Basic properties
| Modulus: | \(6069\) | |
| Conductor: | \(6069\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(816\) | 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.cz
\(\chi_{6069}(11,\cdot)\) \(\chi_{6069}(23,\cdot)\) \(\chi_{6069}(44,\cdot)\) \(\chi_{6069}(74,\cdot)\) \(\chi_{6069}(95,\cdot)\) \(\chi_{6069}(107,\cdot)\) \(\chi_{6069}(116,\cdot)\) \(\chi_{6069}(233,\cdot)\) \(\chi_{6069}(275,\cdot)\) \(\chi_{6069}(284,\cdot)\) \(\chi_{6069}(296,\cdot)\) \(\chi_{6069}(317,\cdot)\) \(\chi_{6069}(326,\cdot)\) \(\chi_{6069}(347,\cdot)\) \(\chi_{6069}(368,\cdot)\) \(\chi_{6069}(380,\cdot)\) \(\chi_{6069}(401,\cdot)\) \(\chi_{6069}(422,\cdot)\) \(\chi_{6069}(431,\cdot)\) \(\chi_{6069}(452,\cdot)\) \(\chi_{6069}(464,\cdot)\) \(\chi_{6069}(473,\cdot)\) \(\chi_{6069}(515,\cdot)\) \(\chi_{6069}(590,\cdot)\) \(\chi_{6069}(632,\cdot)\) \(\chi_{6069}(641,\cdot)\) \(\chi_{6069}(674,\cdot)\) \(\chi_{6069}(683,\cdot)\) \(\chi_{6069}(704,\cdot)\) \(\chi_{6069}(725,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{816})$ |
| Fixed field: | Number field defined by a degree 816 polynomial (not computed) |
Values on generators
\((2024,4336,3760)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{23}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(19\) | \(20\) |
| \( \chi_{ 6069 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{367}{408}\right)\) | \(e\left(\frac{163}{204}\right)\) | \(e\left(\frac{161}{816}\right)\) | \(e\left(\frac{95}{136}\right)\) | \(e\left(\frac{79}{816}\right)\) | \(e\left(\frac{91}{816}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{211}{408}\right)\) | \(e\left(\frac{271}{272}\right)\) |