11}-4q^{13}+2q^{17}+4q^{19}+\cdots\)
1800.2.a.j 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+4q^{11}-4q^{13}-4q^{19}-2q^{23}+\cdots\)
1800.2.a.k 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}-4q^{11}+q^{13}+4q^{17}+q^{19}+\cdots\)
1800.2.a.l 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}+4q^{11}+q^{13}-4q^{17}+q^{19}+\cdots\)
1800.2.a.m 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots\)
1800.2.a.n 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+4q^{11}-6q^{13}-6q^{17}-4q^{19}+\cdots\)
1800.2.a.o 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-4q^{11}-q^{13}-4q^{17}+q^{19}+\cdots\)
1800.2.a.p 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}-q^{13}+4q^{17}+q^{19}+\cdots\)
1800.2.a.q 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-2q^{11}-2q^{13}+6q^{17}+8q^{19}+\cdots\)
1800.2.a.r 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-q^{11}+4q^{13}-5q^{17}+q^{19}+\cdots\)
1800.2.a.s 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}+4q^{11}+4q^{13}-4q^{19}+2q^{23}+\cdots\)
1800.2.a.t 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+3q^{7}-2q^{11}-3q^{13}-6q^{17}-7q^{19}+\cdots\)
1800.2.a.u 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+4q^{7}-4q^{11}-4q^{13}-6q^{17}-4q^{19}+\cdots\)
1800.2.a.v 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+4q^{7}-4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots\)
1800.2.a.w 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+4q^{7}+4q^{11}-4q^{13}+6q^{17}-4q^{19}+\cdots\)
1800.2.a.x 1800.a 1.a $1$ $14.373$ \(\Q\) None None \(0\) \(0\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+5q^{7}+6q^{11}+3q^{13}-2q^{17}+q^{19}+\cdots\)
1800.2.b.a 1800.b 24.f $2$ $14.373$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2q^{4}+3\beta q^{7}-2\beta q^{8}+\beta q^{11}+\cdots\)
1800.2.b.b 1800.b 24.f $2$ $14.373$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}-2q^{4}+3\beta q^{7}+2\beta q^{8}-\beta q^{11}+\cdots\)
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