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.el
\(\chi_{2667}(86,\cdot)\) \(\chi_{2667}(170,\cdot)\) \(\chi_{2667}(212,\cdot)\) \(\chi_{2667}(233,\cdot)\) \(\chi_{2667}(368,\cdot)\) \(\chi_{2667}(464,\cdot)\) \(\chi_{2667}(473,\cdot)\) \(\chi_{2667}(515,\cdot)\) \(\chi_{2667}(620,\cdot)\) \(\chi_{2667}(641,\cdot)\) \(\chi_{2667}(674,\cdot)\) \(\chi_{2667}(683,\cdot)\) \(\chi_{2667}(935,\cdot)\) \(\chi_{2667}(947,\cdot)\) \(\chi_{2667}(956,\cdot)\) \(\chi_{2667}(1019,\cdot)\) \(\chi_{2667}(1094,\cdot)\) \(\chi_{2667}(1166,\cdot)\) \(\chi_{2667}(1208,\cdot)\) \(\chi_{2667}(1325,\cdot)\) \(\chi_{2667}(1388,\cdot)\) \(\chi_{2667}(1577,\cdot)\) \(\chi_{2667}(1640,\cdot)\) \(\chi_{2667}(1871,\cdot)\) \(\chi_{2667}(1934,\cdot)\) \(\chi_{2667}(2006,\cdot)\) \(\chi_{2667}(2123,\cdot)\) \(\chi_{2667}(2216,\cdot)\) \(\chi_{2667}(2300,\cdot)\) \(\chi_{2667}(2342,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((890,1144,2416)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{17}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2667 }(86, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(1\) |