Basic properties
| Modulus: | \(4725\) | |
| Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4725.gs
\(\chi_{4725}(31,\cdot)\) \(\chi_{4725}(61,\cdot)\) \(\chi_{4725}(346,\cdot)\) \(\chi_{4725}(661,\cdot)\) \(\chi_{4725}(691,\cdot)\) \(\chi_{4725}(1006,\cdot)\) \(\chi_{4725}(1291,\cdot)\) \(\chi_{4725}(1321,\cdot)\) \(\chi_{4725}(1606,\cdot)\) \(\chi_{4725}(1636,\cdot)\) \(\chi_{4725}(1921,\cdot)\) \(\chi_{4725}(2236,\cdot)\) \(\chi_{4725}(2266,\cdot)\) \(\chi_{4725}(2581,\cdot)\) \(\chi_{4725}(2866,\cdot)\) \(\chi_{4725}(2896,\cdot)\) \(\chi_{4725}(3181,\cdot)\) \(\chi_{4725}(3211,\cdot)\) \(\chi_{4725}(3496,\cdot)\) \(\chi_{4725}(3811,\cdot)\) \(\chi_{4725}(3841,\cdot)\) \(\chi_{4725}(4156,\cdot)\) \(\chi_{4725}(4441,\cdot)\) \(\chi_{4725}(4471,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{2}{5}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 4725 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) |