Basic properties
Modulus: | \(8023\) | |
Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(560\) | 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 8023.gs
\(\chi_{8023}(17,\cdot)\) \(\chi_{8023}(46,\cdot)\) \(\chi_{8023}(66,\cdot)\) \(\chi_{8023}(137,\cdot)\) \(\chi_{8023}(156,\cdot)\) \(\chi_{8023}(159,\cdot)\) \(\chi_{8023}(188,\cdot)\) \(\chi_{8023}(259,\cdot)\) \(\chi_{8023}(301,\cdot)\) \(\chi_{8023}(372,\cdot)\) \(\chi_{8023}(440,\cdot)\) \(\chi_{8023}(472,\cdot)\) \(\chi_{8023}(511,\cdot)\) \(\chi_{8023}(582,\cdot)\) \(\chi_{8023}(585,\cdot)\) \(\chi_{8023}(705,\cdot)\) \(\chi_{8023}(724,\cdot)\) \(\chi_{8023}(866,\cdot)\) \(\chi_{8023}(898,\cdot)\) \(\chi_{8023}(937,\cdot)\) \(\chi_{8023}(1011,\cdot)\) \(\chi_{8023}(1040,\cdot)\) \(\chi_{8023}(1060,\cdot)\) \(\chi_{8023}(1111,\cdot)\) \(\chi_{8023}(1150,\cdot)\) \(\chi_{8023}(1153,\cdot)\) \(\chi_{8023}(1224,\cdot)\) \(\chi_{8023}(1253,\cdot)\) \(\chi_{8023}(1344,\cdot)\) \(\chi_{8023}(1366,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{560})$ |
Fixed field: | Number field defined by a degree 560 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{5}{112}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8023 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{137}{560}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{171}{560}\right)\) | \(e\left(\frac{549}{560}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{29}{140}\right)\) | \(e\left(\frac{137}{280}\right)\) | \(e\left(\frac{23}{560}\right)\) | \(e\left(\frac{1}{280}\right)\) |