Basic properties
| Modulus: | \(4275\) | |
| Conductor: | \(4275\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | 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.fm
\(\chi_{4275}(16,\cdot)\) \(\chi_{4275}(256,\cdot)\) \(\chi_{4275}(346,\cdot)\) \(\chi_{4275}(481,\cdot)\) \(\chi_{4275}(511,\cdot)\) \(\chi_{4275}(556,\cdot)\) \(\chi_{4275}(871,\cdot)\) \(\chi_{4275}(1111,\cdot)\) \(\chi_{4275}(1336,\cdot)\) \(\chi_{4275}(1366,\cdot)\) \(\chi_{4275}(1411,\cdot)\) \(\chi_{4275}(1966,\cdot)\) \(\chi_{4275}(2056,\cdot)\) \(\chi_{4275}(2191,\cdot)\) \(\chi_{4275}(2221,\cdot)\) \(\chi_{4275}(2266,\cdot)\) \(\chi_{4275}(2581,\cdot)\) \(\chi_{4275}(2821,\cdot)\) \(\chi_{4275}(2911,\cdot)\) \(\chi_{4275}(3046,\cdot)\) \(\chi_{4275}(3121,\cdot)\) \(\chi_{4275}(3436,\cdot)\) \(\chi_{4275}(3766,\cdot)\) \(\chi_{4275}(3931,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((1901,1027,1351)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{5}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 4275 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) |