Basic properties
Modulus: | \(8032\) | |
Conductor: | \(8032\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1000\) | 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)
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Galois orbit 8032.ck
\(\chi_{8032}(13,\cdot)\) \(\chi_{8032}(21,\cdot)\) \(\chi_{8032}(45,\cdot)\) \(\chi_{8032}(85,\cdot)\) \(\chi_{8032}(93,\cdot)\) \(\chi_{8032}(101,\cdot)\) \(\chi_{8032}(117,\cdot)\) \(\chi_{8032}(173,\cdot)\) \(\chi_{8032}(181,\cdot)\) \(\chi_{8032}(189,\cdot)\) \(\chi_{8032}(197,\cdot)\) \(\chi_{8032}(205,\cdot)\) \(\chi_{8032}(221,\cdot)\) \(\chi_{8032}(237,\cdot)\) \(\chi_{8032}(245,\cdot)\) \(\chi_{8032}(309,\cdot)\) \(\chi_{8032}(317,\cdot)\) \(\chi_{8032}(325,\cdot)\) \(\chi_{8032}(357,\cdot)\) \(\chi_{8032}(365,\cdot)\) \(\chi_{8032}(373,\cdot)\) \(\chi_{8032}(405,\cdot)\) \(\chi_{8032}(445,\cdot)\) \(\chi_{8032}(469,\cdot)\) \(\chi_{8032}(509,\cdot)\) \(\chi_{8032}(517,\cdot)\) \(\chi_{8032}(525,\cdot)\) \(\chi_{8032}(533,\cdot)\) \(\chi_{8032}(541,\cdot)\) \(\chi_{8032}(581,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1000})$ |
Fixed field: | Number field defined by a degree 1000 polynomial (not computed) |
Values on generators
\((6527,3013,257)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{91}{125}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8032 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{273}{1000}\right)\) | \(e\left(\frac{103}{200}\right)\) | \(e\left(\frac{147}{500}\right)\) | \(e\left(\frac{273}{500}\right)\) | \(e\left(\frac{983}{1000}\right)\) | \(e\left(\frac{621}{1000}\right)\) | \(e\left(\frac{197}{250}\right)\) | \(e\left(\frac{93}{250}\right)\) | \(e\left(\frac{789}{1000}\right)\) | \(e\left(\frac{567}{1000}\right)\) |