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 \(\chi_{209}(6,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1045.cj
\(\chi_{1045}(6,\cdot)\) \(\chi_{1045}(61,\cdot)\) \(\chi_{1045}(101,\cdot)\) \(\chi_{1045}(156,\cdot)\) \(\chi_{1045}(161,\cdot)\) \(\chi_{1045}(206,\cdot)\) \(\chi_{1045}(226,\cdot)\) \(\chi_{1045}(271,\cdot)\) \(\chi_{1045}(321,\cdot)\) \(\chi_{1045}(446,\cdot)\) \(\chi_{1045}(481,\cdot)\) \(\chi_{1045}(491,\cdot)\) \(\chi_{1045}(536,\cdot)\) \(\chi_{1045}(541,\cdot)\) \(\chi_{1045}(556,\cdot)\) \(\chi_{1045}(651,\cdot)\) \(\chi_{1045}(701,\cdot)\) \(\chi_{1045}(766,\cdot)\) \(\chi_{1045}(776,\cdot)\) \(\chi_{1045}(821,\cdot)\) \(\chi_{1045}(871,\cdot)\) \(\chi_{1045}(921,\cdot)\) \(\chi_{1045}(986,\cdot)\) \(\chi_{1045}(1031,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((837,761,496)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{7}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 1045 }(6, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{29}{45}\right)\) |