Basic properties
| Modulus: | \(221760\) | |
| Conductor: | \(44352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{44352}(3181,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 221760.edh
\(\chi_{221760}(61,\cdot)\) \(\chi_{221760}(2581,\cdot)\) \(\chi_{221760}(3181,\cdot)\) \(\chi_{221760}(5101,\cdot)\) \(\chi_{221760}(13261,\cdot)\) \(\chi_{221760}(15781,\cdot)\) \(\chi_{221760}(17701,\cdot)\) \(\chi_{221760}(18301,\cdot)\) \(\chi_{221760}(27781,\cdot)\) \(\chi_{221760}(30301,\cdot)\) \(\chi_{221760}(30901,\cdot)\) \(\chi_{221760}(32821,\cdot)\) \(\chi_{221760}(40981,\cdot)\) \(\chi_{221760}(43501,\cdot)\) \(\chi_{221760}(45421,\cdot)\) \(\chi_{221760}(46021,\cdot)\) \(\chi_{221760}(55501,\cdot)\) \(\chi_{221760}(58021,\cdot)\) \(\chi_{221760}(58621,\cdot)\) \(\chi_{221760}(60541,\cdot)\) \(\chi_{221760}(68701,\cdot)\) \(\chi_{221760}(71221,\cdot)\) \(\chi_{221760}(73141,\cdot)\) \(\chi_{221760}(73741,\cdot)\) \(\chi_{221760}(83221,\cdot)\) \(\chi_{221760}(85741,\cdot)\) \(\chi_{221760}(86341,\cdot)\) \(\chi_{221760}(88261,\cdot)\) \(\chi_{221760}(96421,\cdot)\) \(\chi_{221760}(98941,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((48511,124741,98561,133057,190081,141121)\) → \((1,e\left(\frac{7}{16}\right),e\left(\frac{1}{3}\right),1,e\left(\frac{1}{6}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 221760 }(3181, a) \) | \(1\) | \(1\) | \(e\left(\frac{199}{240}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{47}{240}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{203}{240}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{113}{240}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{13}{60}\right)\) |