Basic properties
Modulus: | \(861\) | |
Conductor: | \(861\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 861.cl
\(\chi_{861}(11,\cdot)\) \(\chi_{861}(53,\cdot)\) \(\chi_{861}(65,\cdot)\) \(\chi_{861}(95,\cdot)\) \(\chi_{861}(116,\cdot)\) \(\chi_{861}(149,\cdot)\) \(\chi_{861}(158,\cdot)\) \(\chi_{861}(170,\cdot)\) \(\chi_{861}(179,\cdot)\) \(\chi_{861}(212,\cdot)\) \(\chi_{861}(233,\cdot)\) \(\chi_{861}(263,\cdot)\) \(\chi_{861}(275,\cdot)\) \(\chi_{861}(317,\cdot)\) \(\chi_{861}(347,\cdot)\) \(\chi_{861}(380,\cdot)\) \(\chi_{861}(422,\cdot)\) \(\chi_{861}(464,\cdot)\) \(\chi_{861}(473,\cdot)\) \(\chi_{861}(485,\cdot)\) \(\chi_{861}(527,\cdot)\) \(\chi_{861}(548,\cdot)\) \(\chi_{861}(557,\cdot)\) \(\chi_{861}(632,\cdot)\) \(\chi_{861}(641,\cdot)\) \(\chi_{861}(662,\cdot)\) \(\chi_{861}(704,\cdot)\) \(\chi_{861}(716,\cdot)\) \(\chi_{861}(725,\cdot)\) \(\chi_{861}(767,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((575,493,211)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{31}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 861 }(464, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{77}{120}\right)\) |