from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(132300, base_ring=CyclotomicField(630))
M = H._module
chi = DirichletCharacter(H, M([315,35,126,465]))
pari: [g,chi] = znchar(Mod(27191,132300))
χ132300(131,⋅)
χ132300(731,⋅)
χ132300(3911,⋅)
χ132300(4511,⋅)
χ132300(5171,⋅)
χ132300(5771,⋅)
χ132300(6431,⋅)
χ132300(7031,⋅)
χ132300(7691,⋅)
χ132300(8291,⋅)
χ132300(11471,⋅)
χ132300(12071,⋅)
χ132300(12731,⋅)
χ132300(13331,⋅)
χ132300(13991,⋅)
χ132300(14591,⋅)
χ132300(16511,⋅)
χ132300(17111,⋅)
χ132300(17771,⋅)
χ132300(18371,⋅)
χ132300(20291,⋅)
χ132300(20891,⋅)
χ132300(22811,⋅)
χ132300(23411,⋅)
χ132300(24071,⋅)
χ132300(24671,⋅)
χ132300(25331,⋅)
χ132300(25931,⋅)
χ132300(26591,⋅)
χ132300(27191,⋅)
...
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(66151,122501,15877,54001) → (−1,e(181),e(51),e(4231))
a |
−1 | 1 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 |
χ132300(27191,a) |
−1 | 1 | e(315298) | e(630379) | e(3531) | e(53) | e(315113) | e(630467) | e(4517) | e(10579) | e(315257) | e(12619) |