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.nl
\(\chi_{8001}(346,\cdot)\) \(\chi_{8001}(439,\cdot)\) \(\chi_{8001}(817,\cdot)\) \(\chi_{8001}(880,\cdot)\) \(\chi_{8001}(1039,\cdot)\) \(\chi_{8001}(1069,\cdot)\) \(\chi_{8001}(1132,\cdot)\) \(\chi_{8001}(1888,\cdot)\) \(\chi_{8001}(2014,\cdot)\) \(\chi_{8001}(2077,\cdot)\) \(\chi_{8001}(2173,\cdot)\) \(\chi_{8001}(2329,\cdot)\) \(\chi_{8001}(2392,\cdot)\) \(\chi_{8001}(2425,\cdot)\) \(\chi_{8001}(2833,\cdot)\) \(\chi_{8001}(3055,\cdot)\) \(\chi_{8001}(3181,\cdot)\) \(\chi_{8001}(3496,\cdot)\) \(\chi_{8001}(3559,\cdot)\) \(\chi_{8001}(3748,\cdot)\) \(\chi_{8001}(4030,\cdot)\) \(\chi_{8001}(4093,\cdot)\) \(\chi_{8001}(4282,\cdot)\) \(\chi_{8001}(4756,\cdot)\) \(\chi_{8001}(4882,\cdot)\) \(\chi_{8001}(4912,\cdot)\) \(\chi_{8001}(5038,\cdot)\) \(\chi_{8001}(5290,\cdot)\) \(\chi_{8001}(5575,\cdot)\) \(\chi_{8001}(5827,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{6}\right),e\left(\frac{13}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(346, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{11}{126}\right)\) | \(-1\) |