Basic properties
| Modulus: | \(6664\) | |
| Conductor: | \(6664\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | 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 6664.ga
\(\chi_{6664}(5,\cdot)\) \(\chi_{6664}(45,\cdot)\) \(\chi_{6664}(61,\cdot)\) \(\chi_{6664}(173,\cdot)\) \(\chi_{6664}(269,\cdot)\) \(\chi_{6664}(381,\cdot)\) \(\chi_{6664}(397,\cdot)\) \(\chi_{6664}(437,\cdot)\) \(\chi_{6664}(453,\cdot)\) \(\chi_{6664}(549,\cdot)\) \(\chi_{6664}(605,\cdot)\) \(\chi_{6664}(677,\cdot)\) \(\chi_{6664}(789,\cdot)\) \(\chi_{6664}(845,\cdot)\) \(\chi_{6664}(941,\cdot)\) \(\chi_{6664}(957,\cdot)\) \(\chi_{6664}(997,\cdot)\) \(\chi_{6664}(1013,\cdot)\) \(\chi_{6664}(1125,\cdot)\) \(\chi_{6664}(1221,\cdot)\) \(\chi_{6664}(1333,\cdot)\) \(\chi_{6664}(1349,\cdot)\) \(\chi_{6664}(1389,\cdot)\) \(\chi_{6664}(1405,\cdot)\) \(\chi_{6664}(1557,\cdot)\) \(\chi_{6664}(1629,\cdot)\) \(\chi_{6664}(1669,\cdot)\) \(\chi_{6664}(1741,\cdot)\) \(\chi_{6664}(1797,\cdot)\) \(\chi_{6664}(1909,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((4999,3333,4217,785)\) → \((1,-1,e\left(\frac{1}{42}\right),e\left(\frac{13}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 6664 }(5197, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{336}\right)\) | \(e\left(\frac{85}{336}\right)\) | \(e\left(\frac{113}{168}\right)\) | \(e\left(\frac{47}{336}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{31}{336}\right)\) | \(e\left(\frac{85}{168}\right)\) | \(e\left(\frac{1}{112}\right)\) |