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Label Degree Type Faithful Field of Traces $\Q$-character Group Image Image Order Kernel Kernel Order Center
840.118.1a $1$ R \(\Q\) 840.118.1a $C_5\times D_{84}$ $C_1$ $1$ 1.a1.a1 $840$ 1.a1.a1
840.118.1b $1$ R \(\Q\) 840.118.1b $C_5\times D_{84}$ $C_2$ $2$ 2.b1.a1 $420$ 1.a1.a1
840.118.1c $1$ R \(\Q\) 840.118.1c $C_5\times D_{84}$ $C_2$ $2$ 2.a1.b1 $420$ 1.a1.a1
840.118.1d $1$ R \(\Q\) 840.118.1d $C_5\times D_{84}$ $C_2$ $2$ 2.a1.a1 $420$ 1.a1.a1
840.118.1e1 $1$ C \(\Q(\zeta_{5})\) 840.118.1e $C_5\times D_{84}$ $C_5$ $5$ 5.a1.a1 $168$ 1.a1.a1
840.118.1e2 $1$ C \(\Q(\zeta_{5})\) 840.118.1e $C_5\times D_{84}$ $C_5$ $5$ 5.a1.a1 $168$ 1.a1.a1
840.118.1e3 $1$ C \(\Q(\zeta_{5})\) 840.118.1e $C_5\times D_{84}$ $C_5$ $5$ 5.a1.a1 $168$ 1.a1.a1
840.118.1e4 $1$ C \(\Q(\zeta_{5})\) 840.118.1e $C_5\times D_{84}$ $C_5$ $5$ 5.a1.a1 $168$ 1.a1.a1
840.118.1f1 $1$ C \(\Q(\zeta_{5})\) 840.118.1f $C_5\times D_{84}$ $C_{10}$ $10$ 10.b1.a1 $84$ 1.a1.a1
840.118.1f2 $1$ C \(\Q(\zeta_{5})\) 840.118.1f $C_5\times D_{84}$ $C_{10}$ $10$ 10.b1.a1 $84$ 1.a1.a1
840.118.1f3 $1$ C \(\Q(\zeta_{5})\) 840.118.1f $C_5\times D_{84}$ $C_{10}$ $10$ 10.b1.a1 $84$ 1.a1.a1
840.118.1f4 $1$ C \(\Q(\zeta_{5})\) 840.118.1f $C_5\times D_{84}$ $C_{10}$ $10$ 10.b1.a1 $84$ 1.a1.a1
840.118.1g1 $1$ C \(\Q(\zeta_{5})\) 840.118.1g $C_5\times D_{84}$ $C_{10}$ $10$ 10.a1.b1 $84$ 1.a1.a1
840.118.1g2 $1$ C \(\Q(\zeta_{5})\) 840.118.1g $C_5\times D_{84}$ $C_{10}$ $10$ 10.a1.b1 $84$ 1.a1.a1
840.118.1g3 $1$ C \(\Q(\zeta_{5})\) 840.118.1g $C_5\times D_{84}$ $C_{10}$ $10$ 10.a1.b1 $84$ 1.a1.a1
840.118.1g4 $1$ C \(\Q(\zeta_{5})\) 840.118.1g $C_5\times D_{84}$ $C_{10}$ $10$ 10.a1.b1 $84$ 1.a1.a1
840.118.1h1 $1$ C \(\Q(\zeta_{5})\) 840.118.1h $C_5\times D_{84}$ $C_{10}$ $10$ 10.a1.a1 $84$ 1.a1.a1
840.118.1h2 $1$ C \(\Q(\zeta_{5})\) 840.118.1h $C_5\times D_{84}$ $C_{10}$ $10$ 10.a1.a1 $84$ 1.a1.a1
840.118.1h3 $1$ C \(\Q(\zeta_{5})\) 840.118.1h $C_5\times D_{84}$ $C_{10}$ $10$ 10.a1.a1 $84$ 1.a1.a1
840.118.1h4 $1$ C \(\Q(\zeta_{5})\) 840.118.1h $C_5\times D_{84}$ $C_{10}$ $10$ 10.a1.a1 $84$ 1.a1.a1
840.118.2a $2$ R \(\Q\) 840.118.2a $C_5\times D_{84}$ $S_3$ $6$ 6.a1.a1 $140$ 6.a1.a1
840.118.2b $2$ R \(\Q\) 840.118.2b $C_5\times D_{84}$ $D_4$ $8$ 8.a1.a1 $105$ 4.a1.a1
840.118.2c $2$ R \(\Q\) 840.118.2c $C_5\times D_{84}$ $D_6$ $12$ 12.a1.a1 $70$ 6.a1.a1
840.118.2d1 $2$ R \(\Q(\sqrt{3}) \) 840.118.2d $C_5\times D_{84}$ $D_{12}$ $24$ 24.a1.a1 $35$ 12.a1.a1
840.118.2d2 $2$ R \(\Q(\sqrt{3}) \) 840.118.2d $C_5\times D_{84}$ $D_{12}$ $24$ 24.a1.a1 $35$ 12.a1.a1
840.118.2e1 $2$ R \(\Q(\zeta_{7})^+\) 840.118.2e $C_5\times D_{84}$ $D_7$ $14$ 14.a1.a1 $60$ 14.a1.a1
