Basic properties
| Modulus: | \(6069\) | |
| Conductor: | \(2023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(816\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2023}(10,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6069.da
\(\chi_{6069}(10,\cdot)\) \(\chi_{6069}(31,\cdot)\) \(\chi_{6069}(61,\cdot)\) \(\chi_{6069}(73,\cdot)\) \(\chi_{6069}(82,\cdot)\) \(\chi_{6069}(124,\cdot)\) \(\chi_{6069}(199,\cdot)\) \(\chi_{6069}(241,\cdot)\) \(\chi_{6069}(250,\cdot)\) \(\chi_{6069}(262,\cdot)\) \(\chi_{6069}(283,\cdot)\) \(\chi_{6069}(292,\cdot)\) \(\chi_{6069}(313,\cdot)\) \(\chi_{6069}(334,\cdot)\) \(\chi_{6069}(346,\cdot)\) \(\chi_{6069}(367,\cdot)\) \(\chi_{6069}(388,\cdot)\) \(\chi_{6069}(397,\cdot)\) \(\chi_{6069}(418,\cdot)\) \(\chi_{6069}(430,\cdot)\) \(\chi_{6069}(439,\cdot)\) \(\chi_{6069}(481,\cdot)\) \(\chi_{6069}(556,\cdot)\) \(\chi_{6069}(598,\cdot)\) \(\chi_{6069}(607,\cdot)\) \(\chi_{6069}(619,\cdot)\) \(\chi_{6069}(640,\cdot)\) \(\chi_{6069}(649,\cdot)\) \(\chi_{6069}(670,\cdot)\) \(\chi_{6069}(691,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{816})$ |
| Fixed field: | Number field defined by a degree 816 polynomial (not computed) |
Values on generators
\((2024,4336,3760)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{147}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(19\) | \(20\) |
| \( \chi_{ 6069 }(10, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{408}\right)\) | \(e\left(\frac{7}{204}\right)\) | \(e\left(\frac{485}{816}\right)\) | \(e\left(\frac{7}{136}\right)\) | \(e\left(\frac{499}{816}\right)\) | \(e\left(\frac{79}{816}\right)\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{163}{408}\right)\) | \(e\left(\frac{171}{272}\right)\) |