Basic properties
| Modulus: | \(1183\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | 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.bu
\(\chi_{1183}(10,\cdot)\) \(\chi_{1183}(82,\cdot)\) \(\chi_{1183}(101,\cdot)\) \(\chi_{1183}(173,\cdot)\) \(\chi_{1183}(264,\cdot)\) \(\chi_{1183}(283,\cdot)\) \(\chi_{1183}(355,\cdot)\) \(\chi_{1183}(374,\cdot)\) \(\chi_{1183}(446,\cdot)\) \(\chi_{1183}(465,\cdot)\) \(\chi_{1183}(537,\cdot)\) \(\chi_{1183}(556,\cdot)\) \(\chi_{1183}(628,\cdot)\) \(\chi_{1183}(647,\cdot)\) \(\chi_{1183}(719,\cdot)\) \(\chi_{1183}(738,\cdot)\) \(\chi_{1183}(810,\cdot)\) \(\chi_{1183}(829,\cdot)\) \(\chi_{1183}(901,\cdot)\) \(\chi_{1183}(920,\cdot)\) \(\chi_{1183}(1011,\cdot)\) \(\chi_{1183}(1083,\cdot)\) \(\chi_{1183}(1102,\cdot)\) \(\chi_{1183}(1174,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,1016)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{5}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1183 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{71}{78}\right)\) |