Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(336\) | 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 8041.fl
\(\chi_{8041}(10,\cdot)\) \(\chi_{8041}(109,\cdot)\) \(\chi_{8041}(142,\cdot)\) \(\chi_{8041}(197,\cdot)\) \(\chi_{8041}(296,\cdot)\) \(\chi_{8041}(318,\cdot)\) \(\chi_{8041}(384,\cdot)\) \(\chi_{8041}(439,\cdot)\) \(\chi_{8041}(483,\cdot)\) \(\chi_{8041}(615,\cdot)\) \(\chi_{8041}(626,\cdot)\) \(\chi_{8041}(670,\cdot)\) \(\chi_{8041}(703,\cdot)\) \(\chi_{8041}(857,\cdot)\) \(\chi_{8041}(912,\cdot)\) \(\chi_{8041}(1099,\cdot)\) \(\chi_{8041}(1132,\cdot)\) \(\chi_{8041}(1176,\cdot)\) \(\chi_{8041}(1264,\cdot)\) \(\chi_{8041}(1561,\cdot)\) \(\chi_{8041}(1605,\cdot)\) \(\chi_{8041}(1737,\cdot)\) \(\chi_{8041}(1858,\cdot)\) \(\chi_{8041}(1880,\cdot)\) \(\chi_{8041}(2001,\cdot)\) \(\chi_{8041}(2034,\cdot)\) \(\chi_{8041}(2045,\cdot)\) \(\chi_{8041}(2122,\cdot)\) \(\chi_{8041}(2188,\cdot)\) \(\chi_{8041}(2353,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{336})$ |
Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((-1,e\left(\frac{1}{16}\right),e\left(\frac{13}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(1176, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{229}{336}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{265}{336}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{61}{168}\right)\) | \(e\left(\frac{295}{336}\right)\) | \(e\left(\frac{289}{336}\right)\) |