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Data for Artin representations are complete in the following cases based on [MR:3669395, 10.1007/s40993-017-0079-5, arXiv:1610.01228]. In each case, the LMFDB contains all faithful representations for a given group and irreducible representation with conductor less than or equal to the stated bound. Representations are distinguished by their dimension, and the smallest containing permutation representation. In addition, the LMFDB contains data on Artin representations for a variety of other number fields and Galois groups.

GroupDimContainerBound
$C_2$12T110000
$C_3$13T111180
$C_4$14T1796
$C_5$15T1752
$C_6$16T1577
$S_3$23T2177662241
$C_7$17T1492
$C_8$18T1249
$D_4$24T222500
$Q_8$28T5215444
$C_9$19T1387
$D_{5}$25T240000
$A_{4}$34T43375000
$D_{6}$26T222500
$D_{7}$27T240000
$S_{3}C_3$26T52828
$F_{5}$45T31600000000
$C_7:C_3$37T31000000
$S_{4}$34T522497
$S_{4}$36T8635168
$A_{4}C_2$36T622497
$C_{3}^2:C_4$46T103374494
$S_{3}^2$36T97998219
$S_{4} C_2$36T113694
$A_{5}$312T3366627
$A_{5}$45T4613778
$A_{5}$56T1252222435
$C_3^2:D_4$46T1322497
$S_{5}$45T57226
$S_{5}$410T12613778
$S_{5}$56T1452222435
$S_{5}$510T1352222435
$S_{5}$620T354439177045
$A_{6}$56T1527885
$A_{6}$836T125223534089616228
$A_{6}$910T26174981250375214
$A_{6}$1030T8810077696000000000
$S_{6}$56T163600
$S_{6}$512T183216000
$S_{6}$910T3252753592444
$S_{6}$920T145174981250375214
$S_{6}$1030T176167961600000000
$S_{6}$1636T1252553853374064674583164228907