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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1113.bn
\(\chi_{1113}(47,\cdot)\) \(\chi_{1113}(68,\cdot)\) \(\chi_{1113}(89,\cdot)\) \(\chi_{1113}(122,\cdot)\) \(\chi_{1113}(152,\cdot)\) \(\chi_{1113}(206,\cdot)\) \(\chi_{1113}(227,\cdot)\) \(\chi_{1113}(236,\cdot)\) \(\chi_{1113}(248,\cdot)\) \(\chi_{1113}(278,\cdot)\) \(\chi_{1113}(311,\cdot)\) \(\chi_{1113}(362,\cdot)\) \(\chi_{1113}(395,\cdot)\) \(\chi_{1113}(437,\cdot)\) \(\chi_{1113}(521,\cdot)\) \(\chi_{1113}(572,\cdot)\) \(\chi_{1113}(593,\cdot)\) \(\chi_{1113}(731,\cdot)\) \(\chi_{1113}(752,\cdot)\) \(\chi_{1113}(929,\cdot)\) \(\chi_{1113}(950,\cdot)\) \(\chi_{1113}(1076,\cdot)\) \(\chi_{1113}(1088,\cdot)\) \(\chi_{1113}(1109,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((743,955,1009)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{10}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1113 }(152, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{49}{78}\right)\) |