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.cu
\(\chi_{8033}(9,\cdot)\) \(\chi_{8033}(67,\cdot)\) \(\chi_{8033}(71,\cdot)\) \(\chi_{8033}(91,\cdot)\) \(\chi_{8033}(100,\cdot)\) \(\chi_{8033}(154,\cdot)\) \(\chi_{8033}(207,\cdot)\) \(\chi_{8033}(237,\cdot)\) \(\chi_{8033}(238,\cdot)\) \(\chi_{8033}(241,\cdot)\) \(\chi_{8033}(265,\cdot)\) \(\chi_{8033}(270,\cdot)\) \(\chi_{8033}(325,\cdot)\) \(\chi_{8033}(332,\cdot)\) \(\chi_{8033}(448,\cdot)\) \(\chi_{8033}(468,\cdot)\) \(\chi_{8033}(515,\cdot)\) \(\chi_{8033}(557,\cdot)\) \(\chi_{8033}(564,\cdot)\) \(\chi_{8033}(602,\cdot)\) \(\chi_{8033}(642,\cdot)\) \(\chi_{8033}(644,\cdot)\) \(\chi_{8033}(701,\cdot)\) \(\chi_{8033}(792,\cdot)\) \(\chi_{8033}(834,\cdot)\) \(\chi_{8033}(854,\cdot)\) \(\chi_{8033}(879,\cdot)\) \(\chi_{8033}(912,\cdot)\) \(\chi_{8033}(921,\cdot)\) \(\chi_{8033}(1019,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{483})$ |
Fixed field: | Number field defined by a degree 966 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{3}{14}\right),e\left(\frac{62}{69}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(644, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{322}\right)\) | \(e\left(\frac{965}{966}\right)\) | \(e\left(\frac{97}{161}\right)\) | \(e\left(\frac{296}{483}\right)\) | \(e\left(\frac{145}{483}\right)\) | \(e\left(\frac{164}{483}\right)\) | \(e\left(\frac{291}{322}\right)\) | \(e\left(\frac{482}{483}\right)\) | \(e\left(\frac{883}{966}\right)\) | \(e\left(\frac{625}{966}\right)\) |