Basic properties
| Modulus: | \(5225\) | |
| Conductor: | \(5225\) | 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 5225.hz
\(\chi_{5225}(104,\cdot)\) \(\chi_{5225}(119,\cdot)\) \(\chi_{5225}(234,\cdot)\) \(\chi_{5225}(389,\cdot)\) \(\chi_{5225}(669,\cdot)\) \(\chi_{5225}(784,\cdot)\) \(\chi_{5225}(929,\cdot)\) \(\chi_{5225}(1214,\cdot)\) \(\chi_{5225}(1334,\cdot)\) \(\chi_{5225}(1479,\cdot)\) \(\chi_{5225}(1754,\cdot)\) \(\chi_{5225}(1764,\cdot)\) \(\chi_{5225}(2039,\cdot)\) \(\chi_{5225}(2304,\cdot)\) \(\chi_{5225}(2589,\cdot)\) \(\chi_{5225}(2854,\cdot)\) \(\chi_{5225}(3139,\cdot)\) \(\chi_{5225}(3144,\cdot)\) \(\chi_{5225}(3809,\cdot)\) \(\chi_{5225}(3969,\cdot)\) \(\chi_{5225}(4519,\cdot)\) \(\chi_{5225}(4634,\cdot)\) \(\chi_{5225}(4794,\cdot)\) \(\chi_{5225}(5184,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{2}{5}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 5225 }(104, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) |