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.by
\(\chi_{1183}(17,\cdot)\) \(\chi_{1183}(75,\cdot)\) \(\chi_{1183}(108,\cdot)\) \(\chi_{1183}(166,\cdot)\) \(\chi_{1183}(199,\cdot)\) \(\chi_{1183}(257,\cdot)\) \(\chi_{1183}(290,\cdot)\) \(\chi_{1183}(348,\cdot)\) \(\chi_{1183}(381,\cdot)\) \(\chi_{1183}(439,\cdot)\) \(\chi_{1183}(472,\cdot)\) \(\chi_{1183}(563,\cdot)\) \(\chi_{1183}(621,\cdot)\) \(\chi_{1183}(712,\cdot)\) \(\chi_{1183}(745,\cdot)\) \(\chi_{1183}(803,\cdot)\) \(\chi_{1183}(836,\cdot)\) \(\chi_{1183}(894,\cdot)\) \(\chi_{1183}(927,\cdot)\) \(\chi_{1183}(985,\cdot)\) \(\chi_{1183}(1018,\cdot)\) \(\chi_{1183}(1076,\cdot)\) \(\chi_{1183}(1109,\cdot)\) \(\chi_{1183}(1167,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,1016)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{73}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1183 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{59}{78}\right)\) |