Basic properties
| Modulus: | \(1113\) | |
| Conductor: | \(1113\) | 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 1113.bl
\(\chi_{1113}(44,\cdot)\) \(\chi_{1113}(95,\cdot)\) \(\chi_{1113}(116,\cdot)\) \(\chi_{1113}(254,\cdot)\) \(\chi_{1113}(275,\cdot)\) \(\chi_{1113}(452,\cdot)\) \(\chi_{1113}(473,\cdot)\) \(\chi_{1113}(599,\cdot)\) \(\chi_{1113}(611,\cdot)\) \(\chi_{1113}(632,\cdot)\) \(\chi_{1113}(683,\cdot)\) \(\chi_{1113}(704,\cdot)\) \(\chi_{1113}(725,\cdot)\) \(\chi_{1113}(758,\cdot)\) \(\chi_{1113}(788,\cdot)\) \(\chi_{1113}(842,\cdot)\) \(\chi_{1113}(863,\cdot)\) \(\chi_{1113}(872,\cdot)\) \(\chi_{1113}(884,\cdot)\) \(\chi_{1113}(914,\cdot)\) \(\chi_{1113}(947,\cdot)\) \(\chi_{1113}(998,\cdot)\) \(\chi_{1113}(1031,\cdot)\) \(\chi_{1113}(1073,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((743,955,1009)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{2}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1113 }(44, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) |