Basic properties
| Modulus: | \(4725\) | |
| Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | 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.hg
\(\chi_{4725}(187,\cdot)\) \(\chi_{4725}(283,\cdot)\) \(\chi_{4725}(313,\cdot)\) \(\chi_{4725}(472,\cdot)\) \(\chi_{4725}(502,\cdot)\) \(\chi_{4725}(598,\cdot)\) \(\chi_{4725}(628,\cdot)\) \(\chi_{4725}(787,\cdot)\) \(\chi_{4725}(817,\cdot)\) \(\chi_{4725}(913,\cdot)\) \(\chi_{4725}(1102,\cdot)\) \(\chi_{4725}(1228,\cdot)\) \(\chi_{4725}(1258,\cdot)\) \(\chi_{4725}(1417,\cdot)\) \(\chi_{4725}(1447,\cdot)\) \(\chi_{4725}(1573,\cdot)\) \(\chi_{4725}(1762,\cdot)\) \(\chi_{4725}(1858,\cdot)\) \(\chi_{4725}(1888,\cdot)\) \(\chi_{4725}(2047,\cdot)\) \(\chi_{4725}(2077,\cdot)\) \(\chi_{4725}(2173,\cdot)\) \(\chi_{4725}(2203,\cdot)\) \(\chi_{4725}(2362,\cdot)\) \(\chi_{4725}(2392,\cdot)\) \(\chi_{4725}(2488,\cdot)\) \(\chi_{4725}(2677,\cdot)\) \(\chi_{4725}(2803,\cdot)\) \(\chi_{4725}(2833,\cdot)\) \(\chi_{4725}(2992,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{9}{20}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 4725 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{121}{180}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{89}{180}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{77}{180}\right)\) | \(e\left(\frac{131}{180}\right)\) |