Basic properties
| Modulus: | \(6069\) | |
| Conductor: | \(6069\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | 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.by
\(\chi_{6069}(293,\cdot)\) \(\chi_{6069}(608,\cdot)\) \(\chi_{6069}(650,\cdot)\) \(\chi_{6069}(965,\cdot)\) \(\chi_{6069}(1007,\cdot)\) \(\chi_{6069}(1322,\cdot)\) \(\chi_{6069}(1364,\cdot)\) \(\chi_{6069}(1679,\cdot)\) \(\chi_{6069}(1721,\cdot)\) \(\chi_{6069}(2036,\cdot)\) \(\chi_{6069}(2078,\cdot)\) \(\chi_{6069}(2393,\cdot)\) \(\chi_{6069}(2435,\cdot)\) \(\chi_{6069}(2750,\cdot)\) \(\chi_{6069}(2792,\cdot)\) \(\chi_{6069}(3107,\cdot)\) \(\chi_{6069}(3149,\cdot)\) \(\chi_{6069}(3464,\cdot)\) \(\chi_{6069}(3821,\cdot)\) \(\chi_{6069}(3863,\cdot)\) \(\chi_{6069}(4178,\cdot)\) \(\chi_{6069}(4220,\cdot)\) \(\chi_{6069}(4535,\cdot)\) \(\chi_{6069}(4577,\cdot)\) \(\chi_{6069}(4892,\cdot)\) \(\chi_{6069}(4934,\cdot)\) \(\chi_{6069}(5249,\cdot)\) \(\chi_{6069}(5291,\cdot)\) \(\chi_{6069}(5606,\cdot)\) \(\chi_{6069}(5648,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((2024,4336,3760)\) → \((-1,-1,e\left(\frac{27}{68}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(19\) | \(20\) |
| \( \chi_{ 6069 }(293, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{59}{68}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{55}{68}\right)\) |