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Galois conjugate representations are grouped into single lines.
Label Dimension Conductor Defining polynomial of Artin field $G$ Ind $\chi(c)$
35.354...976.70.a.a $35$ $ 2^{30} \cdot 3^{50} \cdot 7^{28}$ x7 - 3x6 + 3x5 + 3x4 - 9x3 + 3x2 + x - 3 $A_7$ $1$ $-1$
35.206...384.70.a.a $35$ $ 2^{75} \cdot 3^{77}$ x7 - x6 + 3x5 - 5x4 + 2x3 - 12x2 + x - 7 $S_7$ $1$ $1$
35.245...344.70.a.a $35$ $ 2^{80} \cdot 3^{74}$ x7 - 3x5 - 2x4 + 3x3 + 12x2 + 19x + 6 $S_7$ $1$ $1$
35.272...416.126.a.a $35$ $ 2^{96} \cdot 3^{64}$ x7 - 3x5 - x4 + 3x3 + 6x2 - x - 9 $S_7$ $1$ $-1$
35.193...736.126.a.a $35$ $ 2^{102} \cdot 3^{62}$ x7 - 2x6 + 6x5 - 10x4 + 14x3 - 12x2 + 4x + 4 $S_7$ $1$ $-1$
35.217...328.70.a.a $35$ $ 2^{99} \cdot 3^{64}$ x7 - 3x5 - x4 + 3x3 + 6x2 - x - 9 $S_7$ $1$ $1$
35.515...296.70.a.a $35$ $ 2^{105} \cdot 3^{61}$ x7 - 2x6 + 6x5 - 10x4 + 14x3 - 12x2 + 4x + 4 $S_7$ $1$ $1$
35.156...016.126.a.a $35$ $ 2^{86} \cdot 3^{74}$ x7 - 3x5 - 2x4 + 3x3 + 12x2 + 19x + 6 $S_7$ $1$ $-1$
35.317...824.126.a.a $35$ $ 2^{84} \cdot 3^{78}$ x7 - x6 + 3x5 - 5x4 + 2x3 - 12x2 + x - 7 $S_7$ $1$ $-1$
35.160...384.70.a.a $35$ $ 2^{96} \cdot 3^{74}$ x7 - 2x6 + 3x5 + x4 - 5x3 + 12x2 - 7x + 5 $S_7$ $1$ $1$
35.542...296.70.a.a $35$ $ 2^{93} \cdot 3^{77}$ x7 - x6 - x4 - 2x3 + 4x + 2 $S_7$ $1$ $1$
35.642...536.126.a.a $35$ $ 2^{98} \cdot 3^{74}$ x7 - 2x6 + 3x5 - 4x4 + 5x3 - 6x2 + 7x - 8 $S_7$ $1$ $-1$
35.642...536.70.a.a $35$ $ 2^{98} \cdot 3^{74}$ x7 - 2x6 + 3x5 - 4x4 + 5x3 - 6x2 + 7x - 8 $S_7$ $1$ $1$
35.257...144.126.a.a $35$ $ 2^{100} \cdot 3^{74}$ x7 - 2x6 + 3x5 + x4 - 5x3 + 12x2 - 7x + 5 $S_7$ $1$ $-1$
35.257...144.70.a.a $35$ $ 2^{100} \cdot 3^{74}$ x7 - 3x6 + 3x5 + x4 - 3x3 - 3x2 - 5x - 3 $S_7$ $1$ $1$
35.867...736.70.a.a $35$ $ 2^{97} \cdot 3^{77}$ x7 - 2x6 + 27x3 - 54x2 + 42x - 12 $S_7$ $1$ $1$
35.102...576.126.a.a $35$ $ 2^{102} \cdot 3^{74}$ x7 - 3x6 + 3x5 + x4 - 3x3 - 3x2 - 5x - 3 $S_7$ $1$ $-1$
35.173...472.70.a.a $35$ $ 2^{98} \cdot 3^{77}$ x7 - x6 + 18x3 - 18x2 - 24x - 48 $S_7$ $1$ $1$
35.294...824.70.a.a $35$ $ 2^{30} \cdot 3^{68} \cdot 11^{24}$ x7 - 2x6 + 2x + 2 $A_7$ $1$ $-1$
35.520...416.126.a.a $35$ $ 2^{98} \cdot 3^{78}$ x7 - x6 + 18x3 - 18x2 - 24x - 48 $S_7$ $1$ $-1$
35.520...416.126.b.a $35$ $ 2^{98} \cdot 3^{78}$ x7 - 2x6 + 27x3 - 54x2 + 42x - 12 $S_7$ $1$ $-1$
35.832...656.126.a.a $35$ $ 2^{102} \cdot 3^{78}$ x7 - x6 - x4 - 2x3 + 4x + 2 $S_7$ $1$ $-1$
35.917...416.70.a.a $35$ $ 2^{30} \cdot 7^{18} \cdot 73^{24}$ x7 - 2x6 + 2x4 - 2x3 - 2x2 + 2x + 2 $A_7$ $1$ $-1$
35.116...471.70.a.a $35$ $ 13^{18} \cdot 17^{15} \cdot 127^{15}$ x7 - x6 + 2x4 + 2x + 1 $S_7$ $1$ $1$
