Basic properties
| Modulus: | \(6069\) | |
| Conductor: | \(6069\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(408\) | 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 6069.cv
\(\chi_{6069}(26,\cdot)\) \(\chi_{6069}(59,\cdot)\) \(\chi_{6069}(185,\cdot)\) \(\chi_{6069}(206,\cdot)\) \(\chi_{6069}(236,\cdot)\) \(\chi_{6069}(257,\cdot)\) \(\chi_{6069}(332,\cdot)\) \(\chi_{6069}(383,\cdot)\) \(\chi_{6069}(416,\cdot)\) \(\chi_{6069}(467,\cdot)\) \(\chi_{6069}(542,\cdot)\) \(\chi_{6069}(563,\cdot)\) \(\chi_{6069}(593,\cdot)\) \(\chi_{6069}(614,\cdot)\) \(\chi_{6069}(689,\cdot)\) \(\chi_{6069}(740,\cdot)\) \(\chi_{6069}(773,\cdot)\) \(\chi_{6069}(824,\cdot)\) \(\chi_{6069}(899,\cdot)\) \(\chi_{6069}(920,\cdot)\) \(\chi_{6069}(950,\cdot)\) \(\chi_{6069}(971,\cdot)\) \(\chi_{6069}(1097,\cdot)\) \(\chi_{6069}(1130,\cdot)\) \(\chi_{6069}(1181,\cdot)\) \(\chi_{6069}(1256,\cdot)\) \(\chi_{6069}(1277,\cdot)\) \(\chi_{6069}(1307,\cdot)\) \(\chi_{6069}(1328,\cdot)\) \(\chi_{6069}(1403,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{408})$ |
| Fixed field: | Number field defined by a degree 408 polynomial (not computed) |
Values on generators
\((2024,4336,3760)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{31}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(19\) | \(20\) |
| \( \chi_{ 6069 }(1328, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{204}\right)\) | \(e\left(\frac{97}{102}\right)\) | \(e\left(\frac{353}{408}\right)\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{139}{408}\right)\) | \(e\left(\frac{31}{408}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{73}{204}\right)\) | \(e\left(\frac{111}{136}\right)\) |