Basic properties
| Modulus: | \(5225\) | |
| Conductor: | \(5225\) | 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 5225.gd
\(\chi_{5225}(36,\cdot)\) \(\chi_{5225}(196,\cdot)\) \(\chi_{5225}(586,\cdot)\) \(\chi_{5225}(731,\cdot)\) \(\chi_{5225}(746,\cdot)\) \(\chi_{5225}(861,\cdot)\) \(\chi_{5225}(1016,\cdot)\) \(\chi_{5225}(1296,\cdot)\) \(\chi_{5225}(1411,\cdot)\) \(\chi_{5225}(1556,\cdot)\) \(\chi_{5225}(1841,\cdot)\) \(\chi_{5225}(1961,\cdot)\) \(\chi_{5225}(2106,\cdot)\) \(\chi_{5225}(2381,\cdot)\) \(\chi_{5225}(2391,\cdot)\) \(\chi_{5225}(2666,\cdot)\) \(\chi_{5225}(2931,\cdot)\) \(\chi_{5225}(3216,\cdot)\) \(\chi_{5225}(3481,\cdot)\) \(\chi_{5225}(3766,\cdot)\) \(\chi_{5225}(3771,\cdot)\) \(\chi_{5225}(4436,\cdot)\) \(\chi_{5225}(4596,\cdot)\) \(\chi_{5225}(5146,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{4}{5}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 5225 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{4}{45}\right)\) |