Basic properties
| Modulus: | \(1113\) | |
| Conductor: | \(371\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{371}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1113.bg
\(\chi_{1113}(16,\cdot)\) \(\chi_{1113}(46,\cdot)\) \(\chi_{1113}(100,\cdot)\) \(\chi_{1113}(121,\cdot)\) \(\chi_{1113}(130,\cdot)\) \(\chi_{1113}(142,\cdot)\) \(\chi_{1113}(172,\cdot)\) \(\chi_{1113}(205,\cdot)\) \(\chi_{1113}(256,\cdot)\) \(\chi_{1113}(289,\cdot)\) \(\chi_{1113}(331,\cdot)\) \(\chi_{1113}(415,\cdot)\) \(\chi_{1113}(466,\cdot)\) \(\chi_{1113}(487,\cdot)\) \(\chi_{1113}(625,\cdot)\) \(\chi_{1113}(646,\cdot)\) \(\chi_{1113}(823,\cdot)\) \(\chi_{1113}(844,\cdot)\) \(\chi_{1113}(970,\cdot)\) \(\chi_{1113}(982,\cdot)\) \(\chi_{1113}(1003,\cdot)\) \(\chi_{1113}(1054,\cdot)\) \(\chi_{1113}(1075,\cdot)\) \(\chi_{1113}(1096,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((743,955,1009)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{10}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1113 }(46, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) |