Basic properties
| Modulus: | \(1183\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 1183.cd
\(\chi_{1183}(45,\cdot)\) \(\chi_{1183}(54,\cdot)\) \(\chi_{1183}(59,\cdot)\) \(\chi_{1183}(136,\cdot)\) \(\chi_{1183}(145,\cdot)\) \(\chi_{1183}(180,\cdot)\) \(\chi_{1183}(227,\cdot)\) \(\chi_{1183}(236,\cdot)\) \(\chi_{1183}(241,\cdot)\) \(\chi_{1183}(271,\cdot)\) \(\chi_{1183}(318,\cdot)\) \(\chi_{1183}(327,\cdot)\) \(\chi_{1183}(332,\cdot)\) \(\chi_{1183}(362,\cdot)\) \(\chi_{1183}(409,\cdot)\) \(\chi_{1183}(423,\cdot)\) \(\chi_{1183}(453,\cdot)\) \(\chi_{1183}(500,\cdot)\) \(\chi_{1183}(509,\cdot)\) \(\chi_{1183}(514,\cdot)\) \(\chi_{1183}(544,\cdot)\) \(\chi_{1183}(591,\cdot)\) \(\chi_{1183}(600,\cdot)\) \(\chi_{1183}(605,\cdot)\) \(\chi_{1183}(635,\cdot)\) \(\chi_{1183}(682,\cdot)\) \(\chi_{1183}(691,\cdot)\) \(\chi_{1183}(696,\cdot)\) \(\chi_{1183}(726,\cdot)\) \(\chi_{1183}(773,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((339,1016)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{149}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1183 }(136, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{67}{156}\right)\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{7}{39}\right)\) |