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.ej
\(\chi_{2667}(44,\cdot)\) \(\chi_{2667}(158,\cdot)\) \(\chi_{2667}(242,\cdot)\) \(\chi_{2667}(275,\cdot)\) \(\chi_{2667}(284,\cdot)\) \(\chi_{2667}(296,\cdot)\) \(\chi_{2667}(338,\cdot)\) \(\chi_{2667}(422,\cdot)\) \(\chi_{2667}(452,\cdot)\) \(\chi_{2667}(494,\cdot)\) \(\chi_{2667}(578,\cdot)\) \(\chi_{2667}(590,\cdot)\) \(\chi_{2667}(653,\cdot)\) \(\chi_{2667}(779,\cdot)\) \(\chi_{2667}(788,\cdot)\) \(\chi_{2667}(1052,\cdot)\) \(\chi_{2667}(1241,\cdot)\) \(\chi_{2667}(1304,\cdot)\) \(\chi_{2667}(1535,\cdot)\) \(\chi_{2667}(1586,\cdot)\) \(\chi_{2667}(1598,\cdot)\) \(\chi_{2667}(1628,\cdot)\) \(\chi_{2667}(1775,\cdot)\) \(\chi_{2667}(1787,\cdot)\) \(\chi_{2667}(1838,\cdot)\) \(\chi_{2667}(1850,\cdot)\) \(\chi_{2667}(1859,\cdot)\) \(\chi_{2667}(2081,\cdot)\) \(\chi_{2667}(2111,\cdot)\) \(\chi_{2667}(2153,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((890,1144,2416)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{10}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2667 }(1052, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(1\) |