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.bx
\(\chi_{1183}(3,\cdot)\) \(\chi_{1183}(61,\cdot)\) \(\chi_{1183}(94,\cdot)\) \(\chi_{1183}(152,\cdot)\) \(\chi_{1183}(185,\cdot)\) \(\chi_{1183}(243,\cdot)\) \(\chi_{1183}(276,\cdot)\) \(\chi_{1183}(334,\cdot)\) \(\chi_{1183}(367,\cdot)\) \(\chi_{1183}(425,\cdot)\) \(\chi_{1183}(458,\cdot)\) \(\chi_{1183}(516,\cdot)\) \(\chi_{1183}(549,\cdot)\) \(\chi_{1183}(607,\cdot)\) \(\chi_{1183}(640,\cdot)\) \(\chi_{1183}(731,\cdot)\) \(\chi_{1183}(789,\cdot)\) \(\chi_{1183}(880,\cdot)\) \(\chi_{1183}(913,\cdot)\) \(\chi_{1183}(971,\cdot)\) \(\chi_{1183}(1004,\cdot)\) \(\chi_{1183}(1062,\cdot)\) \(\chi_{1183}(1095,\cdot)\) \(\chi_{1183}(1153,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,1016)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{31}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1183 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{77}{78}\right)\) |