Basic properties
| Modulus: | \(85600\) | |
| Conductor: | \(85600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2120\) | 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 85600.ig
\(\chi_{85600}(59,\cdot)\) \(\chi_{85600}(139,\cdot)\) \(\chi_{85600}(179,\cdot)\) \(\chi_{85600}(219,\cdot)\) \(\chi_{85600}(259,\cdot)\) \(\chi_{85600}(339,\cdot)\) \(\chi_{85600}(379,\cdot)\) \(\chi_{85600}(419,\cdot)\) \(\chi_{85600}(459,\cdot)\) \(\chi_{85600}(619,\cdot)\) \(\chi_{85600}(659,\cdot)\) \(\chi_{85600}(739,\cdot)\) \(\chi_{85600}(819,\cdot)\) \(\chi_{85600}(1059,\cdot)\) \(\chi_{85600}(1179,\cdot)\) \(\chi_{85600}(1259,\cdot)\) \(\chi_{85600}(1339,\cdot)\) \(\chi_{85600}(1379,\cdot)\) \(\chi_{85600}(1419,\cdot)\) \(\chi_{85600}(1459,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{2120})$ |
| Fixed field: | Number field defined by a degree 2120 polynomial (not computed) |
Values on generators
\((26751,32101,82177,16801)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{1}{10}\right),e\left(\frac{1}{106}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 85600 }(1179, a) \) | \(1\) | \(1\) | \(e\left(\frac{499}{2120}\right)\) | \(e\left(\frac{139}{212}\right)\) | \(e\left(\frac{499}{1060}\right)\) | \(e\left(\frac{1977}{2120}\right)\) | \(e\left(\frac{1923}{2120}\right)\) | \(e\left(\frac{39}{530}\right)\) | \(e\left(\frac{1931}{2120}\right)\) | \(e\left(\frac{1889}{2120}\right)\) | \(e\left(\frac{991}{1060}\right)\) | \(e\left(\frac{1497}{2120}\right)\) |