Basic properties
Modulus: | \(1156\) | |
Conductor: | \(1156\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1156.o
\(\chi_{1156}(47,\cdot)\) \(\chi_{1156}(55,\cdot)\) \(\chi_{1156}(115,\cdot)\) \(\chi_{1156}(123,\cdot)\) \(\chi_{1156}(183,\cdot)\) \(\chi_{1156}(191,\cdot)\) \(\chi_{1156}(259,\cdot)\) \(\chi_{1156}(319,\cdot)\) \(\chi_{1156}(387,\cdot)\) \(\chi_{1156}(395,\cdot)\) \(\chi_{1156}(455,\cdot)\) \(\chi_{1156}(463,\cdot)\) \(\chi_{1156}(523,\cdot)\) \(\chi_{1156}(531,\cdot)\) \(\chi_{1156}(591,\cdot)\) \(\chi_{1156}(599,\cdot)\) \(\chi_{1156}(659,\cdot)\) \(\chi_{1156}(667,\cdot)\) \(\chi_{1156}(727,\cdot)\) \(\chi_{1156}(735,\cdot)\) \(\chi_{1156}(795,\cdot)\) \(\chi_{1156}(803,\cdot)\) \(\chi_{1156}(863,\cdot)\) \(\chi_{1156}(871,\cdot)\) \(\chi_{1156}(931,\cdot)\) \(\chi_{1156}(939,\cdot)\) \(\chi_{1156}(999,\cdot)\) \(\chi_{1156}(1007,\cdot)\) \(\chi_{1156}(1067,\cdot)\) \(\chi_{1156}(1075,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{68})$ |
Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((579,581)\) → \((-1,e\left(\frac{55}{68}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 1156 }(1007, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{15}{68}\right)\) | \(e\left(\frac{59}{68}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{59}{68}\right)\) |