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.cv
\(\chi_{8033}(22,\cdot)\) \(\chi_{8033}(34,\cdot)\) \(\chi_{8033}(62,\cdot)\) \(\chi_{8033}(63,\cdot)\) \(\chi_{8033}(92,\cdot)\) \(\chi_{8033}(121,\cdot)\) \(\chi_{8033}(187,\cdot)\) \(\chi_{8033}(196,\cdot)\) \(\chi_{8033}(254,\cdot)\) \(\chi_{8033}(267,\cdot)\) \(\chi_{8033}(274,\cdot)\) \(\chi_{8033}(299,\cdot)\) \(\chi_{8033}(324,\cdot)\) \(\chi_{8033}(352,\cdot)\) \(\chi_{8033}(383,\cdot)\) \(\chi_{8033}(410,\cdot)\) \(\chi_{8033}(469,\cdot)\) \(\chi_{8033}(473,\cdot)\) \(\chi_{8033}(497,\cdot)\) \(\chi_{8033}(499,\cdot)\) \(\chi_{8033}(506,\cdot)\) \(\chi_{8033}(526,\cdot)\) \(\chi_{8033}(531,\cdot)\) \(\chi_{8033}(544,\cdot)\) \(\chi_{8033}(593,\cdot)\) \(\chi_{8033}(643,\cdot)\) \(\chi_{8033}(660,\cdot)\) \(\chi_{8033}(731,\cdot)\) \(\chi_{8033}(760,\cdot)\) \(\chi_{8033}(776,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{483})$ |
Fixed field: | Number field defined by a degree 966 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{1}{14}\right),e\left(\frac{137}{138}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(410, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{161}\right)\) | \(e\left(\frac{961}{966}\right)\) | \(e\left(\frac{2}{161}\right)\) | \(e\left(\frac{545}{966}\right)\) | \(e\left(\frac{1}{966}\right)\) | \(e\left(\frac{337}{483}\right)\) | \(e\left(\frac{3}{161}\right)\) | \(e\left(\frac{478}{483}\right)\) | \(e\left(\frac{551}{966}\right)\) | \(e\left(\frac{355}{483}\right)\) |