Basic properties
| Modulus: | \(1600\) | |
| Conductor: | \(1600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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 1600.co
\(\chi_{1600}(19,\cdot)\) \(\chi_{1600}(59,\cdot)\) \(\chi_{1600}(139,\cdot)\) \(\chi_{1600}(179,\cdot)\) \(\chi_{1600}(219,\cdot)\) \(\chi_{1600}(259,\cdot)\) \(\chi_{1600}(339,\cdot)\) \(\chi_{1600}(379,\cdot)\) \(\chi_{1600}(419,\cdot)\) \(\chi_{1600}(459,\cdot)\) \(\chi_{1600}(539,\cdot)\) \(\chi_{1600}(579,\cdot)\) \(\chi_{1600}(619,\cdot)\) \(\chi_{1600}(659,\cdot)\) \(\chi_{1600}(739,\cdot)\) \(\chi_{1600}(779,\cdot)\) \(\chi_{1600}(819,\cdot)\) \(\chi_{1600}(859,\cdot)\) \(\chi_{1600}(939,\cdot)\) \(\chi_{1600}(979,\cdot)\) \(\chi_{1600}(1019,\cdot)\) \(\chi_{1600}(1059,\cdot)\) \(\chi_{1600}(1139,\cdot)\) \(\chi_{1600}(1179,\cdot)\) \(\chi_{1600}(1219,\cdot)\) \(\chi_{1600}(1259,\cdot)\) \(\chi_{1600}(1339,\cdot)\) \(\chi_{1600}(1379,\cdot)\) \(\chi_{1600}(1419,\cdot)\) \(\chi_{1600}(1459,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1151,901,577)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1600 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{27}{80}\right)\) |