Basic properties
| Modulus: | \(867\) | |
| 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 \(\chi_{289}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 867.p
\(\chi_{867}(4,\cdot)\) \(\chi_{867}(13,\cdot)\) \(\chi_{867}(55,\cdot)\) \(\chi_{867}(64,\cdot)\) \(\chi_{867}(106,\cdot)\) \(\chi_{867}(115,\cdot)\) \(\chi_{867}(157,\cdot)\) \(\chi_{867}(166,\cdot)\) \(\chi_{867}(208,\cdot)\) \(\chi_{867}(217,\cdot)\) \(\chi_{867}(259,\cdot)\) \(\chi_{867}(268,\cdot)\) \(\chi_{867}(310,\cdot)\) \(\chi_{867}(319,\cdot)\) \(\chi_{867}(361,\cdot)\) \(\chi_{867}(370,\cdot)\) \(\chi_{867}(412,\cdot)\) \(\chi_{867}(421,\cdot)\) \(\chi_{867}(463,\cdot)\) \(\chi_{867}(472,\cdot)\) \(\chi_{867}(514,\cdot)\) \(\chi_{867}(523,\cdot)\) \(\chi_{867}(565,\cdot)\) \(\chi_{867}(574,\cdot)\) \(\chi_{867}(625,\cdot)\) \(\chi_{867}(667,\cdot)\) \(\chi_{867}(676,\cdot)\) \(\chi_{867}(718,\cdot)\) \(\chi_{867}(727,\cdot)\) \(\chi_{867}(769,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((290,292)\) → \((1,e\left(\frac{27}{68}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 867 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{37}{68}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{13}{17}\right)\) |