Basic properties
Modulus: | \(8033\) | |
Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1932\) | 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.cw
\(\chi_{8033}(14,\cdot)\) \(\chi_{8033}(18,\cdot)\) \(\chi_{8033}(50,\cdot)\) \(\chi_{8033}(56,\cdot)\) \(\chi_{8033}(72,\cdot)\) \(\chi_{8033}(77,\cdot)\) \(\chi_{8033}(101,\cdot)\) \(\chi_{8033}(105,\cdot)\) \(\chi_{8033}(114,\cdot)\) \(\chi_{8033}(119,\cdot)\) \(\chi_{8033}(134,\cdot)\) \(\chi_{8033}(135,\cdot)\) \(\chi_{8033}(142,\cdot)\) \(\chi_{8033}(153,\cdot)\) \(\chi_{8033}(166,\cdot)\) \(\chi_{8033}(200,\cdot)\) \(\chi_{8033}(224,\cdot)\) \(\chi_{8033}(234,\cdot)\) \(\chi_{8033}(246,\cdot)\) \(\chi_{8033}(282,\cdot)\) \(\chi_{8033}(288,\cdot)\) \(\chi_{8033}(301,\cdot)\) \(\chi_{8033}(308,\cdot)\) \(\chi_{8033}(321,\cdot)\) \(\chi_{8033}(322,\cdot)\) \(\chi_{8033}(375,\cdot)\) \(\chi_{8033}(387,\cdot)\) \(\chi_{8033}(396,\cdot)\) \(\chi_{8033}(404,\cdot)\) \(\chi_{8033}(414,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1932})$ |
Fixed field: | Number field defined by a degree 1932 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{3}{28}\right),e\left(\frac{203}{276}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(153, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{322}\right)\) | \(e\left(\frac{1567}{1932}\right)\) | \(e\left(\frac{73}{161}\right)\) | \(e\left(\frac{179}{1932}\right)\) | \(e\left(\frac{73}{1932}\right)\) | \(e\left(\frac{451}{966}\right)\) | \(e\left(\frac{219}{322}\right)\) | \(e\left(\frac{601}{966}\right)\) | \(e\left(\frac{617}{1932}\right)\) | \(e\left(\frac{799}{966}\right)\) |