Basic properties
| Modulus: | \(9025\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{475}(54,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9025.bn
\(\chi_{9025}(54,\cdot)\) \(\chi_{9025}(234,\cdot)\) \(\chi_{9025}(389,\cdot)\) \(\chi_{9025}(784,\cdot)\) \(\chi_{9025}(1689,\cdot)\) \(\chi_{9025}(1859,\cdot)\) \(\chi_{9025}(1904,\cdot)\) \(\chi_{9025}(2039,\cdot)\) \(\chi_{9025}(2194,\cdot)\) \(\chi_{9025}(2589,\cdot)\) \(\chi_{9025}(3494,\cdot)\) \(\chi_{9025}(3664,\cdot)\) \(\chi_{9025}(3709,\cdot)\) \(\chi_{9025}(3844,\cdot)\) \(\chi_{9025}(4394,\cdot)\) \(\chi_{9025}(5469,\cdot)\) \(\chi_{9025}(5514,\cdot)\) \(\chi_{9025}(5804,\cdot)\) \(\chi_{9025}(7104,\cdot)\) \(\chi_{9025}(7319,\cdot)\) \(\chi_{9025}(7454,\cdot)\) \(\chi_{9025}(7609,\cdot)\) \(\chi_{9025}(8004,\cdot)\) \(\chi_{9025}(8909,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((5777,3251)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 9025 }(54, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{90}\right)\) |