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.hm
\(\chi_{5225}(289,\cdot)\) \(\chi_{5225}(1054,\cdot)\) \(\chi_{5225}(1434,\cdot)\) \(\chi_{5225}(1879,\cdot)\) \(\chi_{5225}(2194,\cdot)\) \(\chi_{5225}(2259,\cdot)\) \(\chi_{5225}(2429,\cdot)\) \(\chi_{5225}(2704,\cdot)\) \(\chi_{5225}(2764,\cdot)\) \(\chi_{5225}(2809,\cdot)\) \(\chi_{5225}(3019,\cdot)\) \(\chi_{5225}(3084,\cdot)\) \(\chi_{5225}(3254,\cdot)\) \(\chi_{5225}(3569,\cdot)\) \(\chi_{5225}(3589,\cdot)\) \(\chi_{5225}(3634,\cdot)\) \(\chi_{5225}(3804,\cdot)\) \(\chi_{5225}(3844,\cdot)\) \(\chi_{5225}(4139,\cdot)\) \(\chi_{5225}(4184,\cdot)\) \(\chi_{5225}(4394,\cdot)\) \(\chi_{5225}(4414,\cdot)\) \(\chi_{5225}(4944,\cdot)\) \(\chi_{5225}(4964,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{4}{5}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 5225 }(289, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{44}{45}\right)\) |