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.de
\(\chi_{3200}(11,\cdot)\) \(\chi_{3200}(91,\cdot)\) \(\chi_{3200}(131,\cdot)\) \(\chi_{3200}(171,\cdot)\) \(\chi_{3200}(211,\cdot)\) \(\chi_{3200}(291,\cdot)\) \(\chi_{3200}(331,\cdot)\) \(\chi_{3200}(371,\cdot)\) \(\chi_{3200}(411,\cdot)\) \(\chi_{3200}(491,\cdot)\) \(\chi_{3200}(531,\cdot)\) \(\chi_{3200}(571,\cdot)\) \(\chi_{3200}(611,\cdot)\) \(\chi_{3200}(691,\cdot)\) \(\chi_{3200}(731,\cdot)\) \(\chi_{3200}(771,\cdot)\) \(\chi_{3200}(811,\cdot)\) \(\chi_{3200}(891,\cdot)\) \(\chi_{3200}(931,\cdot)\) \(\chi_{3200}(971,\cdot)\) \(\chi_{3200}(1011,\cdot)\) \(\chi_{3200}(1091,\cdot)\) \(\chi_{3200}(1131,\cdot)\) \(\chi_{3200}(1171,\cdot)\) \(\chi_{3200}(1211,\cdot)\) \(\chi_{3200}(1291,\cdot)\) \(\chi_{3200}(1331,\cdot)\) \(\chi_{3200}(1371,\cdot)\) \(\chi_{3200}(1411,\cdot)\) \(\chi_{3200}(1491,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((1151,901,2177)\) → \((-1,e\left(\frac{21}{32}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 3200 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{160}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{13}{160}\right)\) | \(e\left(\frac{7}{160}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{159}{160}\right)\) | \(e\left(\frac{21}{160}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{33}{160}\right)\) |