Basic properties
| Modulus: | \(3968\) | |
| Conductor: | \(3968\) | 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 3968.dh
\(\chi_{3968}(101,\cdot)\) \(\chi_{3968}(109,\cdot)\) \(\chi_{3968}(157,\cdot)\) \(\chi_{3968}(221,\cdot)\) \(\chi_{3968}(349,\cdot)\) \(\chi_{3968}(357,\cdot)\) \(\chi_{3968}(405,\cdot)\) \(\chi_{3968}(469,\cdot)\) \(\chi_{3968}(597,\cdot)\) \(\chi_{3968}(605,\cdot)\) \(\chi_{3968}(653,\cdot)\) \(\chi_{3968}(717,\cdot)\) \(\chi_{3968}(845,\cdot)\) \(\chi_{3968}(853,\cdot)\) \(\chi_{3968}(901,\cdot)\) \(\chi_{3968}(965,\cdot)\) \(\chi_{3968}(1093,\cdot)\) \(\chi_{3968}(1101,\cdot)\) \(\chi_{3968}(1149,\cdot)\) \(\chi_{3968}(1213,\cdot)\) \(\chi_{3968}(1341,\cdot)\) \(\chi_{3968}(1349,\cdot)\) \(\chi_{3968}(1397,\cdot)\) \(\chi_{3968}(1461,\cdot)\) \(\chi_{3968}(1589,\cdot)\) \(\chi_{3968}(1597,\cdot)\) \(\chi_{3968}(1645,\cdot)\) \(\chi_{3968}(1709,\cdot)\) \(\chi_{3968}(1837,\cdot)\) \(\chi_{3968}(1845,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((2047,3845,2049)\) → \((1,e\left(\frac{31}{32}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 3968 }(1101, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{160}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{151}{160}\right)\) | \(e\left(\frac{117}{160}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{13}{160}\right)\) | \(e\left(\frac{63}{160}\right)\) |