Basic properties
| Modulus: | \(891\) | |
| Conductor: | \(297\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{297}(203,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 891.z
\(\chi_{891}(71,\cdot)\) \(\chi_{891}(125,\cdot)\) \(\chi_{891}(152,\cdot)\) \(\chi_{891}(170,\cdot)\) \(\chi_{891}(179,\cdot)\) \(\chi_{891}(224,\cdot)\) \(\chi_{891}(251,\cdot)\) \(\chi_{891}(278,\cdot)\) \(\chi_{891}(368,\cdot)\) \(\chi_{891}(422,\cdot)\) \(\chi_{891}(449,\cdot)\) \(\chi_{891}(467,\cdot)\) \(\chi_{891}(476,\cdot)\) \(\chi_{891}(521,\cdot)\) \(\chi_{891}(548,\cdot)\) \(\chi_{891}(575,\cdot)\) \(\chi_{891}(665,\cdot)\) \(\chi_{891}(719,\cdot)\) \(\chi_{891}(746,\cdot)\) \(\chi_{891}(764,\cdot)\) \(\chi_{891}(773,\cdot)\) \(\chi_{891}(818,\cdot)\) \(\chi_{891}(845,\cdot)\) \(\chi_{891}(872,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((650,244)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 891 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) |