Basic properties
| Modulus: | \(5225\) | |
| Conductor: | \(1045\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1045}(499,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5225.hq
\(\chi_{5225}(499,\cdot)\) \(\chi_{5225}(674,\cdot)\) \(\chi_{5225}(1049,\cdot)\) \(\chi_{5225}(1149,\cdot)\) \(\chi_{5225}(1499,\cdot)\) \(\chi_{5225}(1974,\cdot)\) \(\chi_{5225}(2049,\cdot)\) \(\chi_{5225}(2099,\cdot)\) \(\chi_{5225}(2324,\cdot)\) \(\chi_{5225}(2524,\cdot)\) \(\chi_{5225}(2799,\cdot)\) \(\chi_{5225}(2874,\cdot)\) \(\chi_{5225}(2924,\cdot)\) \(\chi_{5225}(3349,\cdot)\) \(\chi_{5225}(3424,\cdot)\) \(\chi_{5225}(3474,\cdot)\) \(\chi_{5225}(3524,\cdot)\) \(\chi_{5225}(3749,\cdot)\) \(\chi_{5225}(3899,\cdot)\) \(\chi_{5225}(4299,\cdot)\) \(\chi_{5225}(4349,\cdot)\) \(\chi_{5225}(4849,\cdot)\) \(\chi_{5225}(4899,\cdot)\) \(\chi_{5225}(5174,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2927,2851,4676)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 5225 }(499, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{37}{45}\right)\) |