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.db
\(\chi_{8033}(11,\cdot)\) \(\chi_{8033}(31,\cdot)\) \(\chi_{8033}(43,\cdot)\) \(\chi_{8033}(44,\cdot)\) \(\chi_{8033}(68,\cdot)\) \(\chi_{8033}(97,\cdot)\) \(\chi_{8033}(98,\cdot)\) \(\chi_{8033}(124,\cdot)\) \(\chi_{8033}(126,\cdot)\) \(\chi_{8033}(127,\cdot)\) \(\chi_{8033}(137,\cdot)\) \(\chi_{8033}(143,\cdot)\) \(\chi_{8033}(163,\cdot)\) \(\chi_{8033}(172,\cdot)\) \(\chi_{8033}(176,\cdot)\) \(\chi_{8033}(184,\cdot)\) \(\chi_{8033}(205,\cdot)\) \(\chi_{8033}(221,\cdot)\) \(\chi_{8033}(253,\cdot)\) \(\chi_{8033}(259,\cdot)\) \(\chi_{8033}(263,\cdot)\) \(\chi_{8033}(271,\cdot)\) \(\chi_{8033}(272,\cdot)\) \(\chi_{8033}(327,\cdot)\) \(\chi_{8033}(330,\cdot)\) \(\chi_{8033}(333,\cdot)\) \(\chi_{8033}(345,\cdot)\) \(\chi_{8033}(374,\cdot)\) \(\chi_{8033}(380,\cdot)\) \(\chi_{8033}(388,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1932})$ |
Fixed field: | Number field defined by a degree 1932 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{17}{28}\right),e\left(\frac{179}{276}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(137, a) \) | \(1\) | \(1\) | \(e\left(\frac{152}{161}\right)\) | \(e\left(\frac{1861}{1932}\right)\) | \(e\left(\frac{143}{161}\right)\) | \(e\left(\frac{11}{1932}\right)\) | \(e\left(\frac{1753}{1932}\right)\) | \(e\left(\frac{535}{966}\right)\) | \(e\left(\frac{134}{161}\right)\) | \(e\left(\frac{895}{966}\right)\) | \(e\left(\frac{1835}{1932}\right)\) | \(e\left(\frac{347}{483}\right)\) |