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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1183.bz
\(\chi_{1183}(4,\cdot)\) \(\chi_{1183}(95,\cdot)\) \(\chi_{1183}(114,\cdot)\) \(\chi_{1183}(186,\cdot)\) \(\chi_{1183}(205,\cdot)\) \(\chi_{1183}(277,\cdot)\) \(\chi_{1183}(296,\cdot)\) \(\chi_{1183}(368,\cdot)\) \(\chi_{1183}(387,\cdot)\) \(\chi_{1183}(459,\cdot)\) \(\chi_{1183}(478,\cdot)\) \(\chi_{1183}(550,\cdot)\) \(\chi_{1183}(569,\cdot)\) \(\chi_{1183}(641,\cdot)\) \(\chi_{1183}(660,\cdot)\) \(\chi_{1183}(732,\cdot)\) \(\chi_{1183}(751,\cdot)\) \(\chi_{1183}(842,\cdot)\) \(\chi_{1183}(914,\cdot)\) \(\chi_{1183}(933,\cdot)\) \(\chi_{1183}(1005,\cdot)\) \(\chi_{1183}(1024,\cdot)\) \(\chi_{1183}(1096,\cdot)\) \(\chi_{1183}(1115,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,1016)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1183 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) |