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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.1.j.a 100.j 100.j $4$ $0.050$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None 100.1.j.a \(-1\) \(0\) \(-1\) \(0\) \(q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots\)
100.2.a.a 100.a 1.a $1$ $0.799$ \(\Q\) None None 20.2.a.a \(0\) \(2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots\)
100.2.c.a 100.c 5.b $2$ $0.799$ \(\Q(\sqrt{-1}) \) None None 20.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+\beta q^{7}-q^{9}-\beta q^{13}-3\beta q^{17}+\cdots\)
100.2.e.a 100.e 20.e $2$ $0.799$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None 100.2.e.a \(-2\) \(-2\) \(0\) \(6\) $\mathrm{U}(1)[D_{4}]$ \(q+(i-1)q^{2}+(-i-1)q^{3}-2 i q^{4}+\cdots\)
100.2.e.b 100.e 20.e $2$ $0.799$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 20.2.e.a \(2\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(i+1)q^{2}+2 i q^{4}+(2 i-2)q^{8}+\cdots\)
100.2.e.c 100.e 20.e $2$ $0.799$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None 100.2.e.a \(2\) \(2\) \(0\) \(-6\) $\mathrm{U}(1)[D_{4}]$ \(q+(-i+1)q^{2}+(i+1)q^{3}-2 i q^{4}+\cdots\)
100.2.e.d 100.e 20.e $8$ $0.799$ 8.0.3317760000.5 None None 100.2.e.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(-\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+\cdots\)
100.2.g.a 100.g 25.d $12$ $0.799$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None 100.2.g.a \(0\) \(2\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{4}q^{3}+(-1-\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)
100.2.i.a 100.i 25.e $8$ $0.799$ 8.0.58140625.2 None None 100.2.i.a \(0\) \(0\) \(5\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}+\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
100.2.l.a 100.l 100.l $8$ $0.799$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None 100.2.l.a \(2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{20}]$ \(q+(1-\zeta_{20}^{2}+\zeta_{20}^{3}+\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
100.2.l.b 100.l 100.l $96$ $0.799$ None None 100.2.l.b \(-10\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{20}]$
100.3.b.a 100.b 4.b $1$ $2.725$ \(\Q\) \(\Q(\sqrt{-1}) \) None 20.3.d.c \(-2\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{4}-8q^{8}+9q^{9}+24q^{13}+\cdots\)
100.3.b.b 100.b 4.b $1$ $2.725$ \(\Q\) \(\Q(\sqrt{-1}) \) None 20.3.d.c \(2\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+4q^{4}+8q^{8}+9q^{9}-24q^{13}+\cdots\)
100.3.b.c 100.b 4.b $2$ $2.725$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None 20.3.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}+2\beta q^{3}-4 q^{4}-8 q^{6}+2\beta q^{7}+\cdots\)
100.3.b.d 100.b 4.b $4$ $2.725$ 4.0.8405.1 None None 100.3.b.d \(-1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
100.3.b.e 100.b 4.b $4$ $2.725$ 4.0.8405.1 None None 100.3.b.d \(1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
100.3.b.f 100.b 4.b $4$ $2.725$ \(\Q(\zeta_{10})\) None None 20.3.b.a \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{2}+\beta_{2} q^{3}+(\beta_{3}+\beta_{2}+\beta_1-1)q^{4}+\cdots\)
100.3.d.a 100.d 20.d $8$ $2.725$ 8.0.\(\cdots\).3 None None 100.3.b.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
100.3.d.b 100.d 20.d $8$ $2.725$ \(\Q(\zeta_{20})\) None None 20.3.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{2}+\beta_{6} q^{3}+(\beta_{4}+1)q^{4}+\cdots\)
100.3.f.a 100.f 5.c $2$ $2.725$ \(\Q(\sqrt{-1}) \) None None 20.3.f.a \(0\) \(-2\) \(0\) \(14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(i-1)q^{3}+(7 i+7)q^{7}+7 i q^{9}+\cdots\)
100.3.f.b 100.f 5.c $4$ $2.725$ \(\Q(i, \sqrt{6})\) None None 100.3.f.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+3\beta _{1}q^{3}-4\beta _{3}q^{7}+18\beta _{2}q^{9}-15q^{11}+\cdots\)
100.3.h.a 100.h 100.h $8$ $2.725$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None 100.3.h.a \(0\) \(0\) \(-6\) \(0\) $\mathrm{U}(1)[D_{10}]$ \(q+\beta_1 q^{2}+4\beta_{2} q^{4}+(3\beta_{6}-3\beta_{4}+2\beta_{3}+\cdots-3)q^{5}+\cdots\)
100.3.h.b 100.h 100.h $104$ $2.725$ None None 100.3.h.b \(-5\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
100.3.j.a 100.j 100.j $112$ $2.725$ None None 100.3.j.a \(-3\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{10}]$
100.3.k.a 100.k 25.f $40$ $2.725$ None None 100.3.k.a \(0\) \(-2\) \(6\) \(14\) $\mathrm{SU}(2)[C_{20}]$
