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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8023.gx
\(\chi_{8023}(123,\cdot)\) \(\chi_{8023}(189,\cdot)\) \(\chi_{8023}(207,\cdot)\) \(\chi_{8023}(246,\cdot)\) \(\chi_{8023}(281,\cdot)\) \(\chi_{8023}(319,\cdot)\) \(\chi_{8023}(397,\cdot)\) \(\chi_{8023}(414,\cdot)\) \(\chi_{8023}(495,\cdot)\) \(\chi_{8023}(519,\cdot)\) \(\chi_{8023}(541,\cdot)\) \(\chi_{8023}(559,\cdot)\) \(\chi_{8023}(562,\cdot)\) \(\chi_{8023}(633,\cdot)\) \(\chi_{8023}(701,\cdot)\) \(\chi_{8023}(717,\cdot)\) \(\chi_{8023}(723,\cdot)\) \(\chi_{8023}(794,\cdot)\) \(\chi_{8023}(803,\cdot)\) \(\chi_{8023}(828,\cdot)\) \(\chi_{8023}(849,\cdot)\) \(\chi_{8023}(921,\cdot)\) \(\chi_{8023}(984,\cdot)\) \(\chi_{8023}(990,\cdot)\) \(\chi_{8023}(1038,\cdot)\) \(\chi_{8023}(1109,\cdot)\) \(\chi_{8023}(1118,\cdot)\) \(\chi_{8023}(1124,\cdot)\) \(\chi_{8023}(1149,\cdot)\) \(\chi_{8023}(1169,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{560})$ |
Fixed field: | Number field defined by a degree 560 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{51}{70}\right),e\left(\frac{95}{112}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8023 }(123, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{443}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{449}{560}\right)\) | \(e\left(\frac{191}{560}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{163}{280}\right)\) | \(e\left(\frac{197}{560}\right)\) | \(e\left(\frac{99}{280}\right)\) |