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.bw
\(\chi_{1183}(48,\cdot)\) \(\chi_{1183}(55,\cdot)\) \(\chi_{1183}(139,\cdot)\) \(\chi_{1183}(230,\cdot)\) \(\chi_{1183}(237,\cdot)\) \(\chi_{1183}(321,\cdot)\) \(\chi_{1183}(328,\cdot)\) \(\chi_{1183}(412,\cdot)\) \(\chi_{1183}(419,\cdot)\) \(\chi_{1183}(503,\cdot)\) \(\chi_{1183}(510,\cdot)\) \(\chi_{1183}(594,\cdot)\) \(\chi_{1183}(601,\cdot)\) \(\chi_{1183}(685,\cdot)\) \(\chi_{1183}(692,\cdot)\) \(\chi_{1183}(776,\cdot)\) \(\chi_{1183}(783,\cdot)\) \(\chi_{1183}(874,\cdot)\) \(\chi_{1183}(958,\cdot)\) \(\chi_{1183}(965,\cdot)\) \(\chi_{1183}(1049,\cdot)\) \(\chi_{1183}(1056,\cdot)\) \(\chi_{1183}(1140,\cdot)\) \(\chi_{1183}(1147,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,1016)\) → \((-1,e\left(\frac{32}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1183 }(48, a) \) | \(-1\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{23}{26}\right)\) |