100.4.a.a 100.a 1.a $1$ $5.900$ \(\Q\) None None 20.4.a.a \(0\) \(-4\) \(0\) \(16\) $-$ $\mathrm{SU}(2)$ \(q-4q^{3}+2^{4}q^{7}-11q^{9}-60q^{11}+\cdots\)
100.4.a.b 100.a 1.a $1$ $5.900$ \(\Q\) None None 100.4.a.b \(0\) \(-1\) \(0\) \(-26\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-26q^{7}-26q^{9}+45q^{11}-44q^{13}+\cdots\)
100.4.a.c 100.a 1.a $1$ $5.900$ \(\Q\) None None 100.4.a.b \(0\) \(1\) \(0\) \(26\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+26q^{7}-26q^{9}+45q^{11}+44q^{13}+\cdots\)
100.4.a.d 100.a 1.a $2$ $5.900$ \(\Q(\sqrt{19}) \) None None 20.4.c.a \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{7}+7^{2}q^{9}+20q^{11}-6\beta q^{13}+\cdots\)
100.4.c.a 100.c 5.b $2$ $5.900$ \(\Q(\sqrt{-1}) \) None None 20.4.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{3}+8\beta q^{7}+11 q^{9}-60 q^{11}+\cdots\)
100.4.c.b 100.c 5.b $2$ $5.900$ \(\Q(\sqrt{-1}) \) None None 100.4.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{3}-26 i q^{7}+26 q^{9}+45 q^{11}+\cdots\)
100.4.e.a 100.e 20.e $2$ $5.900$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 20.4.e.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-2 i-2)q^{2}+8 i q^{4}+(-16 i+16)q^{8}+\cdots\)
100.4.e.b 100.e 20.e $2$ $5.900$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None 100.4.e.b \(-4\) \(14\) \(0\) \(-18\) $\mathrm{U}(1)[D_{4}]$ \(q+(2 i-2)q^{2}+(7 i+7)q^{3}-8 i q^{4}+\cdots\)
100.4.e.c 100.e 20.e $2$ $5.900$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None 100.4.e.b \(4\) \(-14\) \(0\) \(18\) $\mathrm{U}(1)[D_{4}]$ \(q+(-2 i+2)q^{2}+(-7 i-7)q^{3}+\cdots\)
100.4.e.d 100.e 20.e $8$ $5.900$ 8.0.2342560000.1 None None 100.4.e.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{5}q^{2}+(-\beta _{3}-\beta _{6})q^{3}+(-\beta _{1}-3\beta _{4}+\cdots)q^{4}+\cdots\)
100.4.e.e 100.e 20.e $12$ $5.900$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None 20.4.e.b \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{3}+\beta _{5})q^{2}+\beta _{9}q^{3}+(-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
100.4.e.f 100.e 20.e $24$ $5.900$ None None 100.4.e.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
100.4.g.a 100.g 25.d $28$ $5.900$ None None 100.4.g.a \(0\) \(-4\) \(-25\) \(16\) $\mathrm{SU}(2)[C_{5}]$
100.4.i.a 100.i 25.e $32$ $5.900$ None None 100.4.i.a \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{10}]$
100.4.l.a 100.l 100.l $8$ $5.900$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None 100.4.l.a \(-4\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{20}]$ \(q+(-2+2\zeta_{20}^{2}-2\zeta_{20}^{3}-2\zeta_{20}^{4}+\cdots)q^{2}+\cdots\)
100.4.l.b 100.l 100.l $336$ $5.900$ None None 100.4.l.b \(-4\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{20}]$
100.5.b.a 100.b 4.b $1$ $10.337$ \(\Q\) \(\Q(\sqrt{-1}) \) None 4.5.b.a \(4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{2}+2^{4}q^{4}+2^{6}q^{8}+3^{4}q^{9}+238q^{13}+\cdots\)
100.5.b.b 100.b 4.b $2$ $10.337$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None 20.5.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2\beta q^{2}+\beta q^{3}-16 q^{4}-8 q^{6}+\cdots\)
100.5.b.c 100.b 4.b $8$ $10.337$ 8.0.\(\cdots\).1 None None 20.5.b.a \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{2}+\beta _{3}q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
100.5.b.d 100.b 4.b $8$ $10.337$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None 100.5.b.d \(-3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-6+\cdots)q^{6}+\cdots\)
100.5.b.e 100.b 4.b $8$ $10.337$ 8.0.\(\cdots\).1 None None 20.5.d.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(6+\beta _{6})q^{4}+(-\beta _{4}+\cdots)q^{6}+\cdots\)
100.5.b.f 100.b 4.b $8$ $10.337$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None 100.5.b.d \(3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-6+\cdots)q^{6}+\cdots\)
100.5.d.a 100.d 20.d $2$ $10.337$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 4.5.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2\beta q^{2}-16 q^{4}-32\beta q^{8}-81 q^{9}+\cdots\)
100.5.d.b 100.d 20.d $16$ $10.337$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 100.5.b.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-6+\cdots)q^{6}+\cdots\)
100.5.d.c 100.d 20.d $16$ $10.337$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 20.5.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{8}q^{3}+(2-\beta _{4})q^{4}+(6+\beta _{5}+\cdots)q^{6}+\cdots\)
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