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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3600.1.c.a 3600.c 15.d $4$ $1.797$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\zeta_{8}^{2}q^{13}+\cdots\)
3600.1.e.a 3600.e 4.b $1$ $1.797$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+2q^{29}+2q^{41}+q^{49}-2q^{61}+2q^{89}+\cdots\)
3600.1.e.b 3600.e 4.b $1$ $1.797$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q+2q^{13}-2q^{37}+q^{49}+2q^{61}+2q^{73}+\cdots\)
3600.1.e.c 3600.e 4.b $2$ $1.797$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
3600.1.e.d 3600.e 4.b $2$ $1.797$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{6}-\zeta_{6}^{2})q^{7}+q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
3600.1.j.a 3600.j 20.d $2$ $1.797$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{13}-iq^{37}-q^{49}+q^{61}-iq^{73}+\cdots\)
3600.1.j.b 3600.j 20.d $4$ $1.797$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{5})q^{7}-\zeta_{12}^{3}q^{13}+\cdots\)
3600.1.l.a 3600.l 3.b $2$ $1.797$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+\beta q^{11}-q^{13}-\beta q^{17}-q^{19}+\cdots\)
3600.1.l.b 3600.l 3.b $2$ $1.797$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(2\) \(q+q^{7}-\beta q^{11}+q^{13}-\beta q^{17}-q^{19}+\cdots\)
3600.1.bb.a 3600.bb 80.i $2$ $1.797$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+q^{16}+(-1+i+\cdots)q^{17}+\cdots\)
3600.1.bb.b 3600.bb 80.i $2$ $1.797$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+q^{16}+(1-i+\cdots)q^{17}+\cdots\)
3600.1.bf.a 3600.bf 80.t $2$ $1.797$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{16}+(1-i)q^{17}+\cdots\)
3600.1.bf.b 3600.bf 80.t $2$ $1.797$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{16}+(-1+i+\cdots)q^{17}+\cdots\)
3600.1.bh.a 3600.bh 5.c $2$ $1.797$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{19}+q^{31}-iq^{49}+q^{61}+iq^{79}+\cdots\)
3600.1.bh.b 3600.bh 5.c $4$ $1.797$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{7}+\beta _{3}q^{13}+\beta _{2}q^{19}-q^{31}+\cdots\)
3600.1.bk.a 3600.bk 60.l $4$ $1.797$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-1-\zeta_{8}^{2})q^{13}-\zeta_{8}q^{17}+(-\zeta_{8}+\cdots)q^{29}+\cdots\)
3600.1.bo.a 3600.bo 16.f $4$ $1.797$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}-q^{16}+\cdots\)
3600.1.cc.a 3600.cc 36.f $2$ $1.797$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(-1\) \(0\) \(-3\) \(q-\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
3600.1.cc.b 3600.cc 36.f $2$ $1.797$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(1\) \(0\) \(3\) \(q+\zeta_{6}q^{3}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\cdots)q^{21}+\cdots\)
3600.1.cj.a 3600.cj 100.j $8$ $1.797$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{9}q^{5}+(\zeta_{20}^{6}-\zeta_{20}^{8})q^{13}+(-\zeta_{20}+\cdots)q^{17}+\cdots\)
3600.1.ct.a 3600.ct 100.h $4$ $1.797$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+\zeta_{10}^{4}q^{5}+(-\zeta_{10}+\zeta_{10}^{3})q^{13}+\cdots\)
3600.1.da.a 3600.da 180.v $8$ $1.797$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{3}+\zeta_{24}^{5}q^{7}-\zeta_{24}^{2}q^{9}+\cdots\)
3600.1.dx.a 3600.dx 300.u $16$ $1.797$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{40}^{7}q^{5}+(-\zeta_{40}^{4}+\zeta_{40}^{18})q^{13}+\cdots\)
3600.2.a.a 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-5q^{7}-6q^{11}+3q^{13}-2q^{17}-q^{19}+\cdots\)
3600.2.a.b 3600.a 1.a $1$ $28.746$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) $+$ $N(\mathrm{U}(1))$ \(q-5q^{7}+5q^{13}+q^{19}+7q^{31}-10q^{37}+\cdots\)
3600.2.a.c 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-4q^{11}-4q^{13}+6q^{17}+4q^{19}+\cdots\)
3600.2.a.d 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-4q^{11}-4q^{17}+4q^{23}+6q^{29}+\cdots\)
3600.2.a.e 3600.a 1.a $1$ $28.746$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $N(\mathrm{U}(1))$ \(q-4q^{7}-2q^{13}-8q^{19}+4q^{31}+10q^{37}+\cdots\)
3600.2.a.f 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-4q^{7}-2q^{13}+6q^{17}+4q^{19}+6q^{29}+\cdots\)
3600.2.a.g 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{7}+4q^{11}-4q^{13}-6q^{17}+4q^{19}+\cdots\)
3600.2.a.h 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{7}+4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots\)
3600.2.a.i 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-3q^{7}+2q^{11}-3q^{13}-6q^{17}+7q^{19}+\cdots\)
3600.2.a.j 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-3q^{7}+2q^{11}-q^{13}+2q^{17}+5q^{19}+\cdots\)
3600.2.a.k 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-4q^{11}+4q^{13}+4q^{19}-2q^{23}+\cdots\)
3600.2.a.l 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{11}-4q^{13}+3q^{17}-5q^{19}+\cdots\)
3600.2.a.m 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+q^{11}+4q^{13}-5q^{17}-q^{19}+\cdots\)
3600.2.a.n 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+2q^{11}-2q^{13}+6q^{17}-8q^{19}+\cdots\)
3600.2.a.o 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+2q^{11}+6q^{13}-2q^{17}-4q^{23}+\cdots\)
3600.2.a.p 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}-4q^{11}-q^{13}+4q^{17}-q^{19}+\cdots\)
3600.2.a.q 3600.a 1.a $1$ $28.746$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) $-$ $N(\mathrm{U}(1))$ \(q-q^{7}+7q^{13}+7q^{19}-11q^{31}+10q^{37}+\cdots\)
3600.2.a.r 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}+4q^{11}-q^{13}-4q^{17}-q^{19}+\cdots\)
3600.2.a.s 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}+6q^{11}-5q^{13}-6q^{17}-5q^{19}+\cdots\)
3600.2.a.t 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-4q^{11}-6q^{13}-6q^{17}+4q^{19}+\cdots\)
3600.2.a.u 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots\)
3600.2.a.v 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots\)
3600.2.a.w 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}-4q^{11}+q^{13}-4q^{17}-q^{19}+\cdots\)
3600.2.a.x 3600.a 1.a $1$ $28.746$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) $+$ $N(\mathrm{U}(1))$ \(q+q^{7}-7q^{13}+7q^{19}-11q^{31}-10q^{37}+\cdots\)
3600.2.a.y 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}+q^{13}+4q^{17}-q^{19}+\cdots\)
3600.2.a.z 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}+6q^{11}+5q^{13}+6q^{17}-5q^{19}+\cdots\)
3600.2.a.ba 3600.a 1.a $1$ $28.746$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-6q^{11}+4q^{13}+6q^{17}+4q^{19}+\cdots\)
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