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.en
\(\chi_{2667}(173,\cdot)\) \(\chi_{2667}(185,\cdot)\) \(\chi_{2667}(194,\cdot)\) \(\chi_{2667}(257,\cdot)\) \(\chi_{2667}(332,\cdot)\) \(\chi_{2667}(404,\cdot)\) \(\chi_{2667}(446,\cdot)\) \(\chi_{2667}(563,\cdot)\) \(\chi_{2667}(626,\cdot)\) \(\chi_{2667}(815,\cdot)\) \(\chi_{2667}(878,\cdot)\) \(\chi_{2667}(1109,\cdot)\) \(\chi_{2667}(1172,\cdot)\) \(\chi_{2667}(1244,\cdot)\) \(\chi_{2667}(1361,\cdot)\) \(\chi_{2667}(1454,\cdot)\) \(\chi_{2667}(1538,\cdot)\) \(\chi_{2667}(1580,\cdot)\) \(\chi_{2667}(1634,\cdot)\) \(\chi_{2667}(1748,\cdot)\) \(\chi_{2667}(1760,\cdot)\) \(\chi_{2667}(1790,\cdot)\) \(\chi_{2667}(1823,\cdot)\) \(\chi_{2667}(1874,\cdot)\) \(\chi_{2667}(1991,\cdot)\) \(\chi_{2667}(2075,\cdot)\) \(\chi_{2667}(2117,\cdot)\) \(\chi_{2667}(2138,\cdot)\) \(\chi_{2667}(2273,\cdot)\) \(\chi_{2667}(2369,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((890,1144,2416)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{113}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2667 }(1172, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{1}{6}\right)\) |