Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(112\) | 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.ei
\(\chi_{8041}(54,\cdot)\) \(\chi_{8041}(164,\cdot)\) \(\chi_{8041}(428,\cdot)\) \(\chi_{8041}(692,\cdot)\) \(\chi_{8041}(1000,\cdot)\) \(\chi_{8041}(1110,\cdot)\) \(\chi_{8041}(1374,\cdot)\) \(\chi_{8041}(1440,\cdot)\) \(\chi_{8041}(1473,\cdot)\) \(\chi_{8041}(1638,\cdot)\) \(\chi_{8041}(1693,\cdot)\) \(\chi_{8041}(1847,\cdot)\) \(\chi_{8041}(2111,\cdot)\) \(\chi_{8041}(2166,\cdot)\) \(\chi_{8041}(2386,\cdot)\) \(\chi_{8041}(2419,\cdot)\) \(\chi_{8041}(2793,\cdot)\) \(\chi_{8041}(2859,\cdot)\) \(\chi_{8041}(3002,\cdot)\) \(\chi_{8041}(3057,\cdot)\) \(\chi_{8041}(3475,\cdot)\) \(\chi_{8041}(3530,\cdot)\) \(\chi_{8041}(3805,\cdot)\) \(\chi_{8041}(4058,\cdot)\) \(\chi_{8041}(4278,\cdot)\) \(\chi_{8041}(4311,\cdot)\) \(\chi_{8041}(4476,\cdot)\) \(\chi_{8041}(4685,\cdot)\) \(\chi_{8041}(4784,\cdot)\) \(\chi_{8041}(5004,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{112})$ |
Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((-1,e\left(\frac{13}{16}\right),e\left(\frac{4}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(4058, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{43}{112}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{39}{112}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{73}{112}\right)\) | \(e\left(\frac{111}{112}\right)\) |