Basic properties
| Modulus: | \(4224\) | |
| Conductor: | \(4224\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(160\) | 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 4224.dp
\(\chi_{4224}(5,\cdot)\) \(\chi_{4224}(53,\cdot)\) \(\chi_{4224}(125,\cdot)\) \(\chi_{4224}(245,\cdot)\) \(\chi_{4224}(269,\cdot)\) \(\chi_{4224}(317,\cdot)\) \(\chi_{4224}(389,\cdot)\) \(\chi_{4224}(509,\cdot)\) \(\chi_{4224}(533,\cdot)\) \(\chi_{4224}(581,\cdot)\) \(\chi_{4224}(653,\cdot)\) \(\chi_{4224}(773,\cdot)\) \(\chi_{4224}(797,\cdot)\) \(\chi_{4224}(845,\cdot)\) \(\chi_{4224}(917,\cdot)\) \(\chi_{4224}(1037,\cdot)\) \(\chi_{4224}(1061,\cdot)\) \(\chi_{4224}(1109,\cdot)\) \(\chi_{4224}(1181,\cdot)\) \(\chi_{4224}(1301,\cdot)\) \(\chi_{4224}(1325,\cdot)\) \(\chi_{4224}(1373,\cdot)\) \(\chi_{4224}(1445,\cdot)\) \(\chi_{4224}(1565,\cdot)\) \(\chi_{4224}(1589,\cdot)\) \(\chi_{4224}(1637,\cdot)\) \(\chi_{4224}(1709,\cdot)\) \(\chi_{4224}(1829,\cdot)\) \(\chi_{4224}(1853,\cdot)\) \(\chi_{4224}(1901,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((2047,133,1409,3841)\) → \((1,e\left(\frac{5}{32}\right),-1,e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4224 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{160}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{151}{160}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{63}{160}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{147}{160}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{131}{160}\right)\) |