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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1183.ce
\(\chi_{1183}(18,\cdot)\) \(\chi_{1183}(44,\cdot)\) \(\chi_{1183}(60,\cdot)\) \(\chi_{1183}(86,\cdot)\) \(\chi_{1183}(109,\cdot)\) \(\chi_{1183}(135,\cdot)\) \(\chi_{1183}(151,\cdot)\) \(\chi_{1183}(177,\cdot)\) \(\chi_{1183}(200,\cdot)\) \(\chi_{1183}(226,\cdot)\) \(\chi_{1183}(242,\cdot)\) \(\chi_{1183}(291,\cdot)\) \(\chi_{1183}(317,\cdot)\) \(\chi_{1183}(333,\cdot)\) \(\chi_{1183}(359,\cdot)\) \(\chi_{1183}(382,\cdot)\) \(\chi_{1183}(424,\cdot)\) \(\chi_{1183}(450,\cdot)\) \(\chi_{1183}(473,\cdot)\) \(\chi_{1183}(499,\cdot)\) \(\chi_{1183}(515,\cdot)\) \(\chi_{1183}(541,\cdot)\) \(\chi_{1183}(564,\cdot)\) \(\chi_{1183}(590,\cdot)\) \(\chi_{1183}(632,\cdot)\) \(\chi_{1183}(655,\cdot)\) \(\chi_{1183}(681,\cdot)\) \(\chi_{1183}(697,\cdot)\) \(\chi_{1183}(723,\cdot)\) \(\chi_{1183}(772,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((339,1016)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{31}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1183 }(18, a) \) | \(-1\) | \(1\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{11}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) |