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.ns
\(\chi_{8001}(416,\cdot)\) \(\chi_{8001}(920,\cdot)\) \(\chi_{8001}(1046,\cdot)\) \(\chi_{8001}(1550,\cdot)\) \(\chi_{8001}(2462,\cdot)\) \(\chi_{8001}(2621,\cdot)\) \(\chi_{8001}(2873,\cdot)\) \(\chi_{8001}(2936,\cdot)\) \(\chi_{8001}(3092,\cdot)\) \(\chi_{8001}(3188,\cdot)\) \(\chi_{8001}(3344,\cdot)\) \(\chi_{8001}(3470,\cdot)\) \(\chi_{8001}(3881,\cdot)\) \(\chi_{8001}(4007,\cdot)\) \(\chi_{8001}(4100,\cdot)\) \(\chi_{8001}(4289,\cdot)\) \(\chi_{8001}(4352,\cdot)\) \(\chi_{8001}(5015,\cdot)\) \(\chi_{8001}(5204,\cdot)\) \(\chi_{8001}(5267,\cdot)\) \(\chi_{8001}(5549,\cdot)\) \(\chi_{8001}(5582,\cdot)\) \(\chi_{8001}(5708,\cdot)\) \(\chi_{8001}(5990,\cdot)\) \(\chi_{8001}(6053,\cdot)\) \(\chi_{8001}(6305,\cdot)\) \(\chi_{8001}(6338,\cdot)\) \(\chi_{8001}(6368,\cdot)\) \(\chi_{8001}(6494,\cdot)\) \(\chi_{8001}(6590,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{1}{6}\right),e\left(\frac{62}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(6590, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(-1\) |