Basic properties
| Modulus: | \(8001\) | |
| Conductor: | \(8001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | 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.ls
\(\chi_{8001}(79,\cdot)\) \(\chi_{8001}(142,\cdot)\) \(\chi_{8001}(394,\cdot)\) \(\chi_{8001}(1087,\cdot)\) \(\chi_{8001}(1213,\cdot)\) \(\chi_{8001}(2221,\cdot)\) \(\chi_{8001}(2335,\cdot)\) \(\chi_{8001}(2410,\cdot)\) \(\chi_{8001}(2473,\cdot)\) \(\chi_{8001}(2788,\cdot)\) \(\chi_{8001}(2914,\cdot)\) \(\chi_{8001}(2965,\cdot)\) \(\chi_{8001}(3217,\cdot)\) \(\chi_{8001}(3343,\cdot)\) \(\chi_{8001}(3544,\cdot)\) \(\chi_{8001}(3796,\cdot)\) \(\chi_{8001}(3973,\cdot)\) \(\chi_{8001}(4162,\cdot)\) \(\chi_{8001}(4225,\cdot)\) \(\chi_{8001}(4930,\cdot)\) \(\chi_{8001}(5422,\cdot)\) \(\chi_{8001}(5623,\cdot)\) \(\chi_{8001}(5863,\cdot)\) \(\chi_{8001}(5926,\cdot)\) \(\chi_{8001}(6127,\cdot)\) \(\chi_{8001}(6178,\cdot)\) \(\chi_{8001}(6241,\cdot)\) \(\chi_{8001}(6253,\cdot)\) \(\chi_{8001}(6367,\cdot)\) \(\chi_{8001}(6757,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{3}\right),e\left(\frac{50}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{1}{3}\right)\) |