Basic properties
| Modulus: | \(2112\) | |
| Conductor: | \(704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{704}(283,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2112.cu
\(\chi_{2112}(19,\cdot)\) \(\chi_{2112}(139,\cdot)\) \(\chi_{2112}(211,\cdot)\) \(\chi_{2112}(259,\cdot)\) \(\chi_{2112}(283,\cdot)\) \(\chi_{2112}(403,\cdot)\) \(\chi_{2112}(475,\cdot)\) \(\chi_{2112}(523,\cdot)\) \(\chi_{2112}(547,\cdot)\) \(\chi_{2112}(667,\cdot)\) \(\chi_{2112}(739,\cdot)\) \(\chi_{2112}(787,\cdot)\) \(\chi_{2112}(811,\cdot)\) \(\chi_{2112}(931,\cdot)\) \(\chi_{2112}(1003,\cdot)\) \(\chi_{2112}(1051,\cdot)\) \(\chi_{2112}(1075,\cdot)\) \(\chi_{2112}(1195,\cdot)\) \(\chi_{2112}(1267,\cdot)\) \(\chi_{2112}(1315,\cdot)\) \(\chi_{2112}(1339,\cdot)\) \(\chi_{2112}(1459,\cdot)\) \(\chi_{2112}(1531,\cdot)\) \(\chi_{2112}(1579,\cdot)\) \(\chi_{2112}(1603,\cdot)\) \(\chi_{2112}(1723,\cdot)\) \(\chi_{2112}(1795,\cdot)\) \(\chi_{2112}(1843,\cdot)\) \(\chi_{2112}(1867,\cdot)\) \(\chi_{2112}(1987,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2047,133,1409,1729)\) → \((-1,e\left(\frac{9}{16}\right),1,e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2112 }(283, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{79}{80}\right)\) |