Basic properties
| Modulus: | \(4725\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(92,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4725.ha
\(\chi_{4725}(92,\cdot)\) \(\chi_{4725}(113,\cdot)\) \(\chi_{4725}(302,\cdot)\) \(\chi_{4725}(428,\cdot)\) \(\chi_{4725}(533,\cdot)\) \(\chi_{4725}(617,\cdot)\) \(\chi_{4725}(722,\cdot)\) \(\chi_{4725}(848,\cdot)\) \(\chi_{4725}(1037,\cdot)\) \(\chi_{4725}(1058,\cdot)\) \(\chi_{4725}(1163,\cdot)\) \(\chi_{4725}(1247,\cdot)\) \(\chi_{4725}(1352,\cdot)\) \(\chi_{4725}(1373,\cdot)\) \(\chi_{4725}(1478,\cdot)\) \(\chi_{4725}(1562,\cdot)\) \(\chi_{4725}(1667,\cdot)\) \(\chi_{4725}(1688,\cdot)\) \(\chi_{4725}(1877,\cdot)\) \(\chi_{4725}(2003,\cdot)\) \(\chi_{4725}(2108,\cdot)\) \(\chi_{4725}(2192,\cdot)\) \(\chi_{4725}(2297,\cdot)\) \(\chi_{4725}(2423,\cdot)\) \(\chi_{4725}(2612,\cdot)\) \(\chi_{4725}(2633,\cdot)\) \(\chi_{4725}(2738,\cdot)\) \(\chi_{4725}(2822,\cdot)\) \(\chi_{4725}(2927,\cdot)\) \(\chi_{4725}(2948,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{13}{20}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 4725 }(92, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{180}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{23}{180}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{29}{180}\right)\) | \(e\left(\frac{17}{180}\right)\) |