840.118.2e2 $2$ R \(\Q(\zeta_{7})^+\) 840.118.2e $C_5\times D_{84}$ $D_7$ $14$ 14.a1.a1 $60$ 14.a1.a1
840.118.2e3 $2$ R \(\Q(\zeta_{7})^+\) 840.118.2e $C_5\times D_{84}$ $D_7$ $14$ 14.a1.a1 $60$ 14.a1.a1
840.118.2f1 $2$ R \(\Q(\zeta_{7})^+\) 840.118.2f $C_5\times D_{84}$ $D_{14}$ $28$ 28.a1.a1 $30$ 14.a1.a1
840.118.2f2 $2$ R \(\Q(\zeta_{7})^+\) 840.118.2f $C_5\times D_{84}$ $D_{14}$ $28$ 28.a1.a1 $30$ 14.a1.a1
840.118.2f3 $2$ R \(\Q(\zeta_{7})^+\) 840.118.2f $C_5\times D_{84}$ $D_{14}$ $28$ 28.a1.a1 $30$ 14.a1.a1
840.118.2g1 $2$ C \(\Q(\zeta_{5})\) 840.118.2g $C_5\times D_{84}$ $C_5\times S_3$ $30$ 30.a1.a1 $28$ 6.a1.a1
840.118.2g2 $2$ C \(\Q(\zeta_{5})\) 840.118.2g $C_5\times D_{84}$ $C_5\times S_3$ $30$ 30.a1.a1 $28$ 6.a1.a1
840.118.2g3 $2$ C \(\Q(\zeta_{5})\) 840.118.2g $C_5\times D_{84}$ $C_5\times S_3$ $30$ 30.a1.a1 $28$ 6.a1.a1
840.118.2g4 $2$ C \(\Q(\zeta_{5})\) 840.118.2g $C_5\times D_{84}$ $C_5\times S_3$ $30$ 30.a1.a1 $28$ 6.a1.a1
840.118.2h1 $2$ C \(\Q(\zeta_{5})\) 840.118.2h $C_5\times D_{84}$ $C_5\times D_4$ $40$ 40.a1.a1 $21$ 4.a1.a1
840.118.2h2 $2$ C \(\Q(\zeta_{5})\) 840.118.2h $C_5\times D_{84}$ $C_5\times D_4$ $40$ 40.a1.a1 $21$ 4.a1.a1
840.118.2h3 $2$ C \(\Q(\zeta_{5})\) 840.118.2h $C_5\times D_{84}$ $C_5\times D_4$ $40$ 40.a1.a1 $21$ 4.a1.a1
840.118.2h4 $2$ C \(\Q(\zeta_{5})\) 840.118.2h $C_5\times D_{84}$ $C_5\times D_4$ $40$ 40.a1.a1 $21$ 4.a1.a1
840.118.2i1 $2$ C \(\Q(\zeta_{5})\) 840.118.2i $C_5\times D_{84}$ $S_3\times C_{10}$ $60$ 60.a1.a1 $14$ 6.a1.a1
840.118.2i2 $2$ C \(\Q(\zeta_{5})\) 840.118.2i $C_5\times D_{84}$ $S_3\times C_{10}$ $60$ 60.a1.a1 $14$ 6.a1.a1
840.118.2i3 $2$ C \(\Q(\zeta_{5})\) 840.118.2i $C_5\times D_{84}$ $S_3\times C_{10}$ $60$ 60.a1.a1 $14$ 6.a1.a1
840.118.2i4 $2$ C \(\Q(\zeta_{5})\) 840.118.2i $C_5\times D_{84}$ $S_3\times C_{10}$ $60$ 60.a1.a1 $14$ 6.a1.a1
840.118.2j1 $2$ R \(\Q(\zeta_{21})^+\) 840.118.2j $C_5\times D_{84}$ $D_{21}$ $42$ 42.a1.a1 $20$ 42.a1.a1
840.118.2j2 $2$ R \(\Q(\zeta_{21})^+\) 840.118.2j $C_5\times D_{84}$ $D_{21}$ $42$ 42.a1.a1 $20$ 42.a1.a1
840.118.2j3 $2$ R \(\Q(\zeta_{21})^+\) 840.118.2j $C_5\times D_{84}$ $D_{21}$ $42$ 42.a1.a1 $20$ 42.a1.a1
840.118.2j4 $2$ R \(\Q(\zeta_{21})^+\) 840.118.2j $C_5\times D_{84}$ $D_{21}$ $42$ 42.a1.a1 $20$ 42.a1.a1
840.118.2j5 $2$ R \(\Q(\zeta_{21})^+\) 840.118.2j $C_5\times D_{84}$ $D_{21}$ $42$ 42.a1.a1 $20$ 42.a1.a1
840.118.2j6 $2$ R \(\Q(\zeta_{21})^+\) 840.118.2j $C_5\times D_{84}$ $D_{21}$ $42$ 42.a1.a1 $20$ 42.a1.a1
840.118.2k1 $2$ R \(\Q(\zeta_{28})^+\) 840.118.2k $C_5\times D_{84}$ $D_{28}$ $56$ 56.a1.a1 $15$ 28.a1.a1
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