Basic properties
| Modulus: | \(4225\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(390\) | 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 4225.ct
\(\chi_{4225}(4,\cdot)\) \(\chi_{4225}(69,\cdot)\) \(\chi_{4225}(114,\cdot)\) \(\chi_{4225}(134,\cdot)\) \(\chi_{4225}(179,\cdot)\) \(\chi_{4225}(244,\cdot)\) \(\chi_{4225}(264,\cdot)\) \(\chi_{4225}(309,\cdot)\) \(\chi_{4225}(329,\cdot)\) \(\chi_{4225}(394,\cdot)\) \(\chi_{4225}(439,\cdot)\) \(\chi_{4225}(459,\cdot)\) \(\chi_{4225}(504,\cdot)\) \(\chi_{4225}(569,\cdot)\) \(\chi_{4225}(589,\cdot)\) \(\chi_{4225}(634,\cdot)\) \(\chi_{4225}(719,\cdot)\) \(\chi_{4225}(764,\cdot)\) \(\chi_{4225}(784,\cdot)\) \(\chi_{4225}(829,\cdot)\) \(\chi_{4225}(894,\cdot)\) \(\chi_{4225}(914,\cdot)\) \(\chi_{4225}(959,\cdot)\) \(\chi_{4225}(979,\cdot)\) \(\chi_{4225}(1044,\cdot)\) \(\chi_{4225}(1089,\cdot)\) \(\chi_{4225}(1109,\cdot)\) \(\chi_{4225}(1154,\cdot)\) \(\chi_{4225}(1219,\cdot)\) \(\chi_{4225}(1239,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((677,3551)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{1}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 4225 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{195}\right)\) | \(e\left(\frac{113}{390}\right)\) | \(e\left(\frac{44}{195}\right)\) | \(e\left(\frac{157}{390}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{113}{195}\right)\) | \(e\left(\frac{359}{390}\right)\) | \(e\left(\frac{67}{130}\right)\) | \(e\left(\frac{64}{65}\right)\) |