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The database currently contains approximately 182,000 Galois conjugacy classes of Artin representations, for a total of approximately 165,000 number fields. At present, there are no assertions of completeness.

Browse Artin representations

By dimension: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

By conductor: 1-100, 101-1000, 1001-10000, 10001-100000

By group: $D_4$, $Q_8$, $A_4$, $S_4$, $\GL(2,3)$, $A_5$, $C_3^2:D_4$, $S_5$, $\GL(3,2)$, $A_6$, $S_6$, $A_7$, $S_7$

A random Artin representation from the database.

Go to a specific Artin representation by label

Artin representation: e.g., 3.2e3_7e5.7t3.1c1

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Enter values into one or more boxes to restrict the search.

Dimension e.g. 1, 2-4
Conductor e.g. 50, 100-200
Group e.g. C5, or 8T12, a list of group labels
Ramified primes e.g. 2, 3 (no range allowed)
Unramified primes e.g. 5, 7, 13 (no range allowed)
Root number at the moment, one of 1 or -1
Frobenius-Schur indicator +1 for orthogonal, -1 for symplectic, 0 for non-real character
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