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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4725.gg
\(\chi_{4725}(4,\cdot)\) \(\chi_{4725}(79,\cdot)\) \(\chi_{4725}(319,\cdot)\) \(\chi_{4725}(394,\cdot)\) \(\chi_{4725}(634,\cdot)\) \(\chi_{4725}(709,\cdot)\) \(\chi_{4725}(1264,\cdot)\) \(\chi_{4725}(1339,\cdot)\) \(\chi_{4725}(1579,\cdot)\) \(\chi_{4725}(1654,\cdot)\) \(\chi_{4725}(1894,\cdot)\) \(\chi_{4725}(1969,\cdot)\) \(\chi_{4725}(2209,\cdot)\) \(\chi_{4725}(2284,\cdot)\) \(\chi_{4725}(2839,\cdot)\) \(\chi_{4725}(2914,\cdot)\) \(\chi_{4725}(3154,\cdot)\) \(\chi_{4725}(3229,\cdot)\) \(\chi_{4725}(3469,\cdot)\) \(\chi_{4725}(3544,\cdot)\) \(\chi_{4725}(3784,\cdot)\) \(\chi_{4725}(3859,\cdot)\) \(\chi_{4725}(4414,\cdot)\) \(\chi_{4725}(4489,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{1}{10}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 4725 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{79}{90}\right)\) |