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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2200.1.d.a 2200.d 88.b $1$ $1.098$ \(\Q\) \(\Q(\sqrt{-22}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}-q^{11}+q^{13}+\cdots\)
2200.1.d.b 2200.d 88.b $1$ $1.098$ \(\Q\) \(\Q(\sqrt{-22}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{11}+q^{13}+\cdots\)
2200.1.d.c 2200.d 88.b $1$ $1.098$ \(\Q\) \(\Q(\sqrt{-22}) \) None \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{9}-q^{11}-q^{13}+\cdots\)
2200.1.d.d 2200.d 88.b $1$ $1.098$ \(\Q\) \(\Q(\sqrt{-22}) \) None \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{9}+q^{11}-q^{13}+\cdots\)
2200.1.d.e 2200.d 88.b $2$ $1.098$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-110}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
2200.1.d.f 2200.d 88.b $2$ $1.098$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-110}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{7}-iq^{8}+\cdots\)
2200.1.d.g 2200.d 88.b $4$ $1.098$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\cdots\)
2200.1.o.a 2200.o 440.o $2$ $1.098$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-22}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}-q^{9}-q^{11}-iq^{13}+\cdots\)
2200.1.o.b 2200.o 440.o $2$ $1.098$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-22}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}-q^{9}+q^{11}-iq^{13}+\cdots\)
2200.1.w.a 2200.w 440.w $4$ $1.098$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{22}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
2200.1.w.b 2200.w 440.w $4$ $1.098$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{110}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}+\zeta_{8}^{2}q^{9}+\cdots\)
2200.1.w.c 2200.w 440.w $8$ $1.098$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{9}q^{2}+(\zeta_{24}^{7}+\zeta_{24}^{11})q^{3}-\zeta_{24}^{6}q^{4}+\cdots\)
2200.1.cl.a 2200.cl 88.l $4$ $1.098$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-2}) \) None \(1\) \(2\) \(0\) \(0\) \(q+\zeta_{10}q^{2}+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots\)
2200.1.cl.b 2200.cl 88.l $8$ $1.098$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-2}) \) None \(-2\) \(2\) \(0\) \(0\) \(q-\zeta_{30}^{3}q^{2}+(-\zeta_{30}^{7}-\zeta_{30}^{11})q^{3}+\cdots\)
2200.1.cl.c 2200.cl 88.l $8$ $1.098$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{7}q^{2}-\zeta_{20}^{4}q^{4}+(-\zeta_{20}^{3}+\zeta_{20}^{5}+\cdots)q^{7}+\cdots\)
2200.1.cl.d 2200.cl 88.l $8$ $1.098$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-2}) \) None \(2\) \(-2\) \(0\) \(0\) \(q+\zeta_{30}^{3}q^{2}+(\zeta_{30}^{7}+\zeta_{30}^{11})q^{3}+\zeta_{30}^{6}q^{4}+\cdots\)
2200.1.dd.a 2200.dd 440.ah $8$ $1.098$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{3}q^{2}+(\zeta_{20}-\zeta_{20}^{7})q^{3}+\zeta_{20}^{6}q^{4}+\cdots\)
2200.1.dd.b 2200.dd 440.ah $16$ $1.098$ \(\Q(\zeta_{60})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{60}^{9}q^{2}+(-\zeta_{60}+\zeta_{60}^{23})q^{3}+\cdots\)
2200.1.fr.a 2200.fr 440.ar $16$ $1.098$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{40}^{9}q^{2}+(\zeta_{40}^{3}-\zeta_{40}^{11})q^{3}+\zeta_{40}^{18}q^{4}+\cdots\)
2200.1.fr.b 2200.fr 440.ar $16$ $1.098$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{40}^{19}q^{2}-\zeta_{40}^{18}q^{4}+(\zeta_{40}^{11}+\cdots)q^{7}+\cdots\)
2200.1.fr.c 2200.fr 440.ar $32$ $1.098$ \(\Q(\zeta_{120})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{120}^{39}q^{2}+(-\zeta_{120}-\zeta_{120}^{53})q^{3}+\cdots\)
2200.2.a.a 2200.a 1.a $1$ $17.567$ \(\Q\) None None \(0\) \(-3\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{7}+6q^{9}-q^{11}+6q^{13}+\cdots\)
