Basic properties
| Modulus: | \(119952\) | |
| Conductor: | \(119952\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | 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 119952.bzb
\(\chi_{119952}(29,\cdot)\) \(\chi_{119952}(533,\cdot)\) \(\chi_{119952}(1541,\cdot)\) \(\chi_{119952}(1877,\cdot)\) \(\chi_{119952}(2045,\cdot)\) \(\chi_{119952}(5069,\cdot)\) \(\chi_{119952}(5909,\cdot)\) \(\chi_{119952}(7589,\cdot)\) \(\chi_{119952}(11453,\cdot)\) \(\chi_{119952}(11621,\cdot)\) \(\chi_{119952}(12965,\cdot)\) \(\chi_{119952}(13469,\cdot)\) \(\chi_{119952}(14141,\cdot)\) \(\chi_{119952}(16493,\cdot)\) \(\chi_{119952}(17165,\cdot)\) \(\chi_{119952}(17669,\cdot)\) \(\chi_{119952}(18677,\cdot)\) \(\chi_{119952}(19181,\cdot)\) \(\chi_{119952}(22205,\cdot)\) \(\chi_{119952}(23045,\cdot)\) \(\chi_{119952}(24725,\cdot)\) \(\chi_{119952}(25565,\cdot)\) \(\chi_{119952}(28589,\cdot)\) \(\chi_{119952}(28757,\cdot)\) \(\chi_{119952}(29093,\cdot)\) \(\chi_{119952}(30101,\cdot)\) \(\chi_{119952}(30605,\cdot)\) \(\chi_{119952}(31277,\cdot)\) \(\chi_{119952}(33629,\cdot)\) \(\chi_{119952}(34805,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((104959,29989,106625,117505,14113)\) → \((1,-i,e\left(\frac{1}{6}\right),e\left(\frac{3}{7}\right),e\left(\frac{13}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 119952 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{336}\right)\) | \(e\left(\frac{251}{336}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{271}{336}\right)\) | \(e\left(\frac{25}{168}\right)\) | \(e\left(\frac{233}{336}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{31}{112}\right)\) | \(e\left(\frac{235}{336}\right)\) |