Basic properties
| Modulus: | \(1183\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1183.bk
\(\chi_{1183}(29,\cdot)\) \(\chi_{1183}(113,\cdot)\) \(\chi_{1183}(120,\cdot)\) \(\chi_{1183}(204,\cdot)\) \(\chi_{1183}(211,\cdot)\) \(\chi_{1183}(295,\cdot)\) \(\chi_{1183}(302,\cdot)\) \(\chi_{1183}(386,\cdot)\) \(\chi_{1183}(393,\cdot)\) \(\chi_{1183}(477,\cdot)\) \(\chi_{1183}(568,\cdot)\) \(\chi_{1183}(575,\cdot)\) \(\chi_{1183}(659,\cdot)\) \(\chi_{1183}(666,\cdot)\) \(\chi_{1183}(750,\cdot)\) \(\chi_{1183}(757,\cdot)\) \(\chi_{1183}(841,\cdot)\) \(\chi_{1183}(848,\cdot)\) \(\chi_{1183}(932,\cdot)\) \(\chi_{1183}(939,\cdot)\) \(\chi_{1183}(1023,\cdot)\) \(\chi_{1183}(1030,\cdot)\) \(\chi_{1183}(1114,\cdot)\) \(\chi_{1183}(1121,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((339,1016)\) → \((1,e\left(\frac{10}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1183 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) |