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.dj
\(\chi_{3200}(13,\cdot)\) \(\chi_{3200}(37,\cdot)\) \(\chi_{3200}(117,\cdot)\) \(\chi_{3200}(173,\cdot)\) \(\chi_{3200}(197,\cdot)\) \(\chi_{3200}(253,\cdot)\) \(\chi_{3200}(277,\cdot)\) \(\chi_{3200}(333,\cdot)\) \(\chi_{3200}(413,\cdot)\) \(\chi_{3200}(437,\cdot)\) \(\chi_{3200}(517,\cdot)\) \(\chi_{3200}(573,\cdot)\) \(\chi_{3200}(597,\cdot)\) \(\chi_{3200}(653,\cdot)\) \(\chi_{3200}(677,\cdot)\) \(\chi_{3200}(733,\cdot)\) \(\chi_{3200}(813,\cdot)\) \(\chi_{3200}(837,\cdot)\) \(\chi_{3200}(917,\cdot)\) \(\chi_{3200}(973,\cdot)\) \(\chi_{3200}(997,\cdot)\) \(\chi_{3200}(1053,\cdot)\) \(\chi_{3200}(1077,\cdot)\) \(\chi_{3200}(1133,\cdot)\) \(\chi_{3200}(1213,\cdot)\) \(\chi_{3200}(1237,\cdot)\) \(\chi_{3200}(1317,\cdot)\) \(\chi_{3200}(1373,\cdot)\) \(\chi_{3200}(1397,\cdot)\) \(\chi_{3200}(1453,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((1151,901,2177)\) → \((1,e\left(\frac{15}{32}\right),e\left(\frac{19}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 3200 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{160}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{7}{160}\right)\) | \(e\left(\frac{13}{160}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{141}{160}\right)\) | \(e\left(\frac{79}{160}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{27}{160}\right)\) |