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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4224.dm
\(\chi_{4224}(29,\cdot)\) \(\chi_{4224}(101,\cdot)\) \(\chi_{4224}(149,\cdot)\) \(\chi_{4224}(173,\cdot)\) \(\chi_{4224}(293,\cdot)\) \(\chi_{4224}(365,\cdot)\) \(\chi_{4224}(413,\cdot)\) \(\chi_{4224}(437,\cdot)\) \(\chi_{4224}(557,\cdot)\) \(\chi_{4224}(629,\cdot)\) \(\chi_{4224}(677,\cdot)\) \(\chi_{4224}(701,\cdot)\) \(\chi_{4224}(821,\cdot)\) \(\chi_{4224}(893,\cdot)\) \(\chi_{4224}(941,\cdot)\) \(\chi_{4224}(965,\cdot)\) \(\chi_{4224}(1085,\cdot)\) \(\chi_{4224}(1157,\cdot)\) \(\chi_{4224}(1205,\cdot)\) \(\chi_{4224}(1229,\cdot)\) \(\chi_{4224}(1349,\cdot)\) \(\chi_{4224}(1421,\cdot)\) \(\chi_{4224}(1469,\cdot)\) \(\chi_{4224}(1493,\cdot)\) \(\chi_{4224}(1613,\cdot)\) \(\chi_{4224}(1685,\cdot)\) \(\chi_{4224}(1733,\cdot)\) \(\chi_{4224}(1757,\cdot)\) \(\chi_{4224}(1877,\cdot)\) \(\chi_{4224}(1949,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((2047,133,1409,3841)\) → \((1,e\left(\frac{27}{32}\right),-1,e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4224 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{160}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{57}{160}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{81}{160}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{29}{160}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{77}{160}\right)\) |