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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1300.1.e.a 1300.e 52.b $1$ $0.649$ \(\Q\) \(\Q(\sqrt{-13}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{9}-q^{11}+\cdots\)
1300.1.e.b 1300.e 52.b $1$ $0.649$ \(\Q\) \(\Q(\sqrt{-13}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{9}+q^{11}+\cdots\)
1300.1.e.c 1300.e 52.b $1$ $0.649$ \(\Q\) \(\Q(\sqrt{-13}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{9}-q^{11}+\cdots\)
1300.1.e.d 1300.e 52.b $1$ $0.649$ \(\Q\) \(\Q(\sqrt{-13}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{9}+q^{11}+\cdots\)
1300.1.e.e 1300.e 52.b $2$ $0.649$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) \(\Q(\sqrt{65}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+q^{9}-iq^{13}+\cdots\)
1300.1.g.a 1300.g 260.g $2$ $0.649$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}-q^{9}-q^{11}+\cdots\)
1300.1.g.b 1300.g 260.g $2$ $0.649$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}-q^{9}+q^{11}+\cdots\)
1300.1.k.a 1300.k 65.g $2$ $0.649$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+(1+i)q^{11}-q^{13}+q^{23}+\cdots\)
1300.1.k.b 1300.k 65.g $2$ $0.649$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+(1+i)q^{11}+q^{13}-q^{23}+\cdots\)
1300.1.l.a 1300.l 260.l $2$ $0.649$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+iq^{9}+q^{13}+\cdots\)
1300.1.s.a 1300.s 260.s $2$ $0.649$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+iq^{9}+iq^{13}+q^{16}+\cdots\)
1300.1.t.a 1300.t 13.d $2$ $0.649$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+(1+i)q^{11}-iq^{13}+iq^{23}+\cdots\)
1300.1.t.b 1300.t 13.d $2$ $0.649$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+(1+i)q^{11}+iq^{13}-iq^{23}+\cdots\)
1300.1.w.a 1300.w 260.v $4$ $0.649$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{8}+\cdots\)
1300.1.z.a 1300.z 52.i $4$ $0.649$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}-\zeta_{12}^{2}q^{9}+\cdots\)
1300.1.bc.a 1300.bc 52.j $2$ $0.649$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
1300.1.bd.a 1300.bd 1300.ad $4$ $0.649$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(1\) \(0\) \(q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{5}+\cdots\)
1300.1.bd.b 1300.bd 1300.ad $4$ $0.649$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(-1\) \(0\) \(q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+\zeta_{10}^{2}q^{5}+\cdots\)
1300.1.bm.a 1300.bm 260.ae $4$ $0.649$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+q^{8}-\zeta_{12}q^{9}+\cdots\)
1300.1.bt.a 1300.bt 260.al $4$ $0.649$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{9}+\cdots\)
1300.1.ca.a 1300.ca 1300.ba $8$ $0.649$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+\zeta_{20}^{8}q^{5}-\zeta_{20}^{3}q^{8}+\cdots\)
1300.1.cf.a 1300.cf 1300.bf $8$ $0.649$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{8}q^{2}-\zeta_{20}^{6}q^{4}+\zeta_{20}^{9}q^{5}+\cdots\)
1300.1.cl.a 1300.cl 1300.bl $8$ $0.649$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(1\) \(0\) \(q+\zeta_{30}^{4}q^{2}+\zeta_{30}^{8}q^{4}+\zeta_{30}^{2}q^{5}+\cdots\)
1300.1.cl.b 1300.cl 1300.bl $8$ $0.649$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(1\) \(0\) \(q+\zeta_{30}^{4}q^{2}+\zeta_{30}^{8}q^{4}-\zeta_{30}^{7}q^{5}+\cdots\)
1300.1.cp.a 1300.cp 1300.bp $8$ $0.649$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(1\) \(0\) \(q-\zeta_{30}^{2}q^{2}+\zeta_{30}^{4}q^{4}-\zeta_{30}q^{5}-\zeta_{30}^{6}q^{8}+\cdots\)
1300.1.cp.b 1300.cp 1300.bp $8$ $0.649$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(-1\) \(0\) \(q+\zeta_{30}^{2}q^{2}+\zeta_{30}^{4}q^{4}+\zeta_{30}^{11}q^{5}+\cdots\)
