Basic properties
| Modulus: | \(8033\) | |
| Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(322\) | 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 8033.ck
\(\chi_{8033}(74,\cdot)\) \(\chi_{8033}(281,\cdot)\) \(\chi_{8033}(343,\cdot)\) \(\chi_{8033}(397,\cdot)\) \(\chi_{8033}(538,\cdot)\) \(\chi_{8033}(558,\cdot)\) \(\chi_{8033}(567,\cdot)\) \(\chi_{8033}(575,\cdot)\) \(\chi_{8033}(662,\cdot)\) \(\chi_{8033}(674,\cdot)\) \(\chi_{8033}(779,\cdot)\) \(\chi_{8033}(835,\cdot)\) \(\chi_{8033}(890,\cdot)\) \(\chi_{8033}(895,\cdot)\) \(\chi_{8033}(944,\cdot)\) \(\chi_{8033}(951,\cdot)\) \(\chi_{8033}(953,\cdot)\) \(\chi_{8033}(977,\cdot)\) \(\chi_{8033}(1039,\cdot)\) \(\chi_{8033}(1089,\cdot)\) \(\chi_{8033}(1167,\cdot)\) \(\chi_{8033}(1184,\cdot)\) \(\chi_{8033}(1254,\cdot)\) \(\chi_{8033}(1301,\cdot)\) \(\chi_{8033}(1358,\cdot)\) \(\chi_{8033}(1444,\cdot)\) \(\chi_{8033}(1531,\cdot)\) \(\chi_{8033}(1736,\cdot)\) \(\chi_{8033}(1764,\cdot)\) \(\chi_{8033}(1909,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{161})$ |
| Fixed field: | Number field defined by a degree 322 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{2}{7}\right),e\left(\frac{11}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8033 }(343, a) \) | \(1\) | \(1\) | \(e\left(\frac{141}{322}\right)\) | \(e\left(\frac{62}{161}\right)\) | \(e\left(\frac{141}{161}\right)\) | \(e\left(\frac{169}{322}\right)\) | \(e\left(\frac{265}{322}\right)\) | \(e\left(\frac{111}{161}\right)\) | \(e\left(\frac{101}{322}\right)\) | \(e\left(\frac{124}{161}\right)\) | \(e\left(\frac{155}{161}\right)\) | \(e\left(\frac{263}{322}\right)\) |