Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(140\) | 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.en
\(\chi_{8041}(217,\cdot)\) \(\chi_{8041}(591,\cdot)\) \(\chi_{8041}(667,\cdot)\) \(\chi_{8041}(684,\cdot)\) \(\chi_{8041}(710,\cdot)\) \(\chi_{8041}(948,\cdot)\) \(\chi_{8041}(1322,\cdot)\) \(\chi_{8041}(1415,\cdot)\) \(\chi_{8041}(1458,\cdot)\) \(\chi_{8041}(1636,\cdot)\) \(\chi_{8041}(1679,\cdot)\) \(\chi_{8041}(1900,\cdot)\) \(\chi_{8041}(2010,\cdot)\) \(\chi_{8041}(2053,\cdot)\) \(\chi_{8041}(2129,\cdot)\) \(\chi_{8041}(2367,\cdot)\) \(\chi_{8041}(2631,\cdot)\) \(\chi_{8041}(2741,\cdot)\) \(\chi_{8041}(2877,\cdot)\) \(\chi_{8041}(3098,\cdot)\) \(\chi_{8041}(3141,\cdot)\) \(\chi_{8041}(3209,\cdot)\) \(\chi_{8041}(3319,\cdot)\) \(\chi_{8041}(3362,\cdot)\) \(\chi_{8041}(3472,\cdot)\) \(\chi_{8041}(3515,\cdot)\) \(\chi_{8041}(3940,\cdot)\) \(\chi_{8041}(4050,\cdot)\) \(\chi_{8041}(4560,\cdot)\) \(\chi_{8041}(4628,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{140})$ |
Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{7}{10}\right),i,e\left(\frac{9}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(1679, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{69}{140}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{17}{140}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{17}{28}\right)\) |