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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3432.1.i.a 3432.i 3432.i $1$ $1.713$ \(\Q\) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-858}) \) \(\Q(\sqrt{22}) \) \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3432.1.i.b 3432.i 3432.i $1$ $1.713$ \(\Q\) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-858}) \) \(\Q(\sqrt{22}) \) \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3432.1.i.c 3432.i 3432.i $1$ $1.713$ \(\Q\) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-858}) \) \(\Q(\sqrt{22}) \) \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
3432.1.i.d 3432.i 3432.i $1$ $1.713$ \(\Q\) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-858}) \) \(\Q(\sqrt{22}) \) \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
3432.1.i.e 3432.i 3432.i $2$ $1.713$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-66}) \) \(\Q(\sqrt{78}) \) \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{6}-iq^{7}+iq^{8}+\cdots\)
3432.1.i.f 3432.i 3432.i $2$ $1.713$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-66}) \) \(\Q(\sqrt{78}) \) \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-q^{4}-iq^{6}-iq^{7}-iq^{8}+\cdots\)
3432.1.i.g 3432.i 3432.i $2$ $1.713$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-66}) \) \(\Q(\sqrt{286}) \) \(0\) \(2\) \(0\) \(0\) \(q-iq^{2}+q^{3}-q^{4}-iq^{5}-iq^{6}+iq^{8}+\cdots\)
3432.1.i.h 3432.i 3432.i $2$ $1.713$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-66}) \) \(\Q(\sqrt{286}) \) \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}-iq^{5}+iq^{6}-iq^{8}+\cdots\)
3432.1.i.i 3432.i 3432.i $8$ $1.713$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-143}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{20}^{3}q^{2}+\zeta_{20}^{2}q^{3}+\zeta_{20}^{6}q^{4}+\cdots\)
3432.1.i.j 3432.i 3432.i $8$ $1.713$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-143}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{20}^{3}q^{2}-\zeta_{20}^{8}q^{3}+\zeta_{20}^{6}q^{4}+\cdots\)
3432.1.cg.a 3432.cg 3432.bg $4$ $1.713$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-66}) \) None \(0\) \(-2\) \(0\) \(-6\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\cdots\)
3432.1.cg.b 3432.cg 3432.bg $4$ $1.713$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-66}) \) None \(0\) \(-2\) \(0\) \(6\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\cdots\)
3432.1.cg.c 3432.cg 3432.bg $4$ $1.713$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-66}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+(\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
3432.1.cg.d 3432.cg 3432.bg $4$ $1.713$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-66}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
3432.1.cp.a 3432.cp 3432.bp $2$ $1.713$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-66}) \) None \(-1\) \(-1\) \(-2\) \(1\) \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}+\zeta_{6}^{2}q^{6}+\cdots\)
3432.1.cp.b 3432.cp 3432.bp $2$ $1.713$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-66}) \) None \(-1\) \(-1\) \(2\) \(-1\) \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{6}+\cdots\)
3432.1.cp.c 3432.cp 3432.bp $2$ $1.713$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-66}) \) None \(1\) \(-1\) \(-2\) \(-1\) \(q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
3432.1.cp.d 3432.cp 3432.bp $2$ $1.713$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-66}) \) None \(1\) \(-1\) \(2\) \(1\) \(q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
3432.1.cp.e 3432.cp 3432.bp $4$ $1.713$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-66}) \) None \(-2\) \(2\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
3432.1.cp.f 3432.cp 3432.bp $4$ $1.713$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-66}) \) None \(2\) \(2\) \(0\) \(0\) \(q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
3432.1.eb.a 3432.eb 3432.db $4$ $1.713$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-39}) \) None \(-4\) \(1\) \(0\) \(0\) \(q-q^{2}-\zeta_{10}^{2}q^{3}+q^{4}+(\zeta_{10}^{3}+\zeta_{10}^{4}+\cdots)q^{5}+\cdots\)
3432.1.eb.b 3432.eb 3432.db $4$ $1.713$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-39}) \) None \(-1\) \(1\) \(0\) \(0\) \(q-\zeta_{10}^{3}q^{2}-\zeta_{10}^{2}q^{3}-\zeta_{10}q^{4}+(-\zeta_{10}^{3}+\cdots)q^{5}+\cdots\)
3432.1.eb.c 3432.eb 3432.db $4$ $1.713$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-39}) \) None \(1\) \(1\) \(0\) \(0\) \(q+\zeta_{10}^{3}q^{2}-\zeta_{10}^{2}q^{3}-\zeta_{10}q^{4}+(\zeta_{10}^{3}+\cdots)q^{5}+\cdots\)
