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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
555.1.b.a 555.b 555.b $8$ $0.277$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-111}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{16}-\zeta_{16}^{7})q^{2}+\zeta_{16}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots\)
555.2.a.a 555.a 1.a $1$ $4.432$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
555.2.a.b 555.a 1.a $1$ $4.432$ \(\Q\) None None \(0\) \(1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-2q^{12}+\cdots\)
555.2.a.c 555.a 1.a $2$ $4.432$ \(\Q(\sqrt{5}) \) None None \(-3\) \(2\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+q^{5}+\cdots\)
555.2.a.d 555.a 1.a $2$ $4.432$ \(\Q(\sqrt{13}) \) None None \(-1\) \(-2\) \(2\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
555.2.a.e 555.a 1.a $2$ $4.432$ \(\Q(\sqrt{5}) \) None None \(-1\) \(2\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
555.2.a.f 555.a 1.a $2$ $4.432$ \(\Q(\sqrt{5}) \) None None \(1\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
555.2.a.g 555.a 1.a $2$ $4.432$ \(\Q(\sqrt{13}) \) None None \(1\) \(2\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots\)
555.2.a.h 555.a 1.a $3$ $4.432$ 3.3.469.1 None None \(1\) \(-3\) \(3\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
555.2.a.i 555.a 1.a $3$ $4.432$ 3.3.229.1 None None \(2\) \(3\) \(3\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+q^{5}+\cdots\)
555.2.a.j 555.a 1.a $5$ $4.432$ 5.5.600268.1 None None \(-3\) \(-5\) \(-5\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}-q^{3}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots\)
555.2.c.a 555.c 5.b $2$ $4.432$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+iq^{3}-2q^{4}+(-1+2i)q^{5}+\cdots\)
555.2.c.b 555.c 5.b $8$ $4.432$ 8.0.309760000.3 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
555.2.c.c 555.c 5.b $26$ $4.432$ None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$
555.2.e.a 555.e 37.b $2$ $4.432$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+2q^{4}+iq^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
555.2.e.b 555.e 37.b $10$ $4.432$ 10.0.\(\cdots\).1 None None \(0\) \(10\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+q^{3}+(-1+\beta _{1})q^{4}+\beta _{6}q^{5}+\cdots\)
555.2.e.c 555.e 37.b $12$ $4.432$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-12\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{8}q^{2}-q^{3}+(-2-\beta _{7})q^{4}+\beta _{2}q^{5}+\cdots\)
555.2.g.a 555.g 185.d $40$ $4.432$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
555.2.i.a 555.i 37.c $2$ $4.432$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(-1\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
555.2.i.b 555.i 37.c $4$ $4.432$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-2\) \(-2\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
555.2.i.c 555.i 37.c $4$ $4.432$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{3}+(-1+\cdots)q^{4}+\cdots\)
555.2.i.d 555.i 37.c $10$ $4.432$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(1\) \(-5\) \(-5\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{2})q^{2}-\beta _{6}q^{3}+(\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots\)
555.2.i.e 555.i 37.c $14$ $4.432$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-1\) \(7\) \(-7\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{4}+\beta _{5}+\beta _{7})q^{4}+\cdots\)
555.2.i.f 555.i 37.c $14$ $4.432$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-1\) \(7\) \(7\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{3}-\beta _{5}+\beta _{10}+\cdots)q^{4}+\cdots\)
555.2.j.a 555.j 185.f $76$ $4.432$ None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
555.2.m.a 555.m 555.m $16$ $4.432$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{3}-\beta _{10})q^{3}-2\beta _{9}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
555.2.m.b 555.m 555.m $128$ $4.432$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
555.2.n.a 555.n 555.n $32$ $4.432$ \(\Q(\sqrt{-111}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$
555.2.n.b 555.n 555.n $112$ $4.432$ None None \(0\) \(-8\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
555.2.o.a 555.o 15.e $144$ $4.432$ None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
555.2.s.a 555.s 111.g $104$ $4.432$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
555.2.t.a 555.t 185.k $76$ $4.432$ None None \(-4\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
555.2.x.a 555.x 185.l $80$ $4.432$ None None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$
555.2.z.a 555.z 37.e $20$ $4.432$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(6\) \(-10\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{4}q^{2}+(-1-\beta _{2})q^{3}+(\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots\)
555.2.z.b 555.z 37.e $28$ $4.432$ None None \(6\) \(14\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$
555.2.bb.a 555.bb 185.n $72$ $4.432$ None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
555.2.bc.a 555.bc 37.f $6$ $4.432$ \(\Q(\zeta_{18})\) None None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q-\zeta_{18}^{2}q^{3}+2\zeta_{18}^{5}q^{4}+(-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
555.2.bc.b 555.bc 37.f $36$ $4.432$ None None \(3\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{9}]$
555.2.bc.c 555.bc 37.f $36$ $4.432$ None None \(3\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$
555.2.bc.d 555.bc 37.f $36$ $4.432$ None None \(3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
555.2.bc.e 555.bc 37.f $42$ $4.432$ None None \(3\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$
555.2.bd.a 555.bd 185.p $152$ $4.432$ None None \(4\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{12}]$
555.2.bg.a 555.bg 111.m $208$ $4.432$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
555.2.bh.a 555.bh 555.ah $288$ $4.432$ None None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$
555.2.bi.a 555.bi 555.ai $288$ $4.432$ None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$
555.2.bm.a 555.bm 555.am $288$ $4.432$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
555.2.bn.a 555.bn 185.u $152$ $4.432$ None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{12}]$
555.2.bp.a 555.bp 185.v $240$ $4.432$ None None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
555.2.bs.a 555.bs 185.x $216$ $4.432$ None None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{18}]$
555.2.bt.a 555.bt 37.h $72$ $4.432$ None None \(-6\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{18}]$
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