Basic properties
Modulus: | \(1045\) | |
Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{209}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1045.co
\(\chi_{1045}(71,\cdot)\) \(\chi_{1045}(86,\cdot)\) \(\chi_{1045}(91,\cdot)\) \(\chi_{1045}(136,\cdot)\) \(\chi_{1045}(146,\cdot)\) \(\chi_{1045}(181,\cdot)\) \(\chi_{1045}(306,\cdot)\) \(\chi_{1045}(356,\cdot)\) \(\chi_{1045}(401,\cdot)\) \(\chi_{1045}(421,\cdot)\) \(\chi_{1045}(466,\cdot)\) \(\chi_{1045}(471,\cdot)\) \(\chi_{1045}(526,\cdot)\) \(\chi_{1045}(566,\cdot)\) \(\chi_{1045}(621,\cdot)\) \(\chi_{1045}(641,\cdot)\) \(\chi_{1045}(686,\cdot)\) \(\chi_{1045}(751,\cdot)\) \(\chi_{1045}(801,\cdot)\) \(\chi_{1045}(851,\cdot)\) \(\chi_{1045}(896,\cdot)\) \(\chi_{1045}(906,\cdot)\) \(\chi_{1045}(971,\cdot)\) \(\chi_{1045}(1021,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((837,761,496)\) → \((1,e\left(\frac{4}{5}\right),e\left(\frac{13}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 1045 }(421, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{41}{90}\right)\) |