Basic properties
| Modulus: | \(221760\) | |
| Conductor: | \(22176\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{22176}(13901,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 221760.dnd
\(\chi_{221760}(41,\cdot)\) \(\chi_{221760}(6761,\cdot)\) \(\chi_{221760}(21881,\cdot)\) \(\chi_{221760}(25241,\cdot)\) \(\chi_{221760}(31961,\cdot)\) \(\chi_{221760}(37001,\cdot)\) \(\chi_{221760}(40361,\cdot)\) \(\chi_{221760}(50441,\cdot)\) \(\chi_{221760}(55481,\cdot)\) \(\chi_{221760}(62201,\cdot)\) \(\chi_{221760}(77321,\cdot)\) \(\chi_{221760}(80681,\cdot)\) \(\chi_{221760}(87401,\cdot)\) \(\chi_{221760}(92441,\cdot)\) \(\chi_{221760}(95801,\cdot)\) \(\chi_{221760}(105881,\cdot)\) \(\chi_{221760}(110921,\cdot)\) \(\chi_{221760}(117641,\cdot)\) \(\chi_{221760}(132761,\cdot)\) \(\chi_{221760}(136121,\cdot)\) \(\chi_{221760}(142841,\cdot)\) \(\chi_{221760}(147881,\cdot)\) \(\chi_{221760}(151241,\cdot)\) \(\chi_{221760}(161321,\cdot)\) \(\chi_{221760}(166361,\cdot)\) \(\chi_{221760}(173081,\cdot)\) \(\chi_{221760}(188201,\cdot)\) \(\chi_{221760}(191561,\cdot)\) \(\chi_{221760}(198281,\cdot)\) \(\chi_{221760}(203321,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((48511,124741,98561,133057,190081,141121)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{5}{6}\right),1,-1,e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 221760 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{7}{30}\right)\) |