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.gw
\(\chi_{4725}(164,\cdot)\) \(\chi_{4725}(194,\cdot)\) \(\chi_{4725}(479,\cdot)\) \(\chi_{4725}(509,\cdot)\) \(\chi_{4725}(794,\cdot)\) \(\chi_{4725}(1109,\cdot)\) \(\chi_{4725}(1139,\cdot)\) \(\chi_{4725}(1454,\cdot)\) \(\chi_{4725}(1739,\cdot)\) \(\chi_{4725}(1769,\cdot)\) \(\chi_{4725}(2054,\cdot)\) \(\chi_{4725}(2084,\cdot)\) \(\chi_{4725}(2369,\cdot)\) \(\chi_{4725}(2684,\cdot)\) \(\chi_{4725}(2714,\cdot)\) \(\chi_{4725}(3029,\cdot)\) \(\chi_{4725}(3314,\cdot)\) \(\chi_{4725}(3344,\cdot)\) \(\chi_{4725}(3629,\cdot)\) \(\chi_{4725}(3659,\cdot)\) \(\chi_{4725}(3944,\cdot)\) \(\chi_{4725}(4259,\cdot)\) \(\chi_{4725}(4289,\cdot)\) \(\chi_{4725}(4604,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{3}{10}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 4725 }(164, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{11}{45}\right)\) |