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 \(\chi_{2667}(206,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.mt
\(\chi_{8001}(206,\cdot)\) \(\chi_{8001}(215,\cdot)\) \(\chi_{8001}(269,\cdot)\) \(\chi_{8001}(521,\cdot)\) \(\chi_{8001}(656,\cdot)\) \(\chi_{8001}(719,\cdot)\) \(\chi_{8001}(971,\cdot)\) \(\chi_{8001}(1034,\cdot)\) \(\chi_{8001}(1160,\cdot)\) \(\chi_{8001}(1214,\cdot)\) \(\chi_{8001}(1340,\cdot)\) \(\chi_{8001}(1916,\cdot)\) \(\chi_{8001}(1979,\cdot)\) \(\chi_{8001}(2168,\cdot)\) \(\chi_{8001}(2231,\cdot)\) \(\chi_{8001}(2348,\cdot)\) \(\chi_{8001}(2537,\cdot)\) \(\chi_{8001}(2600,\cdot)\) \(\chi_{8001}(2609,\cdot)\) \(\chi_{8001}(2915,\cdot)\) \(\chi_{8001}(3041,\cdot)\) \(\chi_{8001}(3671,\cdot)\) \(\chi_{8001}(3923,\cdot)\) \(\chi_{8001}(5057,\cdot)\) \(\chi_{8001}(5129,\cdot)\) \(\chi_{8001}(5750,\cdot)\) \(\chi_{8001}(5759,\cdot)\) \(\chi_{8001}(6011,\cdot)\) \(\chi_{8001}(6137,\cdot)\) \(\chi_{8001}(6254,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{50}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(206, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{13}{126}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(-1\) |