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 \(\chi_{371}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1113.bm
\(\chi_{1113}(4,\cdot)\) \(\chi_{1113}(25,\cdot)\) \(\chi_{1113}(37,\cdot)\) \(\chi_{1113}(163,\cdot)\) \(\chi_{1113}(184,\cdot)\) \(\chi_{1113}(361,\cdot)\) \(\chi_{1113}(382,\cdot)\) \(\chi_{1113}(520,\cdot)\) \(\chi_{1113}(541,\cdot)\) \(\chi_{1113}(592,\cdot)\) \(\chi_{1113}(676,\cdot)\) \(\chi_{1113}(718,\cdot)\) \(\chi_{1113}(751,\cdot)\) \(\chi_{1113}(802,\cdot)\) \(\chi_{1113}(835,\cdot)\) \(\chi_{1113}(865,\cdot)\) \(\chi_{1113}(877,\cdot)\) \(\chi_{1113}(886,\cdot)\) \(\chi_{1113}(907,\cdot)\) \(\chi_{1113}(961,\cdot)\) \(\chi_{1113}(991,\cdot)\) \(\chi_{1113}(1024,\cdot)\) \(\chi_{1113}(1045,\cdot)\) \(\chi_{1113}(1066,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((743,955,1009)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{21}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1113 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{17}{78}\right)\) |