Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(840\) | 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.fw
\(\chi_{8041}(19,\cdot)\) \(\chi_{8041}(134,\cdot)\) \(\chi_{8041}(162,\cdot)\) \(\chi_{8041}(206,\cdot)\) \(\chi_{8041}(270,\cdot)\) \(\chi_{8041}(304,\cdot)\) \(\chi_{8041}(321,\cdot)\) \(\chi_{8041}(349,\cdot)\) \(\chi_{8041}(491,\cdot)\) \(\chi_{8041}(501,\cdot)\) \(\chi_{8041}(502,\cdot)\) \(\chi_{8041}(519,\cdot)\) \(\chi_{8041}(535,\cdot)\) \(\chi_{8041}(536,\cdot)\) \(\chi_{8041}(546,\cdot)\) \(\chi_{8041}(678,\cdot)\) \(\chi_{8041}(706,\cdot)\) \(\chi_{8041}(722,\cdot)\) \(\chi_{8041}(750,\cdot)\) \(\chi_{8041}(865,\cdot)\) \(\chi_{8041}(886,\cdot)\) \(\chi_{8041}(893,\cdot)\) \(\chi_{8041}(937,\cdot)\) \(\chi_{8041}(1018,\cdot)\) \(\chi_{8041}(1052,\cdot)\) \(\chi_{8041}(1062,\cdot)\) \(\chi_{8041}(1080,\cdot)\) \(\chi_{8041}(1130,\cdot)\) \(\chi_{8041}(1216,\cdot)\) \(\chi_{8041}(1250,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{840})$ |
Fixed field: | Number field defined by a degree 840 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{3}{8}\right),e\left(\frac{25}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(865, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{479}{840}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{467}{840}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{59}{420}\right)\) | \(e\left(\frac{97}{168}\right)\) | \(e\left(\frac{103}{168}\right)\) |