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 \(\chi_{209}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1045.cm
\(\chi_{1045}(41,\cdot)\) \(\chi_{1045}(51,\cdot)\) \(\chi_{1045}(116,\cdot)\) \(\chi_{1045}(211,\cdot)\) \(\chi_{1045}(261,\cdot)\) \(\chi_{1045}(281,\cdot)\) \(\chi_{1045}(326,\cdot)\) \(\chi_{1045}(336,\cdot)\) \(\chi_{1045}(371,\cdot)\) \(\chi_{1045}(376,\cdot)\) \(\chi_{1045}(431,\cdot)\) \(\chi_{1045}(546,\cdot)\) \(\chi_{1045}(591,\cdot)\) \(\chi_{1045}(611,\cdot)\) \(\chi_{1045}(656,\cdot)\) \(\chi_{1045}(706,\cdot)\) \(\chi_{1045}(756,\cdot)\) \(\chi_{1045}(811,\cdot)\) \(\chi_{1045}(831,\cdot)\) \(\chi_{1045}(876,\cdot)\) \(\chi_{1045}(926,\cdot)\) \(\chi_{1045}(941,\cdot)\) \(\chi_{1045}(1036,\cdot)\) \(\chi_{1045}(1041,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((837,761,496)\) → \((1,e\left(\frac{3}{10}\right),e\left(\frac{13}{18}\right))\)
Values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1045 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{41}{90}\right)\) |