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.ig
\(\chi_{5225}(79,\cdot)\) \(\chi_{5225}(629,\cdot)\) \(\chi_{5225}(789,\cdot)\) \(\chi_{5225}(1454,\cdot)\) \(\chi_{5225}(1459,\cdot)\) \(\chi_{5225}(1744,\cdot)\) \(\chi_{5225}(2009,\cdot)\) \(\chi_{5225}(2294,\cdot)\) \(\chi_{5225}(2559,\cdot)\) \(\chi_{5225}(2834,\cdot)\) \(\chi_{5225}(2844,\cdot)\) \(\chi_{5225}(3119,\cdot)\) \(\chi_{5225}(3264,\cdot)\) \(\chi_{5225}(3384,\cdot)\) \(\chi_{5225}(3669,\cdot)\) \(\chi_{5225}(3814,\cdot)\) \(\chi_{5225}(3929,\cdot)\) \(\chi_{5225}(4209,\cdot)\) \(\chi_{5225}(4364,\cdot)\) \(\chi_{5225}(4479,\cdot)\) \(\chi_{5225}(4494,\cdot)\) \(\chi_{5225}(4639,\cdot)\) \(\chi_{5225}(5029,\cdot)\) \(\chi_{5225}(5189,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{1}{10}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 5225 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{41}{90}\right)\) |