1300.1.ct.a 1300.ct 1300.bt $16$ $0.649$ \(\Q(\zeta_{60})\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{60}^{8}q^{2}+\zeta_{60}^{16}q^{4}-\zeta_{60}^{29}q^{5}+\cdots\)
1300.1.cy.a 1300.cy 1300.by $16$ $0.649$ \(\Q(\zeta_{60})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{60}^{23}q^{2}-\zeta_{60}^{16}q^{4}+\zeta_{60}^{4}q^{5}+\cdots\)
1300.2.a.a 1300.a 1.a $1$ $10.381$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
1300.2.a.b 1300.a 1.a $1$ $10.381$ \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}-2q^{9}-2q^{11}-q^{13}+\cdots\)
1300.2.a.c 1300.a 1.a $1$ $10.381$ \(\Q\) None None \(0\) \(0\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-3q^{7}-3q^{9}+3q^{11}+q^{13}-q^{17}+\cdots\)
1300.2.a.d 1300.a 1.a $1$ $10.381$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}-2q^{11}+q^{13}-6q^{17}+\cdots\)
1300.2.a.e 1300.a 1.a $1$ $10.381$ \(\Q\) None None \(0\) \(0\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+3q^{7}-3q^{9}+3q^{11}-q^{13}+q^{17}+\cdots\)
1300.2.a.f 1300.a 1.a $1$ $10.381$ \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots\)
1300.2.a.g 1300.a 1.a $2$ $10.381$ \(\Q(\sqrt{33}) \) None None \(0\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{7}+(5+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
1300.2.a.h 1300.a 1.a $2$ $10.381$ \(\Q(\sqrt{33}) \) None None \(0\) \(1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{7}+(5+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
1300.2.a.i 1300.a 1.a $3$ $10.381$ 3.3.564.1 None None \(0\) \(-2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(1+\beta _{1})q^{7}+(4+\beta _{1}+\cdots)q^{9}+\cdots\)
1300.2.a.j 1300.a 1.a $3$ $10.381$ 3.3.148.1 None None \(0\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-1-\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
1300.2.a.k 1300.a 1.a $3$ $10.381$ 3.3.148.1 None None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(1+\beta _{1}+\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
1300.2.c.a 1300.c 5.b $2$ $10.381$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}-2iq^{7}-q^{9}+4q^{11}-iq^{13}+\cdots\)
1300.2.c.b 1300.c 5.b $2$ $10.381$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{7}+2q^{9}-2q^{11}+iq^{13}+\cdots\)
1300.2.c.c 1300.c 5.b $2$ $10.381$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}+3q^{9}-2q^{11}-iq^{13}-6iq^{17}+\cdots\)
1300.2.c.d 1300.c 5.b $2$ $10.381$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{7}+3q^{9}+3q^{11}+iq^{13}+iq^{17}+\cdots\)
1300.2.c.e 1300.c 5.b $4$ $10.381$ \(\Q(i, \sqrt{33})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{7}+(-6+\beta _{3})q^{9}+\cdots\)
1300.2.c.f 1300.c 5.b $6$ $10.381$ 6.0.5089536.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{4})q^{3}+(-\beta _{4}-\beta _{5})q^{7}+\cdots\)
1300.2.d.a 1300.d 65.d $4$ $10.381$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{12}q^{3}-\zeta_{12}^{3}q^{7}-q^{9}+3\zeta_{12}^{2}q^{11}+\cdots\)
1300.2.d.b 1300.d 65.d $4$ $10.381$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{7}+2q^{9}+(\zeta_{12}+\cdots)q^{13}+\cdots\)
1300.2.d.c 1300.d 65.d $6$ $10.381$ 6.0.9144576.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{3}q^{7}+(-1+\beta _{3})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots\)
1300.2.d.d 1300.d 65.d $6$ $10.381$ 6.0.9144576.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{3}q^{7}+(-1+\beta _{3})q^{9}+(-\beta _{4}+\cdots)q^{11}+\cdots\)
1300.2.f.a 1300.f 13.b $2$ $10.381$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{3}-\zeta_{6}q^{7}+q^{9}+3\zeta_{6}q^{11}+(1+\cdots)q^{13}+\cdots\)
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