Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(560\) | 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 8023.gu
\(\chi_{8023}(132,\cdot)\) \(\chi_{8023}(220,\cdot)\) \(\chi_{8023}(272,\cdot)\) \(\chi_{8023}(306,\cdot)\) \(\chi_{8023}(362,\cdot)\) \(\chi_{8023}(386,\cdot)\) \(\chi_{8023}(418,\cdot)\) \(\chi_{8023}(510,\cdot)\) \(\chi_{8023}(599,\cdot)\) \(\chi_{8023}(603,\cdot)\) \(\chi_{8023}(631,\cdot)\) \(\chi_{8023}(661,\cdot)\) \(\chi_{8023}(672,\cdot)\) \(\chi_{8023}(683,\cdot)\) \(\chi_{8023}(752,\cdot)\) \(\chi_{8023}(762,\cdot)\) \(\chi_{8023}(814,\cdot)\) \(\chi_{8023}(834,\cdot)\) \(\chi_{8023}(846,\cdot)\) \(\chi_{8023}(850,\cdot)\) \(\chi_{8023}(914,\cdot)\) \(\chi_{8023}(1005,\cdot)\) \(\chi_{8023}(1046,\cdot)\) \(\chi_{8023}(1087,\cdot)\) \(\chi_{8023}(1096,\cdot)\) \(\chi_{8023}(1120,\cdot)\) \(\chi_{8023}(1204,\cdot)\) \(\chi_{8023}(1260,\cdot)\) \(\chi_{8023}(1263,\cdot)\) \(\chi_{8023}(1270,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{560})$ |
| Fixed field: | Number field defined by a degree 560 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{69}{70}\right),e\left(\frac{99}{112}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(132, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{541}{560}\right)\) | \(e\left(\frac{19}{560}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{79}{140}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{271}{280}\right)\) |