Basic properties
Modulus: | \(8033\) | |
Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(966\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8033.ct
\(\chi_{8033}(7,\cdot)\) \(\chi_{8033}(25,\cdot)\) \(\chi_{8033}(36,\cdot)\) \(\chi_{8033}(83,\cdot)\) \(\chi_{8033}(112,\cdot)\) \(\chi_{8033}(123,\cdot)\) \(\chi_{8033}(141,\cdot)\) \(\chi_{8033}(198,\cdot)\) \(\chi_{8033}(210,\cdot)\) \(\chi_{8033}(228,\cdot)\) \(\chi_{8033}(268,\cdot)\) \(\chi_{8033}(284,\cdot)\) \(\chi_{8033}(306,\cdot)\) \(\chi_{8033}(313,\cdot)\) \(\chi_{8033}(339,\cdot)\) \(\chi_{8033}(364,\cdot)\) \(\chi_{8033}(400,\cdot)\) \(\chi_{8033}(487,\cdot)\) \(\chi_{8033}(545,\cdot)\) \(\chi_{8033}(576,\cdot)\) \(\chi_{8033}(616,\cdot)\) \(\chi_{8033}(629,\cdot)\) \(\chi_{8033}(687,\cdot)\) \(\chi_{8033}(741,\cdot)\) \(\chi_{8033}(750,\cdot)\) \(\chi_{8033}(774,\cdot)\) \(\chi_{8033}(803,\cdot)\) \(\chi_{8033}(808,\cdot)\) \(\chi_{8033}(828,\cdot)\) \(\chi_{8033}(865,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{483})$ |
Fixed field: | Number field defined by a degree 966 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{4}{7}\right),e\left(\frac{65}{138}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(141, a) \) | \(1\) | \(1\) | \(e\left(\frac{261}{322}\right)\) | \(e\left(\frac{197}{483}\right)\) | \(e\left(\frac{100}{161}\right)\) | \(e\left(\frac{41}{966}\right)\) | \(e\left(\frac{211}{966}\right)\) | \(e\left(\frac{106}{483}\right)\) | \(e\left(\frac{139}{322}\right)\) | \(e\left(\frac{394}{483}\right)\) | \(e\left(\frac{412}{483}\right)\) | \(e\left(\frac{563}{966}\right)\) |