Basic properties
Modulus: | \(869\) | |
Conductor: | \(869\) | 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 869.x
\(\chi_{869}(32,\cdot)\) \(\chi_{869}(76,\cdot)\) \(\chi_{869}(98,\cdot)\) \(\chi_{869}(208,\cdot)\) \(\chi_{869}(230,\cdot)\) \(\chi_{869}(241,\cdot)\) \(\chi_{869}(263,\cdot)\) \(\chi_{869}(318,\cdot)\) \(\chi_{869}(329,\cdot)\) \(\chi_{869}(406,\cdot)\) \(\chi_{869}(439,\cdot)\) \(\chi_{869}(483,\cdot)\) \(\chi_{869}(494,\cdot)\) \(\chi_{869}(505,\cdot)\) \(\chi_{869}(516,\cdot)\) \(\chi_{869}(593,\cdot)\) \(\chi_{869}(604,\cdot)\) \(\chi_{869}(626,\cdot)\) \(\chi_{869}(637,\cdot)\) \(\chi_{869}(648,\cdot)\) \(\chi_{869}(681,\cdot)\) \(\chi_{869}(736,\cdot)\) \(\chi_{869}(747,\cdot)\) \(\chi_{869}(835,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((475,793)\) → \((-1,e\left(\frac{10}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 869 }(32, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{4}{13}\right)\) |