Basic properties
| Modulus: | \(3200\) | |
| Conductor: | \(3200\) | 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 3200.dh
\(\chi_{3200}(21,\cdot)\) \(\chi_{3200}(61,\cdot)\) \(\chi_{3200}(141,\cdot)\) \(\chi_{3200}(181,\cdot)\) \(\chi_{3200}(221,\cdot)\) \(\chi_{3200}(261,\cdot)\) \(\chi_{3200}(341,\cdot)\) \(\chi_{3200}(381,\cdot)\) \(\chi_{3200}(421,\cdot)\) \(\chi_{3200}(461,\cdot)\) \(\chi_{3200}(541,\cdot)\) \(\chi_{3200}(581,\cdot)\) \(\chi_{3200}(621,\cdot)\) \(\chi_{3200}(661,\cdot)\) \(\chi_{3200}(741,\cdot)\) \(\chi_{3200}(781,\cdot)\) \(\chi_{3200}(821,\cdot)\) \(\chi_{3200}(861,\cdot)\) \(\chi_{3200}(941,\cdot)\) \(\chi_{3200}(981,\cdot)\) \(\chi_{3200}(1021,\cdot)\) \(\chi_{3200}(1061,\cdot)\) \(\chi_{3200}(1141,\cdot)\) \(\chi_{3200}(1181,\cdot)\) \(\chi_{3200}(1221,\cdot)\) \(\chi_{3200}(1261,\cdot)\) \(\chi_{3200}(1341,\cdot)\) \(\chi_{3200}(1381,\cdot)\) \(\chi_{3200}(1421,\cdot)\) \(\chi_{3200}(1461,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((1151,901,2177)\) → \((1,e\left(\frac{13}{32}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 3200 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{160}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{21}{160}\right)\) | \(e\left(\frac{79}{160}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{23}{160}\right)\) | \(e\left(\frac{77}{160}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{41}{160}\right)\) |