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.fy
\(\chi_{3895}(78,\cdot)\) \(\chi_{3895}(98,\cdot)\) \(\chi_{3895}(223,\cdot)\) \(\chi_{3895}(242,\cdot)\) \(\chi_{3895}(262,\cdot)\) \(\chi_{3895}(338,\cdot)\) \(\chi_{3895}(428,\cdot)\) \(\chi_{3895}(447,\cdot)\) \(\chi_{3895}(488,\cdot)\) \(\chi_{3895}(508,\cdot)\) \(\chi_{3895}(592,\cdot)\) \(\chi_{3895}(713,\cdot)\) \(\chi_{3895}(838,\cdot)\) \(\chi_{3895}(857,\cdot)\) \(\chi_{3895}(877,\cdot)\) \(\chi_{3895}(953,\cdot)\) \(\chi_{3895}(1002,\cdot)\) \(\chi_{3895}(1117,\cdot)\) \(\chi_{3895}(1123,\cdot)\) \(\chi_{3895}(1207,\cdot)\) \(\chi_{3895}(1248,\cdot)\) \(\chi_{3895}(1267,\cdot)\) \(\chi_{3895}(1287,\cdot)\) \(\chi_{3895}(1363,\cdot)\) \(\chi_{3895}(1492,\cdot)\) \(\chi_{3895}(1533,\cdot)\) \(\chi_{3895}(1568,\cdot)\) \(\chi_{3895}(1617,\cdot)\) \(\chi_{3895}(1732,\cdot)\) \(\chi_{3895}(1902,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((3117,2871,1236)\) → \((-i,e\left(\frac{5}{18}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 3895 }(488, a) \) | \(1\) | \(1\) | \(e\left(\frac{149}{180}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{79}{180}\right)\) |