Basic properties
| Modulus: | \(1113\) | |
| Conductor: | \(1113\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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.bv
\(\chi_{1113}(2,\cdot)\) \(\chi_{1113}(32,\cdot)\) \(\chi_{1113}(65,\cdot)\) \(\chi_{1113}(74,\cdot)\) \(\chi_{1113}(86,\cdot)\) \(\chi_{1113}(128,\cdot)\) \(\chi_{1113}(137,\cdot)\) \(\chi_{1113}(179,\cdot)\) \(\chi_{1113}(191,\cdot)\) \(\chi_{1113}(200,\cdot)\) \(\chi_{1113}(233,\cdot)\) \(\chi_{1113}(263,\cdot)\) \(\chi_{1113}(284,\cdot)\) \(\chi_{1113}(296,\cdot)\) \(\chi_{1113}(326,\cdot)\) \(\chi_{1113}(338,\cdot)\) \(\chi_{1113}(359,\cdot)\) \(\chi_{1113}(368,\cdot)\) \(\chi_{1113}(389,\cdot)\) \(\chi_{1113}(410,\cdot)\) \(\chi_{1113}(422,\cdot)\) \(\chi_{1113}(443,\cdot)\) \(\chi_{1113}(485,\cdot)\) \(\chi_{1113}(527,\cdot)\) \(\chi_{1113}(548,\cdot)\) \(\chi_{1113}(557,\cdot)\) \(\chi_{1113}(569,\cdot)\) \(\chi_{1113}(578,\cdot)\) \(\chi_{1113}(641,\cdot)\) \(\chi_{1113}(662,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((743,955,1009)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{5}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1113 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{55}{156}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{139}{156}\right)\) |