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.br
\(\chi_{1183}(12,\cdot)\) \(\chi_{1183}(38,\cdot)\) \(\chi_{1183}(103,\cdot)\) \(\chi_{1183}(129,\cdot)\) \(\chi_{1183}(194,\cdot)\) \(\chi_{1183}(220,\cdot)\) \(\chi_{1183}(285,\cdot)\) \(\chi_{1183}(311,\cdot)\) \(\chi_{1183}(376,\cdot)\) \(\chi_{1183}(402,\cdot)\) \(\chi_{1183}(467,\cdot)\) \(\chi_{1183}(493,\cdot)\) \(\chi_{1183}(558,\cdot)\) \(\chi_{1183}(584,\cdot)\) \(\chi_{1183}(649,\cdot)\) \(\chi_{1183}(740,\cdot)\) \(\chi_{1183}(766,\cdot)\) \(\chi_{1183}(831,\cdot)\) \(\chi_{1183}(857,\cdot)\) \(\chi_{1183}(922,\cdot)\) \(\chi_{1183}(948,\cdot)\) \(\chi_{1183}(1039,\cdot)\) \(\chi_{1183}(1104,\cdot)\) \(\chi_{1183}(1130,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,1016)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{9}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1183 }(584, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{35}{78}\right)\) |