Basic properties
Modulus: | \(8001\) | |
Conductor: | \(889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{889}(551,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.nk
\(\chi_{8001}(388,\cdot)\) \(\chi_{8001}(514,\cdot)\) \(\chi_{8001}(586,\cdot)\) \(\chi_{8001}(829,\cdot)\) \(\chi_{8001}(892,\cdot)\) \(\chi_{8001}(1081,\cdot)\) \(\chi_{8001}(2089,\cdot)\) \(\chi_{8001}(2215,\cdot)\) \(\chi_{8001}(2908,\cdot)\) \(\chi_{8001}(3106,\cdot)\) \(\chi_{8001}(3160,\cdot)\) \(\chi_{8001}(3223,\cdot)\) \(\chi_{8001}(3475,\cdot)\) \(\chi_{8001}(3484,\cdot)\) \(\chi_{8001}(3547,\cdot)\) \(\chi_{8001}(3736,\cdot)\) \(\chi_{8001}(3799,\cdot)\) \(\chi_{8001}(4546,\cdot)\) \(\chi_{8001}(4555,\cdot)\) \(\chi_{8001}(4681,\cdot)\) \(\chi_{8001}(4744,\cdot)\) \(\chi_{8001}(4996,\cdot)\) \(\chi_{8001}(5050,\cdot)\) \(\chi_{8001}(5059,\cdot)\) \(\chi_{8001}(5176,\cdot)\) \(\chi_{8001}(5500,\cdot)\) \(\chi_{8001}(5680,\cdot)\) \(\chi_{8001}(6373,\cdot)\) \(\chi_{8001}(6697,\cdot)\) \(\chi_{8001}(6760,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{71}{126}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 8001 }(4996, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(-1\) |