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.cl
\(\chi_{1045}(14,\cdot)\) \(\chi_{1045}(59,\cdot)\) \(\chi_{1045}(124,\cdot)\) \(\chi_{1045}(174,\cdot)\) \(\chi_{1045}(224,\cdot)\) \(\chi_{1045}(269,\cdot)\) \(\chi_{1045}(279,\cdot)\) \(\chi_{1045}(344,\cdot)\) \(\chi_{1045}(394,\cdot)\) \(\chi_{1045}(489,\cdot)\) \(\chi_{1045}(504,\cdot)\) \(\chi_{1045}(509,\cdot)\) \(\chi_{1045}(554,\cdot)\) \(\chi_{1045}(564,\cdot)\) \(\chi_{1045}(599,\cdot)\) \(\chi_{1045}(724,\cdot)\) \(\chi_{1045}(774,\cdot)\) \(\chi_{1045}(819,\cdot)\) \(\chi_{1045}(839,\cdot)\) \(\chi_{1045}(884,\cdot)\) \(\chi_{1045}(889,\cdot)\) \(\chi_{1045}(944,\cdot)\) \(\chi_{1045}(984,\cdot)\) \(\chi_{1045}(1039,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((837,761,496)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{1}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 1045 }(819, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{53}{90}\right)\) |