Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(280\) | 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.fh
\(\chi_{8041}(59,\cdot)\) \(\chi_{8041}(213,\cdot)\) \(\chi_{8041}(236,\cdot)\) \(\chi_{8041}(355,\cdot)\) \(\chi_{8041}(434,\cdot)\) \(\chi_{8041}(570,\cdot)\) \(\chi_{8041}(729,\cdot)\) \(\chi_{8041}(790,\cdot)\) \(\chi_{8041}(852,\cdot)\) \(\chi_{8041}(944,\cdot)\) \(\chi_{8041}(950,\cdot)\) \(\chi_{8041}(1005,\cdot)\) \(\chi_{8041}(1182,\cdot)\) \(\chi_{8041}(1215,\cdot)\) \(\chi_{8041}(1301,\cdot)\) \(\chi_{8041}(1368,\cdot)\) \(\chi_{8041}(1521,\cdot)\) \(\chi_{8041}(1589,\cdot)\) \(\chi_{8041}(1675,\cdot)\) \(\chi_{8041}(1681,\cdot)\) \(\chi_{8041}(1698,\cdot)\) \(\chi_{8041}(1736,\cdot)\) \(\chi_{8041}(1896,\cdot)\) \(\chi_{8041}(2099,\cdot)\) \(\chi_{8041}(2161,\cdot)\) \(\chi_{8041}(2314,\cdot)\) \(\chi_{8041}(2412,\cdot)\) \(\chi_{8041}(2429,\cdot)\) \(\chi_{8041}(2467,\cdot)\) \(\chi_{8041}(2535,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{280})$ |
Fixed field: | Number field defined by a degree 280 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{7}{8}\right),e\left(\frac{3}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(2314, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{253}{280}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{249}{280}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{53}{56}\right)\) |