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.bl
\(\chi_{1183}(53,\cdot)\) \(\chi_{1183}(79,\cdot)\) \(\chi_{1183}(144,\cdot)\) \(\chi_{1183}(235,\cdot)\) \(\chi_{1183}(261,\cdot)\) \(\chi_{1183}(326,\cdot)\) \(\chi_{1183}(352,\cdot)\) \(\chi_{1183}(417,\cdot)\) \(\chi_{1183}(443,\cdot)\) \(\chi_{1183}(534,\cdot)\) \(\chi_{1183}(599,\cdot)\) \(\chi_{1183}(625,\cdot)\) \(\chi_{1183}(690,\cdot)\) \(\chi_{1183}(716,\cdot)\) \(\chi_{1183}(781,\cdot)\) \(\chi_{1183}(807,\cdot)\) \(\chi_{1183}(872,\cdot)\) \(\chi_{1183}(898,\cdot)\) \(\chi_{1183}(963,\cdot)\) \(\chi_{1183}(989,\cdot)\) \(\chi_{1183}(1054,\cdot)\) \(\chi_{1183}(1080,\cdot)\) \(\chi_{1183}(1145,\cdot)\) \(\chi_{1183}(1171,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((339,1016)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{11}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1183 }(599, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) |