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Label Degree Type Faithful Field of Traces $\Q$-character Group Image Image Order Kernel Kernel Order Center
256.26844.1a $1$ R \(\Q\) 256.26844.1a $D_{16}:D_4$ $C_1$ $1$ 1.a1.a1 $256$ 1.a1.a1
256.26844.1b $1$ R \(\Q\) 256.26844.1b $D_{16}:D_4$ $C_2$ $2$ 2.k1.a1 $128$ 1.a1.a1
256.26844.1c $1$ R \(\Q\) 256.26844.1c $D_{16}:D_4$ $C_2$ $2$ 2.j1.a1 $128$ 1.a1.a1
256.26844.1d $1$ R \(\Q\) 256.26844.1d $D_{16}:D_4$ $C_2$ $2$ 2.i1.a1 $128$ 1.a1.a1
256.26844.1e $1$ R \(\Q\) 256.26844.1e $D_{16}:D_4$ $C_2$ $2$ 2.h1.a1 $128$ 1.a1.a1
256.26844.1f $1$ R \(\Q\) 256.26844.1f $D_{16}:D_4$ $C_2$ $2$ 2.d1.b1 $128$ 1.a1.a1
256.26844.1g $1$ R \(\Q\) 256.26844.1g $D_{16}:D_4$ $C_2$ $2$ 2.c1.b1 $128$ 1.a1.a1
256.26844.1h $1$ R \(\Q\) 256.26844.1h $D_{16}:D_4$ $C_2$ $2$ 2.b1.b1 $128$ 1.a1.a1
256.26844.1i $1$ R \(\Q\) 256.26844.1i $D_{16}:D_4$ $C_2$ $2$ 2.a1.b1 $128$ 1.a1.a1
256.26844.1j $1$ R \(\Q\) 256.26844.1j $D_{16}:D_4$ $C_2$ $2$ 2.d1.a1 $128$ 1.a1.a1
256.26844.1k $1$ R \(\Q\) 256.26844.1k $D_{16}:D_4$ $C_2$ $2$ 2.c1.a1 $128$ 1.a1.a1
256.26844.1l $1$ R \(\Q\) 256.26844.1l $D_{16}:D_4$ $C_2$ $2$ 2.b1.a1 $128$ 1.a1.a1
256.26844.1m $1$ R \(\Q\) 256.26844.1m $D_{16}:D_4$ $C_2$ $2$ 2.a1.a1 $128$ 1.a1.a1
256.26844.1n $1$ R \(\Q\) 256.26844.1n $D_{16}:D_4$ $C_2$ $2$ 2.g1.a1 $128$ 1.a1.a1
256.26844.1o $1$ R \(\Q\) 256.26844.1o $D_{16}:D_4$ $C_2$ $2$ 2.f1.a1 $128$ 1.a1.a1
256.26844.1p $1$ R \(\Q\) 256.26844.1p $D_{16}:D_4$ $C_2$ $2$ 2.e1.a1 $128$ 1.a1.a1
256.26844.2a $2$ R \(\Q\) 256.26844.2a $D_{16}:D_4$ $D_4$ $8$ 8.r1.a1 $32$ 4.h1.a1
256.26844.2b $2$ R \(\Q\) 256.26844.2b $D_{16}:D_4$ $D_4$ $8$ 8.q1.a1 $32$ 4.h1.a1
256.26844.2c $2$ R \(\Q\) 256.26844.2c $D_{16}:D_4$ $D_4$ $8$ 8.p1.a1 $32$ 4.h1.a1
256.26844.2d $2$ R \(\Q\) 256.26844.2d $D_{16}:D_4$ $D_4$ $8$ 8.o1.a1 $32$ 4.h1.a1
256.26844.2e $2$ R \(\Q\) 256.26844.2e $D_{16}:D_4$ $D_4$ $8$ 8.i1.a1 $32$ 4.g1.a1
256.26844.2f $2$ R \(\Q\) 256.26844.2f $D_{16}:D_4$ $D_4$ $8$ 8.a1.b1 $32$ 4.g1.a1
256.26844.2g $2$ R \(\Q\) 256.26844.2g $D_{16}:D_4$ $D_4$ $8$ 8.a1.a1 $32$ 4.g1.a1
