Basic properties
Modulus: | \(4033\) | |
Conductor: | \(4033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4033.ij
\(\chi_{4033}(179,\cdot)\) \(\chi_{4033}(364,\cdot)\) \(\chi_{4033}(660,\cdot)\) \(\chi_{4033}(820,\cdot)\) \(\chi_{4033}(882,\cdot)\) \(\chi_{4033}(919,\cdot)\) \(\chi_{4033}(931,\cdot)\) \(\chi_{4033}(1005,\cdot)\) \(\chi_{4033}(1104,\cdot)\) \(\chi_{4033}(1141,\cdot)\) \(\chi_{4033}(1252,\cdot)\) \(\chi_{4033}(1264,\cdot)\) \(\chi_{4033}(1326,\cdot)\) \(\chi_{4033}(1375,\cdot)\) \(\chi_{4033}(1622,\cdot)\) \(\chi_{4033}(1733,\cdot)\) \(\chi_{4033}(1893,\cdot)\) \(\chi_{4033}(1992,\cdot)\) \(\chi_{4033}(2041,\cdot)\) \(\chi_{4033}(2140,\cdot)\) \(\chi_{4033}(2300,\cdot)\) \(\chi_{4033}(2411,\cdot)\) \(\chi_{4033}(2658,\cdot)\) \(\chi_{4033}(2707,\cdot)\) \(\chi_{4033}(2769,\cdot)\) \(\chi_{4033}(2781,\cdot)\) \(\chi_{4033}(2892,\cdot)\) \(\chi_{4033}(2929,\cdot)\) \(\chi_{4033}(3028,\cdot)\) \(\chi_{4033}(3102,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((-i,e\left(\frac{95}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1375, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{11}{108}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{107}{108}\right)\) | \(e\left(\frac{55}{108}\right)\) |