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.fy
\(\chi_{8041}(9,\cdot)\) \(\chi_{8041}(15,\cdot)\) \(\chi_{8041}(25,\cdot)\) \(\chi_{8041}(53,\cdot)\) \(\chi_{8041}(60,\cdot)\) \(\chi_{8041}(185,\cdot)\) \(\chi_{8041}(196,\cdot)\) \(\chi_{8041}(212,\cdot)\) \(\chi_{8041}(229,\cdot)\) \(\chi_{8041}(240,\cdot)\) \(\chi_{8041}(246,\cdot)\) \(\chi_{8041}(400,\cdot)\) \(\chi_{8041}(410,\cdot)\) \(\chi_{8041}(427,\cdot)\) \(\chi_{8041}(444,\cdot)\) \(\chi_{8041}(576,\cdot)\) \(\chi_{8041}(597,\cdot)\) \(\chi_{8041}(654,\cdot)\) \(\chi_{8041}(740,\cdot)\) \(\chi_{8041}(746,\cdot)\) \(\chi_{8041}(784,\cdot)\) \(\chi_{8041}(797,\cdot)\) \(\chi_{8041}(841,\cdot)\) \(\chi_{8041}(916,\cdot)\) \(\chi_{8041}(927,\cdot)\) \(\chi_{8041}(960,\cdot)\) \(\chi_{8041}(961,\cdot)\) \(\chi_{8041}(971,\cdot)\) \(\chi_{8041}(977,\cdot)\) \(\chi_{8041}(984,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{840})$ |
Fixed field: | Number field defined by a degree 840 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{3}{8}\right),e\left(\frac{16}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(185, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{140}\right)\) | \(e\left(\frac{787}{840}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{271}{840}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{37}{140}\right)\) | \(e\left(\frac{367}{420}\right)\) | \(e\left(\frac{125}{168}\right)\) | \(e\left(\frac{131}{168}\right)\) |