256.26844.2h $2$ R \(\Q\) 256.26844.2h $D_{16}:D_4$ $D_4$ $8$ 8.c1.a1 $32$ 4.g1.a1
256.26844.2i1 $2$ R \(\Q(\sqrt{2}) \) 256.26844.2i $D_{16}:D_4$ $D_8$ $16$ 16.j1.a1 $16$ 8.c1.a1
256.26844.2i2 $2$ R \(\Q(\sqrt{2}) \) 256.26844.2i $D_{16}:D_4$ $D_8$ $16$ 16.j1.a1 $16$ 8.c1.a1
256.26844.2j1 $2$ R \(\Q(\sqrt{2}) \) 256.26844.2j $D_{16}:D_4$ $D_8$ $16$ 16.f1.b1 $16$ 8.c1.a1
256.26844.2j2 $2$ R \(\Q(\sqrt{2}) \) 256.26844.2j $D_{16}:D_4$ $D_8$ $16$ 16.f1.b1 $16$ 8.c1.a1
256.26844.2k1 $2$ R \(\Q(\sqrt{2}) \) 256.26844.2k $D_{16}:D_4$ $D_8$ $16$ 16.f1.a1 $16$ 8.c1.a1
256.26844.2k2 $2$ R \(\Q(\sqrt{2}) \) 256.26844.2k $D_{16}:D_4$ $D_8$ $16$ 16.f1.a1 $16$ 8.c1.a1
256.26844.2l1 $2$ R \(\Q(\sqrt{2}) \) 256.26844.2l $D_{16}:D_4$ $D_8$ $16$ 16.g1.a1 $16$ 8.c1.a1
256.26844.2l2 $2$ R \(\Q(\sqrt{2}) \) 256.26844.2l $D_{16}:D_4$ $D_8$ $16$ 16.g1.a1 $16$ 8.c1.a1
256.26844.4a $4$ R \(\Q\) 256.26844.4a $D_{16}:D_4$ $D_4:C_2^2$ $32$ 32.g1.a1 $8$ 16.d1.a1
256.26844.4b1 $4$ R \(\Q(\sqrt{2}) \) 256.26844.4b $D_{16}:D_4$ $D_8:C_2^2$ $64$ 64.a1.a1 $4$ 32.a1.a1
256.26844.4b2 $4$ R \(\Q(\sqrt{2}) \) 256.26844.4b $D_{16}:D_4$ $D_8:C_2^2$ $64$ 64.a1.a1 $4$ 32.a1.a1
256.26844.4c1 $4$ C 4.0.2048.2 256.26844.4c $D_{16}:D_4$ $D_{16}:D_4$ $256$ 256.a1.a1 $1$ 128.a1.a1
256.26844.4c2 $4$ C 4.0.2048.2 256.26844.4c $D_{16}:D_4$ $D_{16}:D_4$ $256$ 256.a1.a1 $1$ 128.a1.a1
256.26844.4c3 $4$ C 4.0.2048.2 256.26844.4c $D_{16}:D_4$ $D_{16}:D_4$ $256$ 256.a1.a1 $1$ 128.a1.a1
256.26844.4c4 $4$ C 4.0.2048.2 256.26844.4c $D_{16}:D_4$ $D_{16}:D_4$ $256$ 256.a1.a1 $1$ 128.a1.a1
256.26844.4d1 $4$ C 4.0.2048.2 256.26844.4d $D_{16}:D_4$ $D_{16}:D_4$ $256$ 256.a1.a1 $1$ 128.a1.a1
256.26844.4d2 $4$ C 4.0.2048.2 256.26844.4d $D_{16}:D_4$ $D_{16}:D_4$ $256$ 256.a1.a1 $1$ 128.a1.a1
256.26844.4d3 $4$ C 4.0.2048.2 256.26844.4d $D_{16}:D_4$ $D_{16}:D_4$ $256$ 256.a1.a1 $1$ 128.a1.a1
256.26844.4d4 $4$ C 4.0.2048.2 256.26844.4d $D_{16}:D_4$ $D_{16}:D_4$ $256$ 256.a1.a1 $1$ 128.a1.a1
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