Basic properties
| Modulus: | \(1183\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1183.bj
\(\chi_{1183}(9,\cdot)\) \(\chi_{1183}(81,\cdot)\) \(\chi_{1183}(100,\cdot)\) \(\chi_{1183}(172,\cdot)\) \(\chi_{1183}(263,\cdot)\) \(\chi_{1183}(282,\cdot)\) \(\chi_{1183}(354,\cdot)\) \(\chi_{1183}(373,\cdot)\) \(\chi_{1183}(445,\cdot)\) \(\chi_{1183}(464,\cdot)\) \(\chi_{1183}(536,\cdot)\) \(\chi_{1183}(555,\cdot)\) \(\chi_{1183}(627,\cdot)\) \(\chi_{1183}(646,\cdot)\) \(\chi_{1183}(718,\cdot)\) \(\chi_{1183}(737,\cdot)\) \(\chi_{1183}(809,\cdot)\) \(\chi_{1183}(828,\cdot)\) \(\chi_{1183}(900,\cdot)\) \(\chi_{1183}(919,\cdot)\) \(\chi_{1183}(1010,\cdot)\) \(\chi_{1183}(1082,\cdot)\) \(\chi_{1183}(1101,\cdot)\) \(\chi_{1183}(1173,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.1 |
Values on generators
\((339,1016)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{28}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1183 }(900, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) |