Basic properties
Modulus: | \(939\) | |
Conductor: | \(939\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 939.y
\(\chi_{939}(11,\cdot)\) \(\chi_{939}(104,\cdot)\) \(\chi_{939}(176,\cdot)\) \(\chi_{939}(194,\cdot)\) \(\chi_{939}(230,\cdot)\) \(\chi_{939}(263,\cdot)\) \(\chi_{939}(287,\cdot)\) \(\chi_{939}(317,\cdot)\) \(\chi_{939}(383,\cdot)\) \(\chi_{939}(398,\cdot)\) \(\chi_{939}(452,\cdot)\) \(\chi_{939}(482,\cdot)\) \(\chi_{939}(494,\cdot)\) \(\chi_{939}(545,\cdot)\) \(\chi_{939}(548,\cdot)\) \(\chi_{939}(617,\cdot)\) \(\chi_{939}(623,\cdot)\) \(\chi_{939}(638,\cdot)\) \(\chi_{939}(683,\cdot)\) \(\chi_{939}(734,\cdot)\) \(\chi_{939}(797,\cdot)\) \(\chi_{939}(818,\cdot)\) \(\chi_{939}(863,\cdot)\) \(\chi_{939}(923,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((314,10)\) → \((-1,e\left(\frac{47}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 939 }(863, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(1\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) |