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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
256.1.c.a 256.c 4.b $1$ $0.128$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{9}-2q^{17}-q^{25}-2q^{41}+q^{49}+\cdots\)
256.2.a.a 256.a 1.a $1$ $2.044$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{3}+q^{9}-6q^{11}-6q^{17}-2q^{19}+\cdots\)
256.2.a.b 256.a 1.a $1$ $2.044$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-4q^{5}-3q^{9}-4q^{13}-2q^{17}+11q^{25}+\cdots\)
256.2.a.c 256.a 1.a $1$ $2.044$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+4q^{5}-3q^{9}+4q^{13}-2q^{17}+11q^{25}+\cdots\)
256.2.a.d 256.a 1.a $1$ $2.044$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+2q^{3}+q^{9}+6q^{11}-6q^{17}+2q^{19}+\cdots\)
256.2.a.e 256.a 1.a $2$ $2.044$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+\beta q^{3}+5q^{9}-\beta q^{11}+6q^{17}-3\beta q^{19}+\cdots\)
256.2.b.a 256.b 8.b $2$ $2.044$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{5}-4q^{7}-q^{9}+iq^{11}+\cdots\)
256.2.b.b 256.b 8.b $2$ $2.044$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}+3q^{9}+3iq^{13}+2q^{17}+q^{25}+\cdots\)
256.2.b.c 256.b 8.b $2$ $2.044$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{5}+4q^{7}-q^{9}+iq^{11}+\cdots\)
256.2.e.a 256.e 16.e $8$ $2.044$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{24}^{2}q^{3}-\zeta_{24}^{7}q^{5}+(\zeta_{24}^{2}-\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
256.2.e.b 256.e 16.e $8$ $2.044$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{24}^{2}q^{3}+\zeta_{24}^{7}q^{5}+(-\zeta_{24}^{2}+\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
256.2.g.a 256.g 32.g $4$ $2.044$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(1+\zeta_{8}+2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{5}+\cdots\)
256.2.g.b 256.g 32.g $4$ $2.044$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(1+\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
256.2.g.c 256.g 32.g $8$ $2.044$ 8.0.18939904.2 None None \(0\) \(-4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1+\beta _{1}+\beta _{6}-\beta _{7})q^{3}+(\beta _{4}-\beta _{7})q^{5}+\cdots\)
256.2.g.d 256.g 32.g $8$ $2.044$ 8.0.18939904.2 None None \(0\) \(4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{8}]$ \(q+(\beta _{2}+\beta _{6}-\beta _{7})q^{3}+(\beta _{6}+\beta _{7})q^{5}+\cdots\)
256.2.i.a 256.i 64.i $56$ $2.044$ None None \(0\) \(8\) \(-8\) \(8\) $\mathrm{SU}(2)[C_{16}]$
256.2.m.a 256.m 256.m $992$ $2.044$ None None \(-32\) \(-32\) \(-32\) \(-32\) $\mathrm{SU}(2)[C_{64}]$
256.3.c.a 256.c 4.b $1$ $6.975$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-8q^{5}+9q^{9}+24q^{13}+30q^{17}+\cdots\)
256.3.c.b 256.c 4.b $1$ $6.975$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(8\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+8q^{5}+9q^{9}-24q^{13}+30q^{17}+\cdots\)
256.3.c.c 256.c 4.b $2$ $6.975$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-4q^{5}+4\beta q^{7}+q^{9}-5\beta q^{11}+\cdots\)
256.3.c.d 256.c 4.b $2$ $6.975$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}-23q^{9}+3\beta q^{11}-2q^{17}+\cdots\)
256.3.c.e 256.c 4.b $2$ $6.975$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{3}+5q^{9}+7iq^{11}+2q^{17}+17iq^{19}+\cdots\)
256.3.c.f 256.c 4.b $2$ $6.975$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+4q^{5}-4\beta q^{7}+q^{9}-5\beta q^{11}+\cdots\)
256.3.c.g 256.c 4.b $4$ $6.975$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-3q^{9}+\cdots\)
256.3.d.a 256.d 8.d $2$ $6.975$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-4q^{3}+iq^{5}-4iq^{7}+7q^{9}-4q^{11}+\cdots\)
256.3.d.b 256.d 8.d $2$ $6.975$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3iq^{5}-9q^{9}+5iq^{13}-30q^{17}+\cdots\)
