Basic properties
| Modulus: | \(8001\) | |
| Conductor: | \(889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{889}(375,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.lq
\(\chi_{8001}(163,\cdot)\) \(\chi_{8001}(352,\cdot)\) \(\chi_{8001}(415,\cdot)\) \(\chi_{8001}(739,\cdot)\) \(\chi_{8001}(1432,\cdot)\) \(\chi_{8001}(1612,\cdot)\) \(\chi_{8001}(1936,\cdot)\) \(\chi_{8001}(2053,\cdot)\) \(\chi_{8001}(2062,\cdot)\) \(\chi_{8001}(2116,\cdot)\) \(\chi_{8001}(2368,\cdot)\) \(\chi_{8001}(2431,\cdot)\) \(\chi_{8001}(2557,\cdot)\) \(\chi_{8001}(2566,\cdot)\) \(\chi_{8001}(3313,\cdot)\) \(\chi_{8001}(3376,\cdot)\) \(\chi_{8001}(3565,\cdot)\) \(\chi_{8001}(3628,\cdot)\) \(\chi_{8001}(3637,\cdot)\) \(\chi_{8001}(3889,\cdot)\) \(\chi_{8001}(3952,\cdot)\) \(\chi_{8001}(4006,\cdot)\) \(\chi_{8001}(4204,\cdot)\) \(\chi_{8001}(4897,\cdot)\) \(\chi_{8001}(5023,\cdot)\) \(\chi_{8001}(6031,\cdot)\) \(\chi_{8001}(6220,\cdot)\) \(\chi_{8001}(6283,\cdot)\) \(\chi_{8001}(6526,\cdot)\) \(\chi_{8001}(6598,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((3557,1144,7750)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{5}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(6598, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(1\) |