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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1755.1.e.a 1755.e 195.e $1$ $0.876$ \(\Q\) \(\Q(\sqrt{-195}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q+q^{4}-q^{5}-q^{7}+q^{11}+q^{13}+q^{16}+\cdots\)
1755.1.e.b 1755.e 195.e $1$ $0.876$ \(\Q\) \(\Q(\sqrt{-195}) \) None \(0\) \(0\) \(-1\) \(1\) \(q+q^{4}-q^{5}+q^{7}+q^{11}-q^{13}+q^{16}+\cdots\)
1755.1.e.c 1755.e 195.e $1$ $0.876$ \(\Q\) \(\Q(\sqrt{-195}) \) None \(0\) \(0\) \(1\) \(-1\) \(q+q^{4}+q^{5}-q^{7}-q^{11}+q^{13}+q^{16}+\cdots\)
1755.1.e.d 1755.e 195.e $1$ $0.876$ \(\Q\) \(\Q(\sqrt{-195}) \) None \(0\) \(0\) \(1\) \(1\) \(q+q^{4}+q^{5}+q^{7}-q^{11}-q^{13}+q^{16}+\cdots\)
1755.1.e.e 1755.e 195.e $8$ $0.876$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{2}+(-1-\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
1755.1.m.a 1755.m 195.j $4$ $0.876$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}-q^{4}-\zeta_{8}^{3}q^{5}+\cdots\)
1755.1.o.a 1755.o 65.h $16$ $0.876$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{48}^{17}-\zeta_{48}^{19})q^{2}+(-\zeta_{48}^{10}+\cdots)q^{4}+\cdots\)
1755.1.x.a 1755.x 195.u $4$ $0.876$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(4\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}+\zeta_{8}q^{5}+q^{7}+\cdots\)
1755.2.a.a 1755.a 1.a $1$ $14.014$ \(\Q\) None None \(-2\) \(0\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+2q^{10}-5q^{11}+\cdots\)
1755.2.a.b 1755.a 1.a $1$ $14.014$ \(\Q\) None None \(-2\) \(0\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots\)
1755.2.a.c 1755.a 1.a $1$ $14.014$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}-q^{7}+q^{13}+4q^{16}+\cdots\)
1755.2.a.d 1755.a 1.a $1$ $14.014$ \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}-q^{7}+q^{13}+4q^{16}+\cdots\)
1755.2.a.e 1755.a 1.a $1$ $14.014$ \(\Q\) None None \(2\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots\)
1755.2.a.f 1755.a 1.a $1$ $14.014$ \(\Q\) None None \(2\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}+2q^{10}+5q^{11}+\cdots\)
1755.2.a.g 1755.a 1.a $2$ $14.014$ \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
1755.2.a.h 1755.a 1.a $2$ $14.014$ \(\Q(\sqrt{3}) \) None None \(-2\) \(0\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}-q^{5}+(2+\cdots)q^{7}+\cdots\)
1755.2.a.i 1755.a 1.a $2$ $14.014$ \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}-2\beta q^{7}+\cdots\)
1755.2.a.j 1755.a 1.a $2$ $14.014$ \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}-2\beta q^{7}+\cdots\)
1755.2.a.k 1755.a 1.a $2$ $14.014$ \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
1755.2.a.l 1755.a 1.a $2$ $14.014$ \(\Q(\sqrt{3}) \) None None \(2\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+q^{5}+(2-\beta )q^{7}+\cdots\)
1755.2.a.m 1755.a 1.a $4$ $14.014$ 4.4.1957.1 None None \(-3\) \(0\) \(4\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(1-\beta _{1}-\beta _{3})q^{4}+\cdots\)
1755.2.a.n 1755.a 1.a $4$ $14.014$ 4.4.3981.1 None None \(-3\) \(0\) \(4\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1755.2.a.o 1755.a 1.a $4$ $14.014$ 4.4.12357.1 None None \(-1\) \(0\) \(-4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
1755.2.a.p 1755.a 1.a $4$ $14.014$ 4.4.8957.1 None None \(-1\) \(0\) \(-4\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
1755.2.a.q 1755.a 1.a $4$ $14.014$ 4.4.12357.1 None None \(1\) \(0\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
