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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3200.dd
\(\chi_{3200}(53,\cdot)\) \(\chi_{3200}(77,\cdot)\) \(\chi_{3200}(133,\cdot)\) \(\chi_{3200}(213,\cdot)\) \(\chi_{3200}(237,\cdot)\) \(\chi_{3200}(317,\cdot)\) \(\chi_{3200}(373,\cdot)\) \(\chi_{3200}(397,\cdot)\) \(\chi_{3200}(453,\cdot)\) \(\chi_{3200}(477,\cdot)\) \(\chi_{3200}(533,\cdot)\) \(\chi_{3200}(613,\cdot)\) \(\chi_{3200}(637,\cdot)\) \(\chi_{3200}(717,\cdot)\) \(\chi_{3200}(773,\cdot)\) \(\chi_{3200}(797,\cdot)\) \(\chi_{3200}(853,\cdot)\) \(\chi_{3200}(877,\cdot)\) \(\chi_{3200}(933,\cdot)\) \(\chi_{3200}(1013,\cdot)\) \(\chi_{3200}(1037,\cdot)\) \(\chi_{3200}(1117,\cdot)\) \(\chi_{3200}(1173,\cdot)\) \(\chi_{3200}(1197,\cdot)\) \(\chi_{3200}(1253,\cdot)\) \(\chi_{3200}(1277,\cdot)\) \(\chi_{3200}(1333,\cdot)\) \(\chi_{3200}(1413,\cdot)\) \(\chi_{3200}(1437,\cdot)\) \(\chi_{3200}(1517,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((1151,901,2177)\) → \((1,e\left(\frac{5}{32}\right),e\left(\frac{7}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 3200 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{147}{160}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{141}{160}\right)\) | \(e\left(\frac{159}{160}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{143}{160}\right)\) | \(e\left(\frac{37}{160}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{121}{160}\right)\) |