Basic properties
Modulus: | \(1089\) | |
Conductor: | \(363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{363}(80,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1089.z
\(\chi_{1089}(26,\cdot)\) \(\chi_{1089}(53,\cdot)\) \(\chi_{1089}(71,\cdot)\) \(\chi_{1089}(80,\cdot)\) \(\chi_{1089}(125,\cdot)\) \(\chi_{1089}(152,\cdot)\) \(\chi_{1089}(170,\cdot)\) \(\chi_{1089}(179,\cdot)\) \(\chi_{1089}(224,\cdot)\) \(\chi_{1089}(278,\cdot)\) \(\chi_{1089}(350,\cdot)\) \(\chi_{1089}(368,\cdot)\) \(\chi_{1089}(377,\cdot)\) \(\chi_{1089}(422,\cdot)\) \(\chi_{1089}(449,\cdot)\) \(\chi_{1089}(467,\cdot)\) \(\chi_{1089}(476,\cdot)\) \(\chi_{1089}(521,\cdot)\) \(\chi_{1089}(548,\cdot)\) \(\chi_{1089}(566,\cdot)\) \(\chi_{1089}(575,\cdot)\) \(\chi_{1089}(620,\cdot)\) \(\chi_{1089}(647,\cdot)\) \(\chi_{1089}(665,\cdot)\) \(\chi_{1089}(674,\cdot)\) \(\chi_{1089}(719,\cdot)\) \(\chi_{1089}(746,\cdot)\) \(\chi_{1089}(764,\cdot)\) \(\chi_{1089}(773,\cdot)\) \(\chi_{1089}(818,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((848,244)\) → \((-1,e\left(\frac{39}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 1089 }(80, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{27}{110}\right)\) |