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.ih
\(\chi_{5225}(129,\cdot)\) \(\chi_{5225}(314,\cdot)\) \(\chi_{5225}(409,\cdot)\) \(\chi_{5225}(469,\cdot)\) \(\chi_{5225}(679,\cdot)\) \(\chi_{5225}(744,\cdot)\) \(\chi_{5225}(1229,\cdot)\) \(\chi_{5225}(1294,\cdot)\) \(\chi_{5225}(1504,\cdot)\) \(\chi_{5225}(2054,\cdot)\) \(\chi_{5225}(2119,\cdot)\) \(\chi_{5225}(2789,\cdot)\) \(\chi_{5225}(2879,\cdot)\) \(\chi_{5225}(2884,\cdot)\) \(\chi_{5225}(3339,\cdot)\) \(\chi_{5225}(3434,\cdot)\) \(\chi_{5225}(3889,\cdot)\) \(\chi_{5225}(3984,\cdot)\) \(\chi_{5225}(4164,\cdot)\) \(\chi_{5225}(4259,\cdot)\) \(\chi_{5225}(4594,\cdot)\) \(\chi_{5225}(4714,\cdot)\) \(\chi_{5225}(4809,\cdot)\) \(\chi_{5225}(5144,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{3}{10}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 5225 }(129, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{5}{18}\right)\) |