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.hj
\(\chi_{4725}(23,\cdot)\) \(\chi_{4725}(137,\cdot)\) \(\chi_{4725}(212,\cdot)\) \(\chi_{4725}(263,\cdot)\) \(\chi_{4725}(338,\cdot)\) \(\chi_{4725}(452,\cdot)\) \(\chi_{4725}(527,\cdot)\) \(\chi_{4725}(578,\cdot)\) \(\chi_{4725}(653,\cdot)\) \(\chi_{4725}(767,\cdot)\) \(\chi_{4725}(842,\cdot)\) \(\chi_{4725}(1208,\cdot)\) \(\chi_{4725}(1283,\cdot)\) \(\chi_{4725}(1397,\cdot)\) \(\chi_{4725}(1472,\cdot)\) \(\chi_{4725}(1523,\cdot)\) \(\chi_{4725}(1598,\cdot)\) \(\chi_{4725}(1712,\cdot)\) \(\chi_{4725}(1787,\cdot)\) \(\chi_{4725}(1838,\cdot)\) \(\chi_{4725}(1913,\cdot)\) \(\chi_{4725}(2027,\cdot)\) \(\chi_{4725}(2102,\cdot)\) \(\chi_{4725}(2153,\cdot)\) \(\chi_{4725}(2228,\cdot)\) \(\chi_{4725}(2342,\cdot)\) \(\chi_{4725}(2417,\cdot)\) \(\chi_{4725}(2783,\cdot)\) \(\chi_{4725}(2858,\cdot)\) \(\chi_{4725}(2972,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{3}{20}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 4725 }(1208, a) \) | \(1\) | \(1\) | \(e\left(\frac{157}{180}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{173}{180}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{179}{180}\right)\) | \(e\left(\frac{47}{180}\right)\) |