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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4033.js
\(\chi_{4033}(15,\cdot)\) \(\chi_{4033}(187,\cdot)\) \(\chi_{4033}(198,\cdot)\) \(\chi_{4033}(315,\cdot)\) \(\chi_{4033}(348,\cdot)\) \(\chi_{4033}(405,\cdot)\) \(\chi_{4033}(439,\cdot)\) \(\chi_{4033}(461,\cdot)\) \(\chi_{4033}(836,\cdot)\) \(\chi_{4033}(1016,\cdot)\) \(\chi_{4033}(1112,\cdot)\) \(\chi_{4033}(1171,\cdot)\) \(\chi_{4033}(1313,\cdot)\) \(\chi_{4033}(1330,\cdot)\) \(\chi_{4033}(1356,\cdot)\) \(\chi_{4033}(1424,\cdot)\) \(\chi_{4033}(1615,\cdot)\) \(\chi_{4033}(1650,\cdot)\) \(\chi_{4033}(1793,\cdot)\) \(\chi_{4033}(1983,\cdot)\) \(\chi_{4033}(2151,\cdot)\) \(\chi_{4033}(2314,\cdot)\) \(\chi_{4033}(2386,\cdot)\) \(\chi_{4033}(2407,\cdot)\) \(\chi_{4033}(2625,\cdot)\) \(\chi_{4033}(2696,\cdot)\) \(\chi_{4033}(2869,\cdot)\) \(\chi_{4033}(3187,\cdot)\) \(\chi_{4033}(3234,\cdot)\) \(\chi_{4033}(3275,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{1}{36}\right),e\left(\frac{17}{27}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(187, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{53}{108}\right)\) | \(e\left(\frac{41}{108}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(-i\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{5}{54}\right)\) |