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Results (40 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
799.1.c.a 799.c 799.c $1$ $0.399$ \(\Q\) \(\Q(\sqrt{-47}) \), \(\Q(\sqrt{-799}) \) \(\Q(\sqrt{17}) \) \(-2\) \(0\) \(0\) \(0\) \(q-2q^{2}+3q^{4}-4q^{8}+q^{9}+5q^{16}+\cdots\)
799.1.c.b 799.c 799.c $2$ $0.399$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-799}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-\beta q^{5}+q^{9}+\beta q^{11}+q^{16}+\cdots\)
799.1.c.c 799.c 799.c $4$ $0.399$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-799}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+q^{4}-\beta _{1}q^{5}+q^{9}+(\beta _{1}+\beta _{3})q^{10}+\cdots\)
799.1.c.d 799.c 799.c $4$ $0.399$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-47}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{3}+\cdots\)
799.1.e.a 799.e 799.e $2$ $0.399$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-47}) \) None \(0\) \(2\) \(0\) \(-2\) \(q-iq^{2}+(1-i)q^{3}-3q^{4}+(-2-2i+\cdots)q^{6}+\cdots\)
799.1.e.b 799.e 799.e $8$ $0.399$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-47}) \) None \(0\) \(-2\) \(0\) \(2\) \(q+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{2}+(-\zeta_{20}+\zeta_{20}^{4}+\cdots)q^{3}+\cdots\)
799.1.h.a 799.h 799.h $4$ $0.399$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-47}) \) None \(0\) \(4\) \(0\) \(0\) \(q+(1-\zeta_{8})q^{3}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
799.1.h.b 799.h 799.h $16$ $0.399$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-47}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+(\zeta_{40}^{11}-\zeta_{40}^{19})q^{2}+(-\zeta_{40}^{7}+\zeta_{40}^{8}+\cdots)q^{3}+\cdots\)
799.2.a.a 799.a 1.a $1$ $6.380$ \(\Q\) None None \(-1\) \(2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-q^{4}-2q^{6}-2q^{7}+3q^{8}+\cdots\)
799.2.a.b 799.a 1.a $1$ $6.380$ \(\Q\) None None \(-1\) \(2\) \(4\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-q^{4}+4q^{5}-2q^{6}-2q^{7}+\cdots\)
799.2.a.c 799.a 1.a $2$ $6.380$ \(\Q(\sqrt{5}) \) None None \(-3\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
799.2.a.d 799.a 1.a $8$ $6.380$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(1\) \(-7\) \(-10\) \(-9\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{6}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}-\beta _{7})q^{4}+\cdots\)
799.2.a.e 799.a 1.a $12$ $6.380$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-4\) \(-1\) \(-11\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
799.2.a.f 799.a 1.a $17$ $6.380$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(3\) \(1\) \(11\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{7}+\cdots)q^{5}+\cdots\)
799.2.a.g 799.a 1.a $20$ $6.380$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(4\) \(3\) \(13\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{17}+\cdots)q^{5}+\cdots\)
799.2.b.a 799.b 17.b $2$ $6.380$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}-q^{4}-iq^{5}+iq^{6}-iq^{7}+\cdots\)
799.2.b.b 799.b 17.b $28$ $6.380$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
799.2.b.c 799.b 17.b $40$ $6.380$ None None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
799.2.f.a 799.f 17.c $60$ $6.380$ None None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
799.2.f.b 799.f 17.c $80$ $6.380$ None None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
799.2.g.a 799.g 17.d $4$ $6.380$ \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
799.2.g.b 799.g 17.d $4$ $6.380$ \(\Q(\zeta_{8})\) None None \(4\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
799.2.g.c 799.g 17.d $112$ $6.380$ None None \(4\) \(4\) \(4\) \(8\) $\mathrm{SU}(2)[C_{8}]$
799.2.g.d 799.g 17.d $152$ $6.380$ None None \(-4\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{8}]$
799.2.j.a 799.j 799.j $80$ $6.380$ \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{16}]$
799.2.j.b 799.j 799.j $480$ $6.380$ None None \(-16\) \(-16\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{16}]$
799.2.k.a 799.k 47.c $704$ $6.380$ None None \(0\) \(-2\) \(-6\) \(21\) $\mathrm{SU}(2)[C_{23}]$
799.2.k.b 799.k 47.c $704$ $6.380$ None None \(0\) \(-2\) \(-2\) \(-21\) $\mathrm{SU}(2)[C_{23}]$
799.2.n.a 799.n 799.n $1540$ $6.380$ None None \(-42\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{46}]$
799.2.o.a 799.o 799.o $3080$ $6.380$ None None \(0\) \(-42\) \(-38\) \(-46\) $\mathrm{SU}(2)[C_{92}]$
799.2.r.a 799.r 799.r $6160$ $6.380$ None None \(-84\) \(-84\) \(-92\) \(-84\) $\mathrm{SU}(2)[C_{184}]$
799.2.s.a 799.s 799.s $12320$ $6.380$ None None \(-168\) \(-168\) \(-184\) \(-168\) $\mathrm{SU}(2)[C_{368}]$
799.4.a.a 799.a 1.a $41$ $47.143$ None None \(-9\) \(-12\) \(-48\) \(-18\) $-$ $\mathrm{SU}(2)$
799.4.a.b 799.a 1.a $43$ $47.143$ None None \(-5\) \(-12\) \(-92\) \(-32\) $-$ $\mathrm{SU}(2)$
799.4.a.c 799.a 1.a $49$ $47.143$ None None \(7\) \(0\) \(72\) \(-46\) $+$ $\mathrm{SU}(2)$
799.4.a.d 799.a 1.a $51$ $47.143$ None None \(11\) \(24\) \(68\) \(108\) $+$ $\mathrm{SU}(2)$
799.6.a.a 799.a 1.a $72$ $128.147$ None None \(-19\) \(-81\) \(-459\) \(-793\) $+$ $\mathrm{SU}(2)$
799.6.a.b 799.a 1.a $74$ $128.147$ None None \(-11\) \(-9\) \(-241\) \(285\) $+$ $\mathrm{SU}(2)$
799.6.a.c 799.a 1.a $80$ $128.147$ None None \(13\) \(27\) \(341\) \(187\) $-$ $\mathrm{SU}(2)$
799.6.a.d 799.a 1.a $82$ $128.147$ None None \(21\) \(27\) \(359\) \(89\) $-$ $\mathrm{SU}(2)$
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