Basic properties
| Modulus: | \(4275\) | |
| Conductor: | \(1425\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1425}(89,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4275.go
\(\chi_{4275}(89,\cdot)\) \(\chi_{4275}(269,\cdot)\) \(\chi_{4275}(314,\cdot)\) \(\chi_{4275}(584,\cdot)\) \(\chi_{4275}(629,\cdot)\) \(\chi_{4275}(944,\cdot)\) \(\chi_{4275}(1079,\cdot)\) \(\chi_{4275}(1169,\cdot)\) \(\chi_{4275}(1439,\cdot)\) \(\chi_{4275}(1484,\cdot)\) \(\chi_{4275}(1934,\cdot)\) \(\chi_{4275}(1979,\cdot)\) \(\chi_{4275}(2294,\cdot)\) \(\chi_{4275}(2339,\cdot)\) \(\chi_{4275}(2654,\cdot)\) \(\chi_{4275}(2789,\cdot)\) \(\chi_{4275}(2834,\cdot)\) \(\chi_{4275}(2879,\cdot)\) \(\chi_{4275}(3194,\cdot)\) \(\chi_{4275}(3509,\cdot)\) \(\chi_{4275}(3644,\cdot)\) \(\chi_{4275}(3689,\cdot)\) \(\chi_{4275}(3734,\cdot)\) \(\chi_{4275}(4004,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1901,1027,1351)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 4275 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) |