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 \(\chi_{1045}(214,\cdot)\) | 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
\((2927,2851,4676)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{8}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 5225 }(3349, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) |