Basic properties
| Modulus: | \(221760\) | |
| Conductor: | \(24640\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{24640}(6739,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 221760.ebt
\(\chi_{221760}(19,\cdot)\) \(\chi_{221760}(1459,\cdot)\) \(\chi_{221760}(3979,\cdot)\) \(\chi_{221760}(12619,\cdot)\) \(\chi_{221760}(16579,\cdot)\) \(\chi_{221760}(22699,\cdot)\) \(\chi_{221760}(25219,\cdot)\) \(\chi_{221760}(26659,\cdot)\) \(\chi_{221760}(27739,\cdot)\) \(\chi_{221760}(29179,\cdot)\) \(\chi_{221760}(31699,\cdot)\) \(\chi_{221760}(40339,\cdot)\) \(\chi_{221760}(44299,\cdot)\) \(\chi_{221760}(50419,\cdot)\) \(\chi_{221760}(52939,\cdot)\) \(\chi_{221760}(54379,\cdot)\) \(\chi_{221760}(55459,\cdot)\) \(\chi_{221760}(56899,\cdot)\) \(\chi_{221760}(59419,\cdot)\) \(\chi_{221760}(68059,\cdot)\) \(\chi_{221760}(72019,\cdot)\) \(\chi_{221760}(78139,\cdot)\) \(\chi_{221760}(80659,\cdot)\) \(\chi_{221760}(82099,\cdot)\) \(\chi_{221760}(83179,\cdot)\) \(\chi_{221760}(84619,\cdot)\) \(\chi_{221760}(87139,\cdot)\) \(\chi_{221760}(95779,\cdot)\) \(\chi_{221760}(99739,\cdot)\) \(\chi_{221760}(105859,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((48511,124741,98561,133057,190081,141121)\) → \((-1,e\left(\frac{7}{16}\right),1,-1,e\left(\frac{5}{6}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 221760 }(80659, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{199}{240}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{121}{240}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{60}\right)\) |