Basic properties
| Modulus: | \(6069\) | |
| Conductor: | \(2023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(204\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2023}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6069.cm
\(\chi_{6069}(4,\cdot)\) \(\chi_{6069}(268,\cdot)\) \(\chi_{6069}(310,\cdot)\) \(\chi_{6069}(319,\cdot)\) \(\chi_{6069}(361,\cdot)\) \(\chi_{6069}(625,\cdot)\) \(\chi_{6069}(667,\cdot)\) \(\chi_{6069}(676,\cdot)\) \(\chi_{6069}(718,\cdot)\) \(\chi_{6069}(982,\cdot)\) \(\chi_{6069}(1024,\cdot)\) \(\chi_{6069}(1033,\cdot)\) \(\chi_{6069}(1075,\cdot)\) \(\chi_{6069}(1339,\cdot)\) \(\chi_{6069}(1381,\cdot)\) \(\chi_{6069}(1390,\cdot)\) \(\chi_{6069}(1432,\cdot)\) \(\chi_{6069}(1738,\cdot)\) \(\chi_{6069}(1747,\cdot)\) \(\chi_{6069}(1789,\cdot)\) \(\chi_{6069}(2053,\cdot)\) \(\chi_{6069}(2095,\cdot)\) \(\chi_{6069}(2104,\cdot)\) \(\chi_{6069}(2146,\cdot)\) \(\chi_{6069}(2410,\cdot)\) \(\chi_{6069}(2452,\cdot)\) \(\chi_{6069}(2461,\cdot)\) \(\chi_{6069}(2503,\cdot)\) \(\chi_{6069}(2767,\cdot)\) \(\chi_{6069}(2809,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((2024,4336,3760)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{27}{68}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(19\) | \(20\) |
| \( \chi_{ 6069 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{102}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{53}{204}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{7}{204}\right)\) | \(e\left(\frac{163}{204}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{91}{102}\right)\) | \(e\left(\frac{55}{68}\right)\) |