Basic properties
Modulus: | \(1113\) | |
Conductor: | \(371\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{371}(40,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1113.bo
\(\chi_{1113}(40,\cdot)\) \(\chi_{1113}(82,\cdot)\) \(\chi_{1113}(115,\cdot)\) \(\chi_{1113}(166,\cdot)\) \(\chi_{1113}(199,\cdot)\) \(\chi_{1113}(229,\cdot)\) \(\chi_{1113}(241,\cdot)\) \(\chi_{1113}(250,\cdot)\) \(\chi_{1113}(271,\cdot)\) \(\chi_{1113}(325,\cdot)\) \(\chi_{1113}(355,\cdot)\) \(\chi_{1113}(388,\cdot)\) \(\chi_{1113}(409,\cdot)\) \(\chi_{1113}(430,\cdot)\) \(\chi_{1113}(481,\cdot)\) \(\chi_{1113}(502,\cdot)\) \(\chi_{1113}(514,\cdot)\) \(\chi_{1113}(640,\cdot)\) \(\chi_{1113}(661,\cdot)\) \(\chi_{1113}(838,\cdot)\) \(\chi_{1113}(859,\cdot)\) \(\chi_{1113}(997,\cdot)\) \(\chi_{1113}(1018,\cdot)\) \(\chi_{1113}(1069,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((743,955,1009)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{25}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1113 }(40, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{29}{39}\right)\) |