3432.1.eb.d 3432.eb 3432.db $4$ $1.713$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-39}) \) None \(4\) \(1\) \(0\) \(0\) \(q+q^{2}-\zeta_{10}^{2}q^{3}+q^{4}+(-\zeta_{10}^{3}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots\)
3432.1.eb.e 3432.eb 3432.db $8$ $1.713$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-39}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{20}^{5}q^{2}+\zeta_{20}^{4}q^{3}-q^{4}+(\zeta_{20}+\cdots)q^{5}+\cdots\)
3432.1.eb.f 3432.eb 3432.db $8$ $1.713$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-39}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{20}q^{2}+\zeta_{20}^{4}q^{3}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\cdots)q^{5}+\cdots\)
3432.1.ee.a 3432.ee 3432.de $16$ $1.713$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{40}^{15}q^{2}-\zeta_{40}^{6}q^{3}-\zeta_{40}^{10}q^{4}+\cdots\)
3432.1.ee.b 3432.ee 3432.de $16$ $1.713$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{40}^{11}q^{2}-\zeta_{40}^{14}q^{3}-\zeta_{40}^{2}q^{4}+\cdots\)
3432.2.a.a 3432.a 1.a $1$ $27.405$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}+q^{11}+q^{13}+2q^{15}+\cdots\)
3432.2.a.b 3432.a 1.a $1$ $27.405$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+3q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3432.2.a.c 3432.a 1.a $1$ $27.405$ \(\Q\) None None \(0\) \(-1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}-q^{11}-q^{13}+8q^{17}+\cdots\)
3432.2.a.d 3432.a 1.a $1$ $27.405$ \(\Q\) None None \(0\) \(1\) \(-3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}+3q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
3432.2.a.e 3432.a 1.a $1$ $27.405$ \(\Q\) None None \(0\) \(1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}+q^{11}-q^{13}-2q^{15}+\cdots\)
3432.2.a.f 3432.a 1.a $1$ $27.405$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+q^{11}-q^{13}-4q^{17}+\cdots\)
3432.2.a.g 3432.a 1.a $1$ $27.405$ \(\Q\) None None \(0\) \(1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}-q^{11}+q^{13}+2q^{15}+\cdots\)
3432.2.a.h 3432.a 1.a $1$ $27.405$ \(\Q\) None None \(0\) \(1\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+4q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
3432.2.a.i 3432.a 1.a $1$ $27.405$ \(\Q\) None None \(0\) \(1\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+4q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3432.2.a.j 3432.a 1.a $2$ $27.405$ \(\Q(\sqrt{6}) \) None None \(0\) \(-2\) \(-4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-2+\beta )q^{5}-2q^{7}+q^{9}+q^{11}+\cdots\)
3432.2.a.k 3432.a 1.a $2$ $27.405$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}+q^{9}-q^{11}-q^{13}+\cdots\)
3432.2.a.l 3432.a 1.a $2$ $27.405$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}+2\beta q^{7}+q^{9}+q^{11}+\cdots\)
3432.2.a.m 3432.a 1.a $2$ $27.405$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}-2q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
3432.2.a.n 3432.a 1.a $3$ $27.405$ 3.3.404.1 None None \(0\) \(3\) \(-4\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta _{2})q^{5}+(-2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
3432.2.a.o 3432.a 1.a $3$ $27.405$ 3.3.892.1 None None \(0\) \(3\) \(-1\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta _{1}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
3432.2.a.p 3432.a 1.a $3$ $27.405$ 3.3.148.1 None None \(0\) \(3\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta _{2}q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
3432.2.a.q 3432.a 1.a $4$ $27.405$ 4.4.22676.1 None None \(0\) \(-4\) \(-3\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{3})q^{7}+\cdots\)
3432.2.a.r 3432.a 1.a $4$ $27.405$ 4.4.70164.1 None None \(0\) \(-4\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+\cdots\)
3432.2.a.s 3432.a 1.a $4$ $27.405$ 4.4.29268.1 None None \(0\) \(-4\) \(4\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
3432.2.a.t 3432.a 1.a $4$ $27.405$ 4.4.23252.1 None None \(0\) \(-4\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+q^{11}+\cdots\)
3432.2.a.u 3432.a 1.a $4$ $27.405$ 4.4.70164.1 None None \(0\) \(4\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta _{2}-\beta _{3})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
3432.2.a.v 3432.a 1.a $4$ $27.405$ 4.4.83476.1 None None \(0\) \(4\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{3}q^{5}+(-1+\beta _{1}+\beta _{3})q^{7}+\cdots\)
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