1755.2.a.r 1755.a 1.a $4$ $14.014$ 4.4.8957.1 None None \(1\) \(0\) \(4\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots\)
1755.2.a.s 1755.a 1.a $4$ $14.014$ 4.4.1957.1 None None \(3\) \(0\) \(-4\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(1-\beta _{1}-\beta _{3})q^{4}-q^{5}+\cdots\)
1755.2.a.t 1755.a 1.a $4$ $14.014$ 4.4.3981.1 None None \(3\) \(0\) \(-4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
1755.2.a.u 1755.a 1.a $7$ $14.014$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-1\) \(0\) \(-7\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}-\beta _{4}q^{7}+\cdots\)
1755.2.a.v 1755.a 1.a $7$ $14.014$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(1\) \(0\) \(7\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}-\beta _{4}q^{7}+\cdots\)
1755.2.b.a 1755.b 13.b $2$ $14.014$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-iq^{5}+3iq^{11}+(2-3i)q^{13}+\cdots\)
1755.2.b.b 1755.b 13.b $2$ $14.014$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-iq^{5}+3iq^{11}+(2+3i)q^{13}+\cdots\)
1755.2.b.c 1755.b 13.b $16$ $14.014$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{12}q^{2}+(-1-\beta _{5})q^{4}+\beta _{1}q^{5}+\cdots\)
1755.2.b.d 1755.b 13.b $18$ $14.014$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{6}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
1755.2.b.e 1755.b 13.b $18$ $14.014$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{6}q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots\)
1755.2.b.f 1755.b 13.b $20$ $14.014$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}+(-1-\beta _{2})q^{4}-\beta _{8}q^{5}-\beta _{9}q^{7}+\cdots\)
1755.2.c.a 1755.c 5.b $16$ $14.014$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{14}q^{2}+(-1-\beta _{2}-\beta _{5})q^{4}+(-\beta _{10}+\cdots)q^{5}+\cdots\)
1755.2.c.b 1755.c 5.b $24$ $14.014$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1755.2.c.c 1755.c 5.b $24$ $14.014$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1755.2.c.d 1755.c 5.b $32$ $14.014$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1755.2.i.a 1755.i 9.c $2$ $14.014$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
1755.2.i.b 1755.i 9.c $2$ $14.014$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1755.2.i.c 1755.i 9.c $2$ $14.014$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1755.2.i.d 1755.i 9.c $2$ $14.014$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}-\zeta_{6}q^{13}+\cdots\)
1755.2.i.e 1755.i 9.c $16$ $14.014$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-1\) \(0\) \(8\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{4}+\beta _{12})q^{4}+\cdots\)
1755.2.i.f 1755.i 9.c $16$ $14.014$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(3\) \(0\) \(-8\) \(11\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{6})q^{2}+(-1+\beta _{2}-\beta _{11}+\cdots)q^{4}+\cdots\)
1755.2.i.g 1755.i 9.c $26$ $14.014$ None None \(-1\) \(0\) \(13\) \(-10\) $\mathrm{SU}(2)[C_{3}]$
1755.2.i.h 1755.i 9.c $30$ $14.014$ None None \(-1\) \(0\) \(-15\) \(-10\) $\mathrm{SU}(2)[C_{3}]$
1755.4.a.a 1755.a 1.a $1$ $103.548$ \(\Q\) None None \(-3\) \(0\) \(5\) \(-25\) $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}+5q^{5}-5^{2}q^{7}+21q^{8}+\cdots\)
1755.4.a.b 1755.a 1.a $1$ $103.548$ \(\Q\) None None \(-3\) \(0\) \(5\) \(11\) $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}+5q^{5}+11q^{7}+21q^{8}+\cdots\)
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