Basic properties
| Modulus: | \(1045\) | |
| Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{209}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1045.ce
\(\chi_{1045}(16,\cdot)\) \(\chi_{1045}(36,\cdot)\) \(\chi_{1045}(81,\cdot)\) \(\chi_{1045}(196,\cdot)\) \(\chi_{1045}(251,\cdot)\) \(\chi_{1045}(256,\cdot)\) \(\chi_{1045}(291,\cdot)\) \(\chi_{1045}(301,\cdot)\) \(\chi_{1045}(346,\cdot)\) \(\chi_{1045}(366,\cdot)\) \(\chi_{1045}(416,\cdot)\) \(\chi_{1045}(511,\cdot)\) \(\chi_{1045}(576,\cdot)\) \(\chi_{1045}(586,\cdot)\) \(\chi_{1045}(631,\cdot)\) \(\chi_{1045}(636,\cdot)\) \(\chi_{1045}(731,\cdot)\) \(\chi_{1045}(746,\cdot)\) \(\chi_{1045}(796,\cdot)\) \(\chi_{1045}(841,\cdot)\) \(\chi_{1045}(861,\cdot)\) \(\chi_{1045}(916,\cdot)\) \(\chi_{1045}(966,\cdot)\) \(\chi_{1045}(1016,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | 45.45.43679806300610465846484971330073185012597520004657724600953543350870941304329239684756561.1 |
Values on generators
\((837,761,496)\) → \((1,e\left(\frac{2}{5}\right),e\left(\frac{2}{9}\right))\)
Values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1045 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) |