Basic properties
| Modulus: | \(4275\) | |
| Conductor: | \(4275\) | 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 4275.gq
\(\chi_{4275}(14,\cdot)\) \(\chi_{4275}(29,\cdot)\) \(\chi_{4275}(59,\cdot)\) \(\chi_{4275}(554,\cdot)\) \(\chi_{4275}(659,\cdot)\) \(\chi_{4275}(794,\cdot)\) \(\chi_{4275}(869,\cdot)\) \(\chi_{4275}(884,\cdot)\) \(\chi_{4275}(914,\cdot)\) \(\chi_{4275}(1409,\cdot)\) \(\chi_{4275}(1514,\cdot)\) \(\chi_{4275}(1739,\cdot)\) \(\chi_{4275}(1769,\cdot)\) \(\chi_{4275}(2264,\cdot)\) \(\chi_{4275}(2369,\cdot)\) \(\chi_{4275}(2504,\cdot)\) \(\chi_{4275}(2579,\cdot)\) \(\chi_{4275}(2594,\cdot)\) \(\chi_{4275}(3119,\cdot)\) \(\chi_{4275}(3359,\cdot)\) \(\chi_{4275}(3434,\cdot)\) \(\chi_{4275}(3479,\cdot)\) \(\chi_{4275}(4079,\cdot)\) \(\chi_{4275}(4214,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1901,1027,1351)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{3}{10}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 4275 }(4214, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{17}{45}\right)\) |