Basic properties
| Modulus: | \(1984\) | |
| Conductor: | \(1984\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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 1984.cq
\(\chi_{1984}(35,\cdot)\) \(\chi_{1984}(163,\cdot)\) \(\chi_{1984}(171,\cdot)\) \(\chi_{1984}(219,\cdot)\) \(\chi_{1984}(283,\cdot)\) \(\chi_{1984}(411,\cdot)\) \(\chi_{1984}(419,\cdot)\) \(\chi_{1984}(467,\cdot)\) \(\chi_{1984}(531,\cdot)\) \(\chi_{1984}(659,\cdot)\) \(\chi_{1984}(667,\cdot)\) \(\chi_{1984}(715,\cdot)\) \(\chi_{1984}(779,\cdot)\) \(\chi_{1984}(907,\cdot)\) \(\chi_{1984}(915,\cdot)\) \(\chi_{1984}(963,\cdot)\) \(\chi_{1984}(1027,\cdot)\) \(\chi_{1984}(1155,\cdot)\) \(\chi_{1984}(1163,\cdot)\) \(\chi_{1984}(1211,\cdot)\) \(\chi_{1984}(1275,\cdot)\) \(\chi_{1984}(1403,\cdot)\) \(\chi_{1984}(1411,\cdot)\) \(\chi_{1984}(1459,\cdot)\) \(\chi_{1984}(1523,\cdot)\) \(\chi_{1984}(1651,\cdot)\) \(\chi_{1984}(1659,\cdot)\) \(\chi_{1984}(1707,\cdot)\) \(\chi_{1984}(1771,\cdot)\) \(\chi_{1984}(1899,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((63,1861,65)\) → \((-1,e\left(\frac{11}{16}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1984 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) |