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.bs
\(\chi_{1183}(25,\cdot)\) \(\chi_{1183}(51,\cdot)\) \(\chi_{1183}(116,\cdot)\) \(\chi_{1183}(142,\cdot)\) \(\chi_{1183}(207,\cdot)\) \(\chi_{1183}(233,\cdot)\) \(\chi_{1183}(298,\cdot)\) \(\chi_{1183}(324,\cdot)\) \(\chi_{1183}(389,\cdot)\) \(\chi_{1183}(415,\cdot)\) \(\chi_{1183}(480,\cdot)\) \(\chi_{1183}(571,\cdot)\) \(\chi_{1183}(597,\cdot)\) \(\chi_{1183}(662,\cdot)\) \(\chi_{1183}(688,\cdot)\) \(\chi_{1183}(753,\cdot)\) \(\chi_{1183}(779,\cdot)\) \(\chi_{1183}(870,\cdot)\) \(\chi_{1183}(935,\cdot)\) \(\chi_{1183}(961,\cdot)\) \(\chi_{1183}(1026,\cdot)\) \(\chi_{1183}(1052,\cdot)\) \(\chi_{1183}(1117,\cdot)\) \(\chi_{1183}(1143,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,1016)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{23}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1183 }(480, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{31}{39}\right)\) |