2200.2.a.b 2200.a 1.a $1$ $17.567$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
2200.2.a.c 2200.a 1.a $1$ $17.567$ \(\Q\) None None \(0\) \(-2\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{7}+q^{9}-q^{11}-4q^{17}+\cdots\)
2200.2.a.d 2200.a 1.a $1$ $17.567$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}-2q^{9}-q^{11}+q^{17}+q^{19}+\cdots\)
2200.2.a.e 2200.a 1.a $1$ $17.567$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-3q^{9}-q^{11}-6q^{13}+6q^{17}+\cdots\)
2200.2.a.f 2200.a 1.a $1$ $17.567$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}-q^{11}-8q^{19}+8q^{23}+\cdots\)
2200.2.a.g 2200.a 1.a $1$ $17.567$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}+q^{11}+4q^{13}+4q^{17}+\cdots\)
2200.2.a.h 2200.a 1.a $1$ $17.567$ \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}-2q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)
2200.2.a.i 2200.a 1.a $1$ $17.567$ \(\Q\) None None \(0\) \(2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{7}+q^{9}-q^{11}+4q^{17}+\cdots\)
2200.2.a.j 2200.a 1.a $1$ $17.567$ \(\Q\) None None \(0\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
2200.2.a.k 2200.a 1.a $1$ $17.567$ \(\Q\) None None \(0\) \(3\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{7}+6q^{9}-q^{11}+6q^{17}+\cdots\)
2200.2.a.l 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-2-\beta )q^{7}+(1+\beta )q^{9}-q^{11}+\cdots\)
2200.2.a.m 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-2+\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
2200.2.a.n 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{5}) \) None None \(0\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}-q^{11}+\cdots\)
2200.2.a.o 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+2\beta q^{7}+(1+\beta )q^{9}-q^{11}+\cdots\)
2200.2.a.p 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{5}) \) None None \(0\) \(-1\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1+\beta )q^{7}+(-2+\beta )q^{9}+q^{11}+\cdots\)
2200.2.a.q 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{5}) \) None None \(0\) \(1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
2200.2.a.r 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{5}) \) None None \(0\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
2200.2.a.s 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{7}+(1+\beta )q^{9}+q^{11}-2q^{13}+\cdots\)
2200.2.a.t 2200.a 1.a $3$ $17.567$ 3.3.837.1 None None \(0\) \(-3\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
2200.2.a.u 2200.a 1.a $3$ $17.567$ 3.3.1229.1 None None \(0\) \(-1\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
2200.2.a.v 2200.a 1.a $3$ $17.567$ 3.3.1229.1 None None \(0\) \(1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
2200.2.a.w 2200.a 1.a $3$ $17.567$ 3.3.837.1 None None \(0\) \(3\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{2})q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
2200.2.a.x 2200.a 1.a $4$ $17.567$ 4.4.54764.1 None None \(0\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{9}+\cdots\)
2200.2.a.y 2200.a 1.a $4$ $17.567$ 4.4.54764.1 None None \(0\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{9}+\cdots\)
2200.2.b.a 2200.b 5.b $2$ $17.567$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-2iq^{7}-6q^{9}-q^{11}-6iq^{17}+\cdots\)
2200.2.b.b 2200.b 5.b $2$ $17.567$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-iq^{7}-6q^{9}-q^{11}-6iq^{13}+\cdots\)
2200.2.b.c 2200.b 5.b $2$ $17.567$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}+3q^{9}-q^{11}-3iq^{13}-3iq^{17}+\cdots\)
2200.2.b.d 2200.b 5.b $2$ $17.567$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+3q^{9}-q^{11}+8q^{19}-4iq^{23}+\cdots\)
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