35.546...247.70.a.a $35$ $ 23^{15} \cdot 709^{18}$ x7 - x6 - 3x5 + 5x4 + 2x3 - 8x2 - 2x + 1 $S_7$ $1$ $5$
35.123...888.70.a.a $35$ $ 2^{54} \cdot 8363^{15}$ x7 - x6 + 3x5 - 4x4 + 3x3 - 4x2 + 2x - 1 $S_7$ $1$ $1$
35.629...343.70.a.a $35$ $ 7^{18} \cdot 31^{15} \cdot 353^{15}$ x7 - x6 + 2x5 + x4 + 2x2 + x + 1 $S_7$ $1$ $1$
35.103...367.70.a.a $35$ $ 7^{15} \cdot 29^{24} \cdot 89^{15}$ x7 - 2x6 + 2x5 - x4 - x3 + 3x2 - 2x + 1 $S_7$ $1$ $1$
35.149...991.70.a.a $35$ $ 11^{24} \cdot 3511^{15}$ x7 - x6 - x4 + 2x3 - x2 + 2x - 1 $S_7$ $1$ $1$
35.253...375.70.a.a $35$ $ 5^{24} \cdot 37^{15} \cdot 347^{15}$ x7 - x6 + x5 - x4 + 2x2 - 2x + 1 $S_7$ $1$ $1$
35.351...721.126.a.a $35$ $ 23^{20} \cdot 709^{18}$ x7 - x6 - 3x5 + 5x4 + 2x3 - 8x2 - 2x + 1 $S_7$ $1$ $-5$
35.985...943.70.a.a $35$ $ 184607^{15}$ x7 - x6 - x5 + x4 - x2 + x + 1 $S_7$ $1$ $1$
35.196...143.70.a.a $35$ $ 193327^{15}$ x7 - x6 + 2x4 - 2x3 + 2x - 1 $S_7$ $1$ $1$
35.201...943.70.a.a $35$ $ 193607^{15}$ x7 - x4 - x3 + x2 + 1 $S_7$ $1$ $1$
35.244...143.70.a.a $35$ $ 29^{15} \cdot 6763^{15}$ x7 - 2x6 + 2x5 - x4 + 2x2 - 2x + 1 $S_7$ $1$ $1$
35.317...399.70.a.a $35$ $ 199559^{15}$ x7 - x6 + x3 - x + 1 $S_7$ $1$ $1$
35.363...151.70.a.a $35$ $ 7^{24} \cdot 8951^{15}$ x7 - 2x6 + 2x5 - 2x4 + x3 + 1 $S_7$ $1$ $1$
35.371...551.70.a.a $35$ $ 17^{15} \cdot 11863^{15}$ x7 - x6 + 2x5 - 2x4 + 2x3 - 2x2 + 2x - 1 $S_7$ $1$ $1$
35.393...551.70.a.a $35$ $ 202471^{15}$ x7 - x6 - x5 + 2x4 - x2 + 1 $S_7$ $1$ $1$
35.586...151.70.a.a $35$ $ 11^{15} \cdot 41^{15} \cdot 461^{15}$ x7 - x5 - x4 - x3 + x2 + x + 1 $S_7$ $1$ $1$
35.775...951.70.a.a $35$ $ 19^{15} \cdot 11149^{15}$ x7 - x6 + 2x5 - x4 + x2 - 2x + 1 $S_7$ $1$ $1$
35.943...943.70.a.a $35$ $ 214607^{15}$ x7 - x6 + 2x5 - 2x4 + 2x3 - 2x2 - 1 $S_7$ $1$ $1$
35.187...343.70.a.a $35$ $ 277^{15} \cdot 811^{15}$ x7 - 2x5 - x4 + 2x3 + 2x2 - 1 $S_7$ $1$ $1$
35.223...743.70.a.a $35$ $ 167^{15} \cdot 1361^{15}$ x7 - 2x6 + 3x5 - 3x4 + 3x3 - 2x2 + 2x - 1 $S_7$ $1$ $1$
35.438...751.70.a.a $35$ $ 23^{15} \cdot 10337^{15}$ x7 - x6 + x5 - x4 + x3 + x2 - 2x + 1 $S_7$ $1$ $1$
35.495...623.70.a.a $35$ $ 3^{48} \cdot 7127^{15}$ x7 - 2x6 + x5 + x2 - x - 1 $S_7$ $1$ $1$
35.577...843.70.a.a $35$ $ 242147^{15}$ x7 - 2x6 + 2x5 - x4 - x3 + 2x2 - x + 1 $S_7$ $1$ $1$
35.586...423.70.a.a $35$ $ 3^{48} \cdot 7207^{15}$ x7 - x6 - x4 + x + 1 $S_7$ $1$ $1$
35.607...051.70.a.a $35$ $ 242971^{15}$ x7 - x6 - x5 + 2x4 - 2x2 + x + 1 $S_7$ $1$ $1$
35.896...817.70.a.a $35$ $ 11^{18} \cdot 14033^{15}$ x7 - 2x5 - 4x4 - x3 + 4x2 + 4x + 1 $S_7$ $1$ $-1$
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