Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1680\) | 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 8041.gd
\(\chi_{8041}(3,\cdot)\) \(\chi_{8041}(5,\cdot)\) \(\chi_{8041}(20,\cdot)\) \(\chi_{8041}(48,\cdot)\) \(\chi_{8041}(71,\cdot)\) \(\chi_{8041}(91,\cdot)\) \(\chi_{8041}(114,\cdot)\) \(\chi_{8041}(141,\cdot)\) \(\chi_{8041}(147,\cdot)\) \(\chi_{8041}(148,\cdot)\) \(\chi_{8041}(158,\cdot)\) \(\chi_{8041}(159,\cdot)\) \(\chi_{8041}(163,\cdot)\) \(\chi_{8041}(190,\cdot)\) \(\chi_{8041}(192,\cdot)\) \(\chi_{8041}(201,\cdot)\) \(\chi_{8041}(218,\cdot)\) \(\chi_{8041}(235,\cdot)\) \(\chi_{8041}(245,\cdot)\) \(\chi_{8041}(278,\cdot)\) \(\chi_{8041}(284,\cdot)\) \(\chi_{8041}(313,\cdot)\) \(\chi_{8041}(334,\cdot)\) \(\chi_{8041}(335,\cdot)\) \(\chi_{8041}(377,\cdot)\) \(\chi_{8041}(405,\cdot)\) \(\chi_{8041}(449,\cdot)\) \(\chi_{8041}(456,\cdot)\) \(\chi_{8041}(499,\cdot)\) \(\chi_{8041}(521,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1680})$ |
Fixed field: | Number field defined by a degree 1680 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{9}{16}\right),e\left(\frac{17}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(456, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{280}\right)\) | \(e\left(\frac{281}{1680}\right)\) | \(e\left(\frac{57}{140}\right)\) | \(e\left(\frac{893}{1680}\right)\) | \(e\left(\frac{89}{240}\right)\) | \(e\left(\frac{37}{240}\right)\) | \(e\left(\frac{171}{280}\right)\) | \(e\left(\frac{281}{840}\right)\) | \(e\left(\frac{247}{336}\right)\) | \(e\left(\frac{193}{336}\right)\) |