Basic properties
Modulus: | \(1045\) | |
Conductor: | \(1045\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1045.cp
\(\chi_{1045}(24,\cdot)\) \(\chi_{1045}(74,\cdot)\) \(\chi_{1045}(139,\cdot)\) \(\chi_{1045}(149,\cdot)\) \(\chi_{1045}(194,\cdot)\) \(\chi_{1045}(244,\cdot)\) \(\chi_{1045}(294,\cdot)\) \(\chi_{1045}(359,\cdot)\) \(\chi_{1045}(404,\cdot)\) \(\chi_{1045}(424,\cdot)\) \(\chi_{1045}(479,\cdot)\) \(\chi_{1045}(519,\cdot)\) \(\chi_{1045}(574,\cdot)\) \(\chi_{1045}(579,\cdot)\) \(\chi_{1045}(624,\cdot)\) \(\chi_{1045}(644,\cdot)\) \(\chi_{1045}(689,\cdot)\) \(\chi_{1045}(739,\cdot)\) \(\chi_{1045}(864,\cdot)\) \(\chi_{1045}(899,\cdot)\) \(\chi_{1045}(909,\cdot)\) \(\chi_{1045}(954,\cdot)\) \(\chi_{1045}(959,\cdot)\) \(\chi_{1045}(974,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((837,761,496)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{2}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 1045 }(149, a) \) | \(-1\) | \(1\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) |