Basic properties
| Modulus: | \(2667\) | |
| Conductor: | \(889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{889}(220,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2667.eo
\(\chi_{2667}(220,\cdot)\) \(\chi_{2667}(283,\cdot)\) \(\chi_{2667}(355,\cdot)\) \(\chi_{2667}(472,\cdot)\) \(\chi_{2667}(565,\cdot)\) \(\chi_{2667}(649,\cdot)\) \(\chi_{2667}(691,\cdot)\) \(\chi_{2667}(745,\cdot)\) \(\chi_{2667}(859,\cdot)\) \(\chi_{2667}(871,\cdot)\) \(\chi_{2667}(901,\cdot)\) \(\chi_{2667}(934,\cdot)\) \(\chi_{2667}(985,\cdot)\) \(\chi_{2667}(1102,\cdot)\) \(\chi_{2667}(1186,\cdot)\) \(\chi_{2667}(1228,\cdot)\) \(\chi_{2667}(1249,\cdot)\) \(\chi_{2667}(1384,\cdot)\) \(\chi_{2667}(1480,\cdot)\) \(\chi_{2667}(1489,\cdot)\) \(\chi_{2667}(1531,\cdot)\) \(\chi_{2667}(1636,\cdot)\) \(\chi_{2667}(1657,\cdot)\) \(\chi_{2667}(1690,\cdot)\) \(\chi_{2667}(1699,\cdot)\) \(\chi_{2667}(1951,\cdot)\) \(\chi_{2667}(1963,\cdot)\) \(\chi_{2667}(1972,\cdot)\) \(\chi_{2667}(2035,\cdot)\) \(\chi_{2667}(2110,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((890,1144,2416)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{47}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2667 }(220, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{1}{6}\right)\) |