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.ll
\(\chi_{8001}(88,\cdot)\) \(\chi_{8001}(121,\cdot)\) \(\chi_{8001}(247,\cdot)\) \(\chi_{8001}(529,\cdot)\) \(\chi_{8001}(592,\cdot)\) \(\chi_{8001}(844,\cdot)\) \(\chi_{8001}(877,\cdot)\) \(\chi_{8001}(907,\cdot)\) \(\chi_{8001}(1033,\cdot)\) \(\chi_{8001}(1129,\cdot)\) \(\chi_{8001}(1789,\cdot)\) \(\chi_{8001}(1852,\cdot)\) \(\chi_{8001}(2041,\cdot)\) \(\chi_{8001}(2104,\cdot)\) \(\chi_{8001}(2263,\cdot)\) \(\chi_{8001}(2482,\cdot)\) \(\chi_{8001}(2956,\cdot)\) \(\chi_{8001}(3460,\cdot)\) \(\chi_{8001}(3586,\cdot)\) \(\chi_{8001}(4090,\cdot)\) \(\chi_{8001}(5002,\cdot)\) \(\chi_{8001}(5161,\cdot)\) \(\chi_{8001}(5413,\cdot)\) \(\chi_{8001}(5476,\cdot)\) \(\chi_{8001}(5632,\cdot)\) \(\chi_{8001}(5728,\cdot)\) \(\chi_{8001}(5884,\cdot)\) \(\chi_{8001}(6010,\cdot)\) \(\chi_{8001}(6421,\cdot)\) \(\chi_{8001}(6547,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{2}{3}\right),e\left(\frac{16}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(88, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{2}{3}\right)\) |