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.ek
\(\chi_{2667}(206,\cdot)\) \(\chi_{2667}(215,\cdot)\) \(\chi_{2667}(248,\cdot)\) \(\chi_{2667}(269,\cdot)\) \(\chi_{2667}(374,\cdot)\) \(\chi_{2667}(416,\cdot)\) \(\chi_{2667}(425,\cdot)\) \(\chi_{2667}(521,\cdot)\) \(\chi_{2667}(656,\cdot)\) \(\chi_{2667}(677,\cdot)\) \(\chi_{2667}(719,\cdot)\) \(\chi_{2667}(803,\cdot)\) \(\chi_{2667}(920,\cdot)\) \(\chi_{2667}(971,\cdot)\) \(\chi_{2667}(1004,\cdot)\) \(\chi_{2667}(1034,\cdot)\) \(\chi_{2667}(1046,\cdot)\) \(\chi_{2667}(1160,\cdot)\) \(\chi_{2667}(1214,\cdot)\) \(\chi_{2667}(1256,\cdot)\) \(\chi_{2667}(1340,\cdot)\) \(\chi_{2667}(1433,\cdot)\) \(\chi_{2667}(1550,\cdot)\) \(\chi_{2667}(1622,\cdot)\) \(\chi_{2667}(1685,\cdot)\) \(\chi_{2667}(1916,\cdot)\) \(\chi_{2667}(1979,\cdot)\) \(\chi_{2667}(2168,\cdot)\) \(\chi_{2667}(2231,\cdot)\) \(\chi_{2667}(2348,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((890,1144,2416)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{50}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2667 }(206, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{13}{126}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(-1\) |