Basic properties
| Modulus: | \(8001\) | |
| Conductor: | \(8001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 8001.ny
\(\chi_{8001}(23,\cdot)\) \(\chi_{8001}(1157,\cdot)\) \(\chi_{8001}(1409,\cdot)\) \(\chi_{8001}(2039,\cdot)\) \(\chi_{8001}(2090,\cdot)\) \(\chi_{8001}(2165,\cdot)\) \(\chi_{8001}(2468,\cdot)\) \(\chi_{8001}(2480,\cdot)\) \(\chi_{8001}(2531,\cdot)\) \(\chi_{8001}(2543,\cdot)\) \(\chi_{8001}(2720,\cdot)\) \(\chi_{8001}(2732,\cdot)\) \(\chi_{8001}(2783,\cdot)\) \(\chi_{8001}(3539,\cdot)\) \(\chi_{8001}(3665,\cdot)\) \(\chi_{8001}(3728,\cdot)\) \(\chi_{8001}(3740,\cdot)\) \(\chi_{8001}(3866,\cdot)\) \(\chi_{8001}(3980,\cdot)\) \(\chi_{8001}(4043,\cdot)\) \(\chi_{8001}(4484,\cdot)\) \(\chi_{8001}(4559,\cdot)\) \(\chi_{8001}(4811,\cdot)\) \(\chi_{8001}(4874,\cdot)\) \(\chi_{8001}(5126,\cdot)\) \(\chi_{8001}(5681,\cdot)\) \(\chi_{8001}(5744,\cdot)\) \(\chi_{8001}(5933,\cdot)\) \(\chi_{8001}(6197,\cdot)\) \(\chi_{8001}(6563,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{3}\right),e\left(\frac{121}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{1}{3}\right)\) |