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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1380.1.b.a 1380.b 1380.b $2$ $0.689$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-69}) \) \(\Q(\sqrt{345}) \) \(0\) \(0\) \(-2\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{5}-q^{6}+iq^{7}+\cdots\)
1380.1.b.b 1380.b 1380.b $2$ $0.689$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-69}) \) \(\Q(\sqrt{115}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}-iq^{5}+q^{6}+iq^{8}+\cdots\)
1380.1.b.c 1380.b 1380.b $2$ $0.689$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-69}) \) \(\Q(\sqrt{115}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}-iq^{5}+q^{6}-iq^{8}+\cdots\)
1380.1.b.d 1380.b 1380.b $2$ $0.689$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-69}) \) \(\Q(\sqrt{345}) \) \(0\) \(0\) \(2\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}+q^{5}-q^{6}-iq^{7}+\cdots\)
1380.1.bn.a 1380.bn 1380.an $20$ $0.689$ \(\Q(\zeta_{44})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{44}^{21}q^{2}+\zeta_{44}^{13}q^{3}-\zeta_{44}^{20}q^{4}+\cdots\)
1380.1.bn.b 1380.bn 1380.an $20$ $0.689$ \(\Q(\zeta_{44})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{44}^{13}q^{2}+\zeta_{44}^{3}q^{3}-\zeta_{44}^{4}q^{4}+\cdots\)
1380.1.bn.c 1380.bn 1380.an $20$ $0.689$ \(\Q(\zeta_{44})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{44}^{7}q^{2}+\zeta_{44}^{3}q^{3}+\zeta_{44}^{14}q^{4}+\cdots\)
1380.1.bn.d 1380.bn 1380.an $20$ $0.689$ \(\Q(\zeta_{44})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{44}^{21}q^{2}-\zeta_{44}^{15}q^{3}-\zeta_{44}^{20}q^{4}+\cdots\)
1380.2.a.a 1380.a 1.a $1$ $11.019$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-5q^{7}+q^{9}+4q^{13}+q^{15}+\cdots\)
1380.2.a.b 1380.a 1.a $1$ $11.019$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-6q^{13}+q^{15}+2q^{17}+\cdots\)
1380.2.a.c 1380.a 1.a $1$ $11.019$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-4q^{13}-q^{15}+\cdots\)
1380.2.a.d 1380.a 1.a $1$ $11.019$ \(\Q\) None None \(0\) \(1\) \(1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
1380.2.a.e 1380.a 1.a $1$ $11.019$ \(\Q\) None None \(0\) \(1\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
1380.2.a.f 1380.a 1.a $2$ $11.019$ \(\Q(\sqrt{6}) \) None None \(0\) \(-2\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
1380.2.a.g 1380.a 1.a $2$ $11.019$ \(\Q(\sqrt{17}) \) None None \(0\) \(-2\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+\beta q^{7}+q^{9}+2\beta q^{11}+\cdots\)
1380.2.a.h 1380.a 1.a $2$ $11.019$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(1+2\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
1380.2.a.i 1380.a 1.a $2$ $11.019$ \(\Q(\sqrt{15}) \) None None \(0\) \(2\) \(2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+3q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
1380.2.a.j 1380.a 1.a $3$ $11.019$ 3.3.3144.1 None None \(0\) \(3\) \(-3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(1-\beta _{1})q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
1380.2.f.a 1380.f 5.b $6$ $11.019$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{4})q^{5}-\beta _{3}q^{7}+\cdots\)
1380.2.f.b 1380.f 5.b $14$ $11.019$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{3}+\beta _{10}q^{5}+\beta _{13}q^{7}-q^{9}+\cdots\)
1380.2.i.a 1380.i 69.c $16$ $11.019$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{3}-q^{5}-\beta _{8}q^{7}-\beta _{6}q^{9}-\beta _{9}q^{11}+\cdots\)
1380.2.i.b 1380.i 69.c $16$ $11.019$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+q^{5}-\beta _{8}q^{7}+\beta _{2}q^{9}+\beta _{9}q^{11}+\cdots\)
1380.2.n.a 1380.n 345.h $48$ $11.019$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1380.2.p.a 1380.p 92.b $48$ $11.019$ None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1380.2.p.b 1380.p 92.b $48$ $11.019$ None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1380.2.r.a 1380.r 15.e $4$ $11.019$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
1380.2.r.b 1380.r 15.e $4$ $11.019$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
1380.2.r.c 1380.r 15.e $80$ $11.019$ None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
1380.2.t.a 1380.t 115.e $48$ $11.019$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
1380.3.c.a 1380.c 15.d $88$ $37.602$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1380.3.d.a 1380.d 23.b $32$ $37.602$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1380.3.k.a 1380.k 115.c $48$ $37.602$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1380.3.l.a 1380.l 3.b $60$ $37.602$ None None \(0\) \(-8\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$
1380.3.v.a 1380.v 5.c $88$ $37.602$ None None \(0\) \(0\) \(-16\) \(-16\) $\mathrm{SU}(2)[C_{4}]$
1380.4.a.a 1380.a 1.a $1$ $81.423$ \(\Q\) None None \(0\) \(-3\) \(-5\) \(-16\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}-2^{4}q^{7}+9q^{9}+30q^{11}+\cdots\)
1380.4.a.b 1380.a 1.a $2$ $81.423$ \(\Q(\sqrt{561}) \) None None \(0\) \(-6\) \(10\) \(-17\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}+(-8-\beta )q^{7}+9q^{9}+\cdots\)
1380.4.a.c 1380.a 1.a $3$ $81.423$ 3.3.72332.1 None None \(0\) \(-9\) \(15\) \(22\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}+(8-2\beta _{1}-\beta _{2})q^{7}+\cdots\)
1380.4.a.d 1380.a 1.a $4$ $81.423$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None None \(0\) \(-12\) \(-20\) \(35\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}+(9-\beta _{3})q^{7}+9q^{9}+\cdots\)
1380.4.a.e 1380.a 1.a $5$ $81.423$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-15\) \(-25\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}+(-1-\beta _{2})q^{7}+9q^{9}+\cdots\)
1380.4.a.f 1380.a 1.a $5$ $81.423$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-15\) \(25\) \(-25\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}+(-5-\beta _{1})q^{7}+9q^{9}+\cdots\)
1380.4.a.g 1380.a 1.a $5$ $81.423$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(15\) \(-25\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}+(-1-\beta _{1})q^{7}+9q^{9}+\cdots\)
1380.4.a.h 1380.a 1.a $5$ $81.423$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(15\) \(25\) \(-23\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}+(-5-\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)
1380.4.a.i 1380.a 1.a $7$ $81.423$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(21\) \(-35\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}+(-1+\beta _{1})q^{7}+9q^{9}+\cdots\)
1380.4.a.j 1380.a 1.a $7$ $81.423$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(21\) \(35\) \(35\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}+(5-\beta _{1})q^{7}+9q^{9}+\cdots\)
1380.4.f.a 1380.f 5.b $30$ $81.423$ None None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1380.4.f.b 1380.f 5.b $38$ $81.423$ None None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1380.4.i.a 1380.i 69.c $48$ $81.423$ None None \(0\) \(0\) \(-240\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1380.4.i.b 1380.i 69.c $48$ $81.423$ None None \(0\) \(0\) \(240\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1380.5.d.a 1380.d 23.b $64$ $142.651$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1380.5.k.a 1380.k 115.c $96$ $142.651$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
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