Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(168\) | 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.eu
\(\chi_{8041}(76,\cdot)\) \(\chi_{8041}(263,\cdot)\) \(\chi_{8041}(406,\cdot)\) \(\chi_{8041}(417,\cdot)\) \(\chi_{8041}(450,\cdot)\) \(\chi_{8041}(593,\cdot)\) \(\chi_{8041}(648,\cdot)\) \(\chi_{8041}(835,\cdot)\) \(\chi_{8041}(1022,\cdot)\) \(\chi_{8041}(1209,\cdot)\) \(\chi_{8041}(1352,\cdot)\) \(\chi_{8041}(1396,\cdot)\) \(\chi_{8041}(1539,\cdot)\) \(\chi_{8041}(2133,\cdot)\) \(\chi_{8041}(2463,\cdot)\) \(\chi_{8041}(2694,\cdot)\) \(\chi_{8041}(3079,\cdot)\) \(\chi_{8041}(3211,\cdot)\) \(\chi_{8041}(3255,\cdot)\) \(\chi_{8041}(3409,\cdot)\) \(\chi_{8041}(3640,\cdot)\) \(\chi_{8041}(3959,\cdot)\) \(\chi_{8041}(4146,\cdot)\) \(\chi_{8041}(4157,\cdot)\) \(\chi_{8041}(4190,\cdot)\) \(\chi_{8041}(4201,\cdot)\) \(\chi_{8041}(4333,\cdot)\) \(\chi_{8041}(4377,\cdot)\) \(\chi_{8041}(4520,\cdot)\) \(\chi_{8041}(4707,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{168})$ |
Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{11}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(3255, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{149}{168}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{113}{168}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{167}{168}\right)\) | \(e\left(\frac{89}{168}\right)\) |