Basic properties
| Modulus: | \(4800\) | |
| Conductor: | \(1600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1600}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4800.fd
\(\chi_{4800}(19,\cdot)\) \(\chi_{4800}(139,\cdot)\) \(\chi_{4800}(259,\cdot)\) \(\chi_{4800}(379,\cdot)\) \(\chi_{4800}(619,\cdot)\) \(\chi_{4800}(739,\cdot)\) \(\chi_{4800}(859,\cdot)\) \(\chi_{4800}(979,\cdot)\) \(\chi_{4800}(1219,\cdot)\) \(\chi_{4800}(1339,\cdot)\) \(\chi_{4800}(1459,\cdot)\) \(\chi_{4800}(1579,\cdot)\) \(\chi_{4800}(1819,\cdot)\) \(\chi_{4800}(1939,\cdot)\) \(\chi_{4800}(2059,\cdot)\) \(\chi_{4800}(2179,\cdot)\) \(\chi_{4800}(2419,\cdot)\) \(\chi_{4800}(2539,\cdot)\) \(\chi_{4800}(2659,\cdot)\) \(\chi_{4800}(2779,\cdot)\) \(\chi_{4800}(3019,\cdot)\) \(\chi_{4800}(3139,\cdot)\) \(\chi_{4800}(3259,\cdot)\) \(\chi_{4800}(3379,\cdot)\) \(\chi_{4800}(3619,\cdot)\) \(\chi_{4800}(3739,\cdot)\) \(\chi_{4800}(3859,\cdot)\) \(\chi_{4800}(3979,\cdot)\) \(\chi_{4800}(4219,\cdot)\) \(\chi_{4800}(4339,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4351,901,1601,577)\) → \((-1,e\left(\frac{7}{16}\right),1,e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 4800 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{29}{40}\right)\) |