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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1045.ck
\(\chi_{1045}(4,\cdot)\) \(\chi_{1045}(9,\cdot)\) \(\chi_{1045}(104,\cdot)\) \(\chi_{1045}(119,\cdot)\) \(\chi_{1045}(169,\cdot)\) \(\chi_{1045}(214,\cdot)\) \(\chi_{1045}(234,\cdot)\) \(\chi_{1045}(289,\cdot)\) \(\chi_{1045}(339,\cdot)\) \(\chi_{1045}(389,\cdot)\) \(\chi_{1045}(434,\cdot)\) \(\chi_{1045}(454,\cdot)\) \(\chi_{1045}(499,\cdot)\) \(\chi_{1045}(614,\cdot)\) \(\chi_{1045}(669,\cdot)\) \(\chi_{1045}(674,\cdot)\) \(\chi_{1045}(709,\cdot)\) \(\chi_{1045}(719,\cdot)\) \(\chi_{1045}(764,\cdot)\) \(\chi_{1045}(784,\cdot)\) \(\chi_{1045}(834,\cdot)\) \(\chi_{1045}(929,\cdot)\) \(\chi_{1045}(994,\cdot)\) \(\chi_{1045}(1004,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((837,761,496)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1045 }(104, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) |