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.jm
\(\chi_{4033}(103,\cdot)\) \(\chi_{4033}(119,\cdot)\) \(\chi_{4033}(341,\cdot)\) \(\chi_{4033}(378,\cdot)\) \(\chi_{4033}(489,\cdot)\) \(\chi_{4033}(495,\cdot)\) \(\chi_{4033}(615,\cdot)\) \(\chi_{4033}(800,\cdot)\) \(\chi_{4033}(828,\cdot)\) \(\chi_{4033}(859,\cdot)\) \(\chi_{4033}(939,\cdot)\) \(\chi_{4033}(1355,\cdot)\) \(\chi_{4033}(1377,\cdot)\) \(\chi_{4033}(1583,\cdot)\) \(\chi_{4033}(1605,\cdot)\) \(\chi_{4033}(1762,\cdot)\) \(\chi_{4033}(1768,\cdot)\) \(\chi_{4033}(1864,\cdot)\) \(\chi_{4033}(2169,\cdot)\) \(\chi_{4033}(2265,\cdot)\) \(\chi_{4033}(2271,\cdot)\) \(\chi_{4033}(2428,\cdot)\) \(\chi_{4033}(2450,\cdot)\) \(\chi_{4033}(2656,\cdot)\) \(\chi_{4033}(2678,\cdot)\) \(\chi_{4033}(3094,\cdot)\) \(\chi_{4033}(3174,\cdot)\) \(\chi_{4033}(3205,\cdot)\) \(\chi_{4033}(3233,\cdot)\) \(\chi_{4033}(3418,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{31}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(2656, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{25}{108}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{19}{108}\right)\) | \(e\left(\frac{35}{108}\right)\) |