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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2667.em
\(\chi_{2667}(11,\cdot)\) \(\chi_{2667}(74,\cdot)\) \(\chi_{2667}(263,\cdot)\) \(\chi_{2667}(326,\cdot)\) \(\chi_{2667}(443,\cdot)\) \(\chi_{2667}(485,\cdot)\) \(\chi_{2667}(557,\cdot)\) \(\chi_{2667}(632,\cdot)\) \(\chi_{2667}(695,\cdot)\) \(\chi_{2667}(704,\cdot)\) \(\chi_{2667}(716,\cdot)\) \(\chi_{2667}(968,\cdot)\) \(\chi_{2667}(977,\cdot)\) \(\chi_{2667}(1010,\cdot)\) \(\chi_{2667}(1031,\cdot)\) \(\chi_{2667}(1136,\cdot)\) \(\chi_{2667}(1178,\cdot)\) \(\chi_{2667}(1187,\cdot)\) \(\chi_{2667}(1283,\cdot)\) \(\chi_{2667}(1418,\cdot)\) \(\chi_{2667}(1439,\cdot)\) \(\chi_{2667}(1481,\cdot)\) \(\chi_{2667}(1565,\cdot)\) \(\chi_{2667}(1682,\cdot)\) \(\chi_{2667}(1733,\cdot)\) \(\chi_{2667}(1766,\cdot)\) \(\chi_{2667}(1796,\cdot)\) \(\chi_{2667}(1808,\cdot)\) \(\chi_{2667}(1922,\cdot)\) \(\chi_{2667}(1976,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((890,1144,2416)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{26}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2667 }(1136, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{1}{3}\right)\) |