Basic properties
| Modulus: | \(221760\) | |
| Conductor: | \(221760\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | 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 221760.dxi
\(\chi_{221760}(13,\cdot)\) \(\chi_{221760}(3373,\cdot)\) \(\chi_{221760}(5557,\cdot)\) \(\chi_{221760}(8917,\cdot)\) \(\chi_{221760}(10093,\cdot)\) \(\chi_{221760}(15133,\cdot)\) \(\chi_{221760}(15637,\cdot)\) \(\chi_{221760}(18493,\cdot)\) \(\chi_{221760}(20677,\cdot)\) \(\chi_{221760}(24037,\cdot)\) \(\chi_{221760}(28573,\cdot)\) \(\chi_{221760}(33613,\cdot)\) \(\chi_{221760}(34117,\cdot)\) \(\chi_{221760}(39157,\cdot)\) \(\chi_{221760}(40333,\cdot)\) \(\chi_{221760}(45877,\cdot)\) \(\chi_{221760}(55453,\cdot)\) \(\chi_{221760}(58813,\cdot)\) \(\chi_{221760}(60997,\cdot)\) \(\chi_{221760}(64357,\cdot)\) \(\chi_{221760}(65533,\cdot)\) \(\chi_{221760}(70573,\cdot)\) \(\chi_{221760}(71077,\cdot)\) \(\chi_{221760}(73933,\cdot)\) \(\chi_{221760}(76117,\cdot)\) \(\chi_{221760}(79477,\cdot)\) \(\chi_{221760}(84013,\cdot)\) \(\chi_{221760}(89053,\cdot)\) \(\chi_{221760}(89557,\cdot)\) \(\chi_{221760}(94597,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((48511,124741,98561,133057,190081,141121)\) → \((1,e\left(\frac{15}{16}\right),e\left(\frac{1}{3}\right),-i,-1,e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 221760 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{139}{240}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{203}{240}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{19}{30}\right)\) |