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.he
\(\chi_{4725}(13,\cdot)\) \(\chi_{4725}(97,\cdot)\) \(\chi_{4725}(202,\cdot)\) \(\chi_{4725}(223,\cdot)\) \(\chi_{4725}(328,\cdot)\) \(\chi_{4725}(412,\cdot)\) \(\chi_{4725}(517,\cdot)\) \(\chi_{4725}(538,\cdot)\) \(\chi_{4725}(727,\cdot)\) \(\chi_{4725}(853,\cdot)\) \(\chi_{4725}(958,\cdot)\) \(\chi_{4725}(1042,\cdot)\) \(\chi_{4725}(1147,\cdot)\) \(\chi_{4725}(1273,\cdot)\) \(\chi_{4725}(1462,\cdot)\) \(\chi_{4725}(1483,\cdot)\) \(\chi_{4725}(1588,\cdot)\) \(\chi_{4725}(1672,\cdot)\) \(\chi_{4725}(1777,\cdot)\) \(\chi_{4725}(1798,\cdot)\) \(\chi_{4725}(1903,\cdot)\) \(\chi_{4725}(1987,\cdot)\) \(\chi_{4725}(2092,\cdot)\) \(\chi_{4725}(2113,\cdot)\) \(\chi_{4725}(2302,\cdot)\) \(\chi_{4725}(2428,\cdot)\) \(\chi_{4725}(2533,\cdot)\) \(\chi_{4725}(2617,\cdot)\) \(\chi_{4725}(2722,\cdot)\) \(\chi_{4725}(2848,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{7}{20}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 4725 }(328, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{180}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{7}{180}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{13}{180}\right)\) |