Basic properties
Modulus: | \(8033\) | |
Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1932\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8033.cz
\(\chi_{8033}(3,\cdot)\) \(\chi_{8033}(10,\cdot)\) \(\chi_{8033}(48,\cdot)\) \(\chi_{8033}(55,\cdot)\) \(\chi_{8033}(79,\cdot)\) \(\chi_{8033}(85,\cdot)\) \(\chi_{8033}(90,\cdot)\) \(\chi_{8033}(147,\cdot)\) \(\chi_{8033}(156,\cdot)\) \(\chi_{8033}(171,\cdot)\) \(\chi_{8033}(185,\cdot)\) \(\chi_{8033}(188,\cdot)\) \(\chi_{8033}(214,\cdot)\) \(\chi_{8033}(230,\cdot)\) \(\chi_{8033}(243,\cdot)\) \(\chi_{8033}(280,\cdot)\) \(\chi_{8033}(287,\cdot)\) \(\chi_{8033}(300,\cdot)\) \(\chi_{8033}(305,\cdot)\) \(\chi_{8033}(334,\cdot)\) \(\chi_{8033}(356,\cdot)\) \(\chi_{8033}(358,\cdot)\) \(\chi_{8033}(362,\cdot)\) \(\chi_{8033}(367,\cdot)\) \(\chi_{8033}(421,\cdot)\) \(\chi_{8033}(424,\cdot)\) \(\chi_{8033}(433,\cdot)\) \(\chi_{8033}(462,\cdot)\) \(\chi_{8033}(467,\cdot)\) \(\chi_{8033}(479,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1932})$ |
Fixed field: | Number field defined by a degree 1932 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{23}{28}\right),e\left(\frac{37}{69}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{417}{644}\right)\) | \(e\left(\frac{1775}{1932}\right)\) | \(e\left(\frac{95}{322}\right)\) | \(e\left(\frac{587}{966}\right)\) | \(e\left(\frac{547}{966}\right)\) | \(e\left(\frac{316}{483}\right)\) | \(e\left(\frac{607}{644}\right)\) | \(e\left(\frac{809}{966}\right)\) | \(e\left(\frac{493}{1932}\right)\) | \(e\left(\frac{559}{1932}\right)\) |