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.bv
\(\chi_{1183}(40,\cdot)\) \(\chi_{1183}(66,\cdot)\) \(\chi_{1183}(131,\cdot)\) \(\chi_{1183}(157,\cdot)\) \(\chi_{1183}(222,\cdot)\) \(\chi_{1183}(248,\cdot)\) \(\chi_{1183}(313,\cdot)\) \(\chi_{1183}(404,\cdot)\) \(\chi_{1183}(430,\cdot)\) \(\chi_{1183}(495,\cdot)\) \(\chi_{1183}(521,\cdot)\) \(\chi_{1183}(586,\cdot)\) \(\chi_{1183}(612,\cdot)\) \(\chi_{1183}(703,\cdot)\) \(\chi_{1183}(768,\cdot)\) \(\chi_{1183}(794,\cdot)\) \(\chi_{1183}(859,\cdot)\) \(\chi_{1183}(885,\cdot)\) \(\chi_{1183}(950,\cdot)\) \(\chi_{1183}(976,\cdot)\) \(\chi_{1183}(1041,\cdot)\) \(\chi_{1183}(1067,\cdot)\) \(\chi_{1183}(1132,\cdot)\) \(\chi_{1183}(1158,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,1016)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1183 }(40, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) |