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 \(\chi_{889}(289,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.ln
\(\chi_{8001}(289,\cdot)\) \(\chi_{8001}(298,\cdot)\) \(\chi_{8001}(550,\cdot)\) \(\chi_{8001}(676,\cdot)\) \(\chi_{8001}(793,\cdot)\) \(\chi_{8001}(919,\cdot)\) \(\chi_{8001}(1306,\cdot)\) \(\chi_{8001}(1423,\cdot)\) \(\chi_{8001}(1495,\cdot)\) \(\chi_{8001}(1558,\cdot)\) \(\chi_{8001}(2494,\cdot)\) \(\chi_{8001}(2746,\cdot)\) \(\chi_{8001}(2755,\cdot)\) \(\chi_{8001}(2809,\cdot)\) \(\chi_{8001}(3061,\cdot)\) \(\chi_{8001}(3196,\cdot)\) \(\chi_{8001}(3259,\cdot)\) \(\chi_{8001}(3511,\cdot)\) \(\chi_{8001}(3574,\cdot)\) \(\chi_{8001}(3700,\cdot)\) \(\chi_{8001}(3754,\cdot)\) \(\chi_{8001}(3880,\cdot)\) \(\chi_{8001}(4456,\cdot)\) \(\chi_{8001}(4519,\cdot)\) \(\chi_{8001}(4708,\cdot)\) \(\chi_{8001}(4771,\cdot)\) \(\chi_{8001}(4888,\cdot)\) \(\chi_{8001}(5077,\cdot)\) \(\chi_{8001}(5140,\cdot)\) \(\chi_{8001}(5149,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((3557,1144,7750)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{38}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(289, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{1}{3}\right)\) |