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.cn
\(\chi_{1045}(29,\cdot)\) \(\chi_{1045}(79,\cdot)\) \(\chi_{1045}(129,\cdot)\) \(\chi_{1045}(184,\cdot)\) \(\chi_{1045}(204,\cdot)\) \(\chi_{1045}(249,\cdot)\) \(\chi_{1045}(299,\cdot)\) \(\chi_{1045}(314,\cdot)\) \(\chi_{1045}(409,\cdot)\) \(\chi_{1045}(414,\cdot)\) \(\chi_{1045}(459,\cdot)\) \(\chi_{1045}(469,\cdot)\) \(\chi_{1045}(534,\cdot)\) \(\chi_{1045}(629,\cdot)\) \(\chi_{1045}(679,\cdot)\) \(\chi_{1045}(699,\cdot)\) \(\chi_{1045}(744,\cdot)\) \(\chi_{1045}(754,\cdot)\) \(\chi_{1045}(789,\cdot)\) \(\chi_{1045}(794,\cdot)\) \(\chi_{1045}(849,\cdot)\) \(\chi_{1045}(964,\cdot)\) \(\chi_{1045}(1009,\cdot)\) \(\chi_{1045}(1029,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((837,761,496)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1045 }(849, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{67}{90}\right)\) |