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.eg
\(\chi_{2667}(23,\cdot)\) \(\chi_{2667}(53,\cdot)\) \(\chi_{2667}(65,\cdot)\) \(\chi_{2667}(116,\cdot)\) \(\chi_{2667}(347,\cdot)\) \(\chi_{2667}(410,\cdot)\) \(\chi_{2667}(599,\cdot)\) \(\chi_{2667}(863,\cdot)\) \(\chi_{2667}(872,\cdot)\) \(\chi_{2667}(998,\cdot)\) \(\chi_{2667}(1061,\cdot)\) \(\chi_{2667}(1073,\cdot)\) \(\chi_{2667}(1157,\cdot)\) \(\chi_{2667}(1199,\cdot)\) \(\chi_{2667}(1229,\cdot)\) \(\chi_{2667}(1313,\cdot)\) \(\chi_{2667}(1355,\cdot)\) \(\chi_{2667}(1367,\cdot)\) \(\chi_{2667}(1376,\cdot)\) \(\chi_{2667}(1409,\cdot)\) \(\chi_{2667}(1493,\cdot)\) \(\chi_{2667}(1607,\cdot)\) \(\chi_{2667}(1817,\cdot)\) \(\chi_{2667}(1892,\cdot)\) \(\chi_{2667}(1997,\cdot)\) \(\chi_{2667}(2039,\cdot)\) \(\chi_{2667}(2090,\cdot)\) \(\chi_{2667}(2144,\cdot)\) \(\chi_{2667}(2165,\cdot)\) \(\chi_{2667}(2207,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((890,1144,2416)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{115}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2667 }(2039, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{1}{3}\right)\) |