Basic properties
| Modulus: | \(8001\) | |
| Conductor: | \(2667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2667}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.me
\(\chi_{8001}(17,\cdot)\) \(\chi_{8001}(26,\cdot)\) \(\chi_{8001}(773,\cdot)\) \(\chi_{8001}(836,\cdot)\) \(\chi_{8001}(1025,\cdot)\) \(\chi_{8001}(1088,\cdot)\) \(\chi_{8001}(1097,\cdot)\) \(\chi_{8001}(1349,\cdot)\) \(\chi_{8001}(1412,\cdot)\) \(\chi_{8001}(1466,\cdot)\) \(\chi_{8001}(1664,\cdot)\) \(\chi_{8001}(2357,\cdot)\) \(\chi_{8001}(2483,\cdot)\) \(\chi_{8001}(3491,\cdot)\) \(\chi_{8001}(3680,\cdot)\) \(\chi_{8001}(3743,\cdot)\) \(\chi_{8001}(3986,\cdot)\) \(\chi_{8001}(4058,\cdot)\) \(\chi_{8001}(4184,\cdot)\) \(\chi_{8001}(4616,\cdot)\) \(\chi_{8001}(4814,\cdot)\) \(\chi_{8001}(4868,\cdot)\) \(\chi_{8001}(4994,\cdot)\) \(\chi_{8001}(5066,\cdot)\) \(\chi_{8001}(5624,\cdot)\) \(\chi_{8001}(5813,\cdot)\) \(\chi_{8001}(5876,\cdot)\) \(\chi_{8001}(6200,\cdot)\) \(\chi_{8001}(6893,\cdot)\) \(\chi_{8001}(7073,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{19}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{1}{6}\right)\) |