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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3344.1.p.a 3344.p 836.h $1$ $1.669$ \(\Q\) \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-209}) \) \(\Q(\sqrt{11}) \) \(0\) \(0\) \(-2\) \(-2\) \(q-2q^{5}-2q^{7}-q^{9}-q^{11}+q^{19}+\cdots\)
3344.1.p.b 3344.p 836.h $1$ $1.669$ \(\Q\) \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-209}) \) \(\Q(\sqrt{11}) \) \(0\) \(0\) \(-2\) \(2\) \(q-2q^{5}+2q^{7}-q^{9}+q^{11}-q^{19}+\cdots\)
3344.1.p.c 3344.p 836.h $2$ $1.669$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(-2\) \(q+q^{5}-q^{7}-q^{9}+\zeta_{6}^{2}q^{11}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{17}+\cdots\)
3344.1.p.d 3344.p 836.h $2$ $1.669$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(2\) \(q+q^{5}+q^{7}-q^{9}-\zeta_{6}^{2}q^{11}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{17}+\cdots\)
3344.1.p.e 3344.p 836.h $4$ $1.669$ \(\Q(\zeta_{20})^+\) \(\Q(\sqrt{-209}) \) None \(0\) \(0\) \(2\) \(-2\) \(q+\beta _{3}q^{3}+(1+\beta _{2})q^{5}+\beta _{2}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)
3344.1.p.f 3344.p 836.h $4$ $1.669$ \(\Q(\zeta_{20})^+\) \(\Q(\sqrt{-209}) \) None \(0\) \(0\) \(2\) \(2\) \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(1+\beta _{2})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3344.1.bb.a 3344.bb 209.h $4$ $1.669$ \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(-2\) \(0\) \(q-\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{5}-\zeta_{12}^{3}q^{11}+\cdots\)
3344.1.bc.a 3344.bc 836.m $2$ $1.669$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{11}) \) \(0\) \(0\) \(-1\) \(-2\) \(q+\zeta_{6}^{2}q^{5}-q^{7}+\zeta_{6}q^{9}+q^{11}-\zeta_{6}^{2}q^{19}+\cdots\)
3344.1.bc.b 3344.bc 836.m $2$ $1.669$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{11}) \) \(0\) \(0\) \(-1\) \(2\) \(q+\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}q^{9}-q^{11}+\zeta_{6}^{2}q^{19}+\cdots\)
3344.1.bq.a 3344.bq 836.s $4$ $1.669$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(-3\) \(q+(\zeta_{10}-\zeta_{10}^{2})q^{5}+(-1-\zeta_{10}^{4})q^{7}+\cdots\)
3344.1.bq.b 3344.bq 836.s $4$ $1.669$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(3\) \(q+(\zeta_{10}-\zeta_{10}^{2})q^{5}+(1+\zeta_{10}^{4})q^{7}+\cdots\)
3344.1.bq.c 3344.bq 836.s $8$ $1.669$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-3\) \(q+(\zeta_{30}^{11}+\zeta_{30}^{13})q^{5}+(\zeta_{30}^{2}+\zeta_{30}^{10}+\cdots)q^{7}+\cdots\)
3344.1.bq.d 3344.bq 836.s $8$ $1.669$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(3\) \(q+(\zeta_{30}-\zeta_{30}^{8})q^{5}+(\zeta_{30}^{5}+\zeta_{30}^{7}+\cdots)q^{7}+\cdots\)
3344.1.bx.a 3344.bx 209.m $4$ $1.669$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-3\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{5}+(-1+\zeta_{10}^{3}+\cdots)q^{7}+\cdots\)
3344.1.bx.b 3344.bx 209.m $8$ $1.669$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(3\) \(q+(-\zeta_{30}+\zeta_{30}^{2})q^{5}+(-\zeta_{30}^{10}-\zeta_{30}^{14}+\cdots)q^{7}+\cdots\)
3344.1.ck.a 3344.ck 3344.bk $8$ $1.669$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}+\zeta_{24}^{9}+\cdots)q^{7}+\cdots\)
3344.2.a.a 3344.a 1.a $1$ $26.702$ \(\Q\) None None \(0\) \(-3\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{5}-q^{7}+6q^{9}-q^{11}+\cdots\)
3344.2.a.b 3344.a 1.a $1$ $26.702$ \(\Q\) None None \(0\) \(-2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+q^{9}-q^{11}+4q^{13}+\cdots\)
3344.2.a.c 3344.a 1.a $1$ $26.702$ \(\Q\) None None \(0\) \(-1\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-2q^{7}-2q^{9}+q^{11}+\cdots\)
3344.2.a.d 3344.a 1.a $1$ $26.702$ \(\Q\) None None \(0\) \(-1\) \(-3\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+4q^{7}-2q^{9}-q^{11}+\cdots\)
3344.2.a.e 3344.a 1.a $1$ $26.702$ \(\Q\) None None \(0\) \(-1\) \(2\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+3q^{7}-2q^{9}+q^{11}+\cdots\)
3344.2.a.f 3344.a 1.a $1$ $26.702$ \(\Q\) None None \(0\) \(0\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{7}-3q^{9}+q^{11}+2q^{13}+\cdots\)
