Basic properties
| Modulus: | \(6069\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{289}(64,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6069.bz
\(\chi_{6069}(64,\cdot)\) \(\chi_{6069}(106,\cdot)\) \(\chi_{6069}(421,\cdot)\) \(\chi_{6069}(463,\cdot)\) \(\chi_{6069}(778,\cdot)\) \(\chi_{6069}(820,\cdot)\) \(\chi_{6069}(1135,\cdot)\) \(\chi_{6069}(1177,\cdot)\) \(\chi_{6069}(1492,\cdot)\) \(\chi_{6069}(1534,\cdot)\) \(\chi_{6069}(1849,\cdot)\) \(\chi_{6069}(1891,\cdot)\) \(\chi_{6069}(2206,\cdot)\) \(\chi_{6069}(2248,\cdot)\) \(\chi_{6069}(2605,\cdot)\) \(\chi_{6069}(2920,\cdot)\) \(\chi_{6069}(2962,\cdot)\) \(\chi_{6069}(3277,\cdot)\) \(\chi_{6069}(3319,\cdot)\) \(\chi_{6069}(3634,\cdot)\) \(\chi_{6069}(3676,\cdot)\) \(\chi_{6069}(3991,\cdot)\) \(\chi_{6069}(4033,\cdot)\) \(\chi_{6069}(4348,\cdot)\) \(\chi_{6069}(4390,\cdot)\) \(\chi_{6069}(4705,\cdot)\) \(\chi_{6069}(4747,\cdot)\) \(\chi_{6069}(5062,\cdot)\) \(\chi_{6069}(5104,\cdot)\) \(\chi_{6069}(5419,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((2024,4336,3760)\) → \((1,1,e\left(\frac{13}{68}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(19\) | \(20\) |
| \( \chi_{ 6069 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{29}{68}\right)\) |