Basic properties
| Modulus: | \(2667\) | |
| Conductor: | \(2667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 2667.eh
\(\chi_{2667}(17,\cdot)\) \(\chi_{2667}(26,\cdot)\) \(\chi_{2667}(290,\cdot)\) \(\chi_{2667}(479,\cdot)\) \(\chi_{2667}(542,\cdot)\) \(\chi_{2667}(773,\cdot)\) \(\chi_{2667}(824,\cdot)\) \(\chi_{2667}(836,\cdot)\) \(\chi_{2667}(866,\cdot)\) \(\chi_{2667}(1013,\cdot)\) \(\chi_{2667}(1025,\cdot)\) \(\chi_{2667}(1076,\cdot)\) \(\chi_{2667}(1088,\cdot)\) \(\chi_{2667}(1097,\cdot)\) \(\chi_{2667}(1319,\cdot)\) \(\chi_{2667}(1349,\cdot)\) \(\chi_{2667}(1391,\cdot)\) \(\chi_{2667}(1412,\cdot)\) \(\chi_{2667}(1466,\cdot)\) \(\chi_{2667}(1517,\cdot)\) \(\chi_{2667}(1559,\cdot)\) \(\chi_{2667}(1664,\cdot)\) \(\chi_{2667}(1739,\cdot)\) \(\chi_{2667}(1949,\cdot)\) \(\chi_{2667}(2063,\cdot)\) \(\chi_{2667}(2147,\cdot)\) \(\chi_{2667}(2180,\cdot)\) \(\chi_{2667}(2189,\cdot)\) \(\chi_{2667}(2201,\cdot)\) \(\chi_{2667}(2243,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((890,1144,2416)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{19}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2667 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{1}{6}\right)\) |