3344.2.a.g 3344.a 1.a $1$ $26.702$ \(\Q\) None None \(0\) \(0\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-3q^{9}-q^{11}-2q^{13}+\cdots\)
3344.2.a.h 3344.a 1.a $1$ $26.702$ \(\Q\) None None \(0\) \(1\) \(-2\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+3q^{7}-2q^{9}+q^{11}+\cdots\)
3344.2.a.i 3344.a 1.a $1$ $26.702$ \(\Q\) None None \(0\) \(1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{9}+q^{11}-2q^{13}+\cdots\)
3344.2.a.j 3344.a 1.a $2$ $26.702$ \(\Q(\sqrt{13}) \) None None \(0\) \(-1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-\beta q^{5}+(-1+\beta )q^{7}+\beta q^{9}+\cdots\)
3344.2.a.k 3344.a 1.a $2$ $26.702$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(4\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+2q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
3344.2.a.l 3344.a 1.a $2$ $26.702$ \(\Q(\sqrt{21}) \) None None \(0\) \(1\) \(3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2-\beta )q^{5}+(3-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
3344.2.a.m 3344.a 1.a $2$ $26.702$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}-\beta q^{7}+2\beta q^{9}-q^{11}+\cdots\)
3344.2.a.n 3344.a 1.a $2$ $26.702$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+(2+\beta )q^{7}+2\beta q^{9}+\cdots\)
3344.2.a.o 3344.a 1.a $2$ $26.702$ \(\Q(\sqrt{13}) \) None None \(0\) \(3\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+\beta q^{7}+(1+\cdots)q^{9}+\cdots\)
3344.2.a.p 3344.a 1.a $3$ $26.702$ 3.3.469.1 None None \(0\) \(-1\) \(5\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(2-\beta _{1})q^{5}+\beta _{2}q^{7}+(1+\beta _{2})q^{9}+\cdots\)
3344.2.a.q 3344.a 1.a $3$ $26.702$ 3.3.621.1 None None \(0\) \(0\) \(-3\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
3344.2.a.r 3344.a 1.a $3$ $26.702$ 3.3.229.1 None None \(0\) \(0\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{1}q^{5}+(-1-\beta _{1})q^{7}+\beta _{2}q^{9}+\cdots\)
3344.2.a.s 3344.a 1.a $4$ $26.702$ 4.4.13676.1 None None \(0\) \(1\) \(-3\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
3344.2.a.t 3344.a 1.a $5$ $26.702$ 5.5.246832.1 None None \(0\) \(-1\) \(-5\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
3344.2.a.u 3344.a 1.a $5$ $26.702$ 5.5.3979184.1 None None \(0\) \(-1\) \(7\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{3}+(1+\beta _{1})q^{5}+(-2+\beta _{1})q^{7}+\cdots\)
3344.2.a.v 3344.a 1.a $6$ $26.702$ 6.6.576096652.1 None None \(0\) \(-4\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+\beta _{4}q^{5}-\beta _{3}q^{7}+(1+\cdots)q^{9}+\cdots\)
3344.2.a.w 3344.a 1.a $6$ $26.702$ 6.6.744786576.1 None None \(0\) \(-1\) \(5\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{5})q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
3344.2.a.x 3344.a 1.a $6$ $26.702$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{4}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3344.2.a.y 3344.a 1.a $6$ $26.702$ 6.6.57500224.1 None None \(0\) \(4\) \(-4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1-\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
3344.2.a.z 3344.a 1.a $6$ $26.702$ 6.6.106392688.1 None None \(0\) \(4\) \(-3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1+\beta _{5})q^{5}+\beta _{5}q^{7}+\cdots\)
3344.2.a.ba 3344.a 1.a $7$ $26.702$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(-2\) \(2\) \(-10\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-\beta _{4}q^{5}+(-2-\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)
3344.2.a.bb 3344.a 1.a $9$ $26.702$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(-1\) \(6\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{7})q^{5}-\beta _{8}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3344.2.o.a 3344.o 76.d $36$ $26.702$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
3344.2.o.b 3344.o 76.d $64$ $26.702$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
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