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 \(\chi_{889}(467,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2667.er
\(\chi_{2667}(166,\cdot)\) \(\chi_{2667}(241,\cdot)\) \(\chi_{2667}(346,\cdot)\) \(\chi_{2667}(388,\cdot)\) \(\chi_{2667}(439,\cdot)\) \(\chi_{2667}(493,\cdot)\) \(\chi_{2667}(514,\cdot)\) \(\chi_{2667}(556,\cdot)\) \(\chi_{2667}(586,\cdot)\) \(\chi_{2667}(808,\cdot)\) \(\chi_{2667}(817,\cdot)\) \(\chi_{2667}(829,\cdot)\) \(\chi_{2667}(880,\cdot)\) \(\chi_{2667}(892,\cdot)\) \(\chi_{2667}(1039,\cdot)\) \(\chi_{2667}(1069,\cdot)\) \(\chi_{2667}(1081,\cdot)\) \(\chi_{2667}(1132,\cdot)\) \(\chi_{2667}(1363,\cdot)\) \(\chi_{2667}(1426,\cdot)\) \(\chi_{2667}(1615,\cdot)\) \(\chi_{2667}(1879,\cdot)\) \(\chi_{2667}(1888,\cdot)\) \(\chi_{2667}(2014,\cdot)\) \(\chi_{2667}(2077,\cdot)\) \(\chi_{2667}(2089,\cdot)\) \(\chi_{2667}(2173,\cdot)\) \(\chi_{2667}(2215,\cdot)\) \(\chi_{2667}(2245,\cdot)\) \(\chi_{2667}(2329,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((890,1144,2416)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{17}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2667 }(2245, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(-1\) |