Basic properties
| Modulus: | \(1425\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{475}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1425.ce
\(\chi_{1425}(16,\cdot)\) \(\chi_{1425}(61,\cdot)\) \(\chi_{1425}(196,\cdot)\) \(\chi_{1425}(256,\cdot)\) \(\chi_{1425}(271,\cdot)\) \(\chi_{1425}(346,\cdot)\) \(\chi_{1425}(481,\cdot)\) \(\chi_{1425}(511,\cdot)\) \(\chi_{1425}(541,\cdot)\) \(\chi_{1425}(556,\cdot)\) \(\chi_{1425}(586,\cdot)\) \(\chi_{1425}(631,\cdot)\) \(\chi_{1425}(766,\cdot)\) \(\chi_{1425}(796,\cdot)\) \(\chi_{1425}(841,\cdot)\) \(\chi_{1425}(871,\cdot)\) \(\chi_{1425}(916,\cdot)\) \(\chi_{1425}(1081,\cdot)\) \(\chi_{1425}(1111,\cdot)\) \(\chi_{1425}(1156,\cdot)\) \(\chi_{1425}(1336,\cdot)\) \(\chi_{1425}(1366,\cdot)\) \(\chi_{1425}(1396,\cdot)\) \(\chi_{1425}(1411,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((476,1027,1351)\) → \((1,e\left(\frac{1}{5}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 1425 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{13}{45}\right)\) |