256.3.d.c 256.d 8.d $2$ $6.975$ \(\Q(\sqrt{-1}) \) None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4q^{3}+iq^{5}+4iq^{7}+7q^{9}+4q^{11}+\cdots\)
256.3.d.d 256.d 8.d $4$ $6.975$ \(\Q(\zeta_{8})\) None None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2-\zeta_{8}^{2})q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
256.3.d.e 256.d 8.d $4$ $6.975$ \(\Q(\zeta_{8})\) None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-\zeta_{8}^{2})q^{3}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+(2\zeta_{8}+\cdots)q^{7}+\cdots\)
256.3.f.a 256.f 16.f $8$ $6.975$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{24}^{2}q^{3}+(-2-2\zeta_{24}+\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
256.3.f.b 256.f 16.f $8$ $6.975$ 8.0.8540717056.1 None None \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}+(-2-2\beta _{1}-\beta _{6})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
256.3.f.c 256.f 16.f $8$ $6.975$ 8.0.8540717056.1 None None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}+(2+2\beta _{1}+\beta _{6})q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
256.3.f.d 256.f 16.f $8$ $6.975$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{24}^{2}q^{3}+(2+2\zeta_{24}-\zeta_{24}^{4})q^{5}+\cdots\)
256.3.h.a 256.h 32.h $28$ $6.975$ None None \(0\) \(-4\) \(4\) \(4\) $\mathrm{SU}(2)[C_{8}]$
256.3.h.b 256.h 32.h $28$ $6.975$ None None \(0\) \(4\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
256.3.j.a 256.j 64.j $120$ $6.975$ None None \(0\) \(8\) \(-8\) \(8\) $\mathrm{SU}(2)[C_{16}]$
256.3.n.a 256.n 256.n $2016$ $6.975$ None None \(-32\) \(-32\) \(-32\) \(-32\) $\mathrm{SU}(2)[C_{64}]$
256.4.a.a 256.a 1.a $1$ $15.104$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(0\) \(-10\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-10q^{3}+73q^{9}+18q^{11}+90q^{17}+\cdots\)
256.4.a.b 256.a 1.a $1$ $15.104$ \(\Q\) None None \(0\) \(-8\) \(-12\) \(32\) $-$ $\mathrm{SU}(2)$ \(q-8q^{3}-12q^{5}+2^{5}q^{7}+37q^{9}+8q^{11}+\cdots\)
256.4.a.c 256.a 1.a $1$ $15.104$ \(\Q\) None None \(0\) \(-8\) \(12\) \(-32\) $+$ $\mathrm{SU}(2)$ \(q-8q^{3}+12q^{5}-2^{5}q^{7}+37q^{9}+8q^{11}+\cdots\)
256.4.a.d 256.a 1.a $1$ $15.104$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-4q^{5}-3^{3}q^{9}+92q^{13}+94q^{17}+\cdots\)
256.4.a.e 256.a 1.a $1$ $15.104$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+4q^{5}-3^{3}q^{9}-92q^{13}+94q^{17}+\cdots\)
256.4.a.f 256.a 1.a $1$ $15.104$ \(\Q\) None None \(0\) \(8\) \(-12\) \(-32\) $-$ $\mathrm{SU}(2)$ \(q+8q^{3}-12q^{5}-2^{5}q^{7}+37q^{9}-8q^{11}+\cdots\)
256.4.a.g 256.a 1.a $1$ $15.104$ \(\Q\) None None \(0\) \(8\) \(12\) \(32\) $+$ $\mathrm{SU}(2)$ \(q+8q^{3}+12q^{5}+2^{5}q^{7}+37q^{9}-8q^{11}+\cdots\)
256.4.a.h 256.a 1.a $1$ $15.104$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(0\) \(10\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q+10q^{3}+73q^{9}-18q^{11}+90q^{17}+\cdots\)
256.4.a.i 256.a 1.a $2$ $15.104$ \(\Q(\sqrt{3}) \) None None \(0\) \(-4\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-\beta q^{5}-2\beta q^{7}-23q^{9}+42q^{11}+\cdots\)
256.4.a.j 256.a 1.a $2$ $15.104$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(-16\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2\beta q^{5}-8q^{7}+q^{9}+3\beta q^{11}+\cdots\)
256.4.a.k 256.a 1.a $2$ $15.104$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+\beta q^{3}-19q^{9}-5^{2}\beta q^{11}-90q^{17}+\cdots\)
256.4.a.l 256.a 1.a $2$ $15.104$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(16\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2\beta q^{5}+8q^{7}+q^{9}+3\beta q^{11}+\cdots\)
256.4.a.m 256.a 1.a $2$ $15.104$ \(\Q(\sqrt{3}) \) None None \(0\) \(4\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-\beta q^{5}+2\beta q^{7}-23q^{9}-42q^{11}+\cdots\)
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