Basic properties
| Modulus: | \(8001\) | |
| Conductor: | \(889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{889}(388,\cdot)\) | 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
\((3557,1144,7750)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{115}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(388, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{37}{126}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{107}{126}\right)\) | \(-1\) |