Basic properties
| Modulus: | \(3895\) | |
| Conductor: | \(3895\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | 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 3895.gb
\(\chi_{3895}(74,\cdot)\) \(\chi_{3895}(169,\cdot)\) \(\chi_{3895}(244,\cdot)\) \(\chi_{3895}(289,\cdot)\) \(\chi_{3895}(389,\cdot)\) \(\chi_{3895}(484,\cdot)\) \(\chi_{3895}(579,\cdot)\) \(\chi_{3895}(594,\cdot)\) \(\chi_{3895}(689,\cdot)\) \(\chi_{3895}(784,\cdot)\) \(\chi_{3895}(859,\cdot)\) \(\chi_{3895}(1004,\cdot)\) \(\chi_{3895}(1099,\cdot)\) \(\chi_{3895}(1184,\cdot)\) \(\chi_{3895}(1194,\cdot)\) \(\chi_{3895}(1279,\cdot)\) \(\chi_{3895}(1374,\cdot)\) \(\chi_{3895}(1594,\cdot)\) \(\chi_{3895}(1619,\cdot)\) \(\chi_{3895}(1689,\cdot)\) \(\chi_{3895}(1714,\cdot)\) \(\chi_{3895}(1784,\cdot)\) \(\chi_{3895}(1809,\cdot)\) \(\chi_{3895}(2004,\cdot)\) \(\chi_{3895}(2099,\cdot)\) \(\chi_{3895}(2134,\cdot)\) \(\chi_{3895}(2194,\cdot)\) \(\chi_{3895}(2209,\cdot)\) \(\chi_{3895}(2304,\cdot)\) \(\chi_{3895}(2399,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((3117,2871,1236)\) → \((-1,e\left(\frac{5}{9}\right),e\left(\frac{11}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 3895 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{59}{180}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{59}{180}\right)\) |