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.cl
\(\chi_{8033}(4,\cdot)\) \(\chi_{8033}(13,\cdot)\) \(\chi_{8033}(64,\cdot)\) \(\chi_{8033}(120,\cdot)\) \(\chi_{8033}(122,\cdot)\) \(\chi_{8033}(208,\cdot)\) \(\chi_{8033}(225,\cdot)\) \(\chi_{8033}(341,\cdot)\) \(\chi_{8033}(353,\cdot)\) \(\chi_{8033}(390,\cdot)\) \(\chi_{8033}(399,\cdot)\) \(\chi_{8033}(470,\cdot)\) \(\chi_{8033}(502,\cdot)\) \(\chi_{8033}(527,\cdot)\) \(\chi_{8033}(535,\cdot)\) \(\chi_{8033}(613,\cdot)\) \(\chi_{8033}(618,\cdot)\) \(\chi_{8033}(676,\cdot)\) \(\chi_{8033}(700,\cdot)\) \(\chi_{8033}(747,\cdot)\) \(\chi_{8033}(905,\cdot)\) \(\chi_{8033}(933,\cdot)\) \(\chi_{8033}(1024,\cdot)\) \(\chi_{8033}(1078,\cdot)\) \(\chi_{8033}(1182,\cdot)\) \(\chi_{8033}(1369,\cdot)\) \(\chi_{8033}(1398,\cdot)\) \(\chi_{8033}(1426,\cdot)\) \(\chi_{8033}(1459,\cdot)\) \(\chi_{8033}(1646,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{161})$ |
Fixed field: | Number field defined by a degree 322 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{13}{14}\right),e\left(\frac{29}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(1646, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{161}\right)\) | \(e\left(\frac{53}{322}\right)\) | \(e\left(\frac{33}{161}\right)\) | \(e\left(\frac{19}{322}\right)\) | \(e\left(\frac{247}{322}\right)\) | \(e\left(\frac{2}{161}\right)\) | \(e\left(\frac{130}{161}\right)\) | \(e\left(\frac{53}{161}\right)\) | \(e\left(\frac{213}{322}\right)\) | \(e\left(\frac{101}{161}\right)\) |