Basic properties
| Modulus: | \(4800\) | |
| Conductor: | \(4800\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4800.fc
\(\chi_{4800}(59,\cdot)\) \(\chi_{4800}(179,\cdot)\) \(\chi_{4800}(419,\cdot)\) \(\chi_{4800}(539,\cdot)\) \(\chi_{4800}(659,\cdot)\) \(\chi_{4800}(779,\cdot)\) \(\chi_{4800}(1019,\cdot)\) \(\chi_{4800}(1139,\cdot)\) \(\chi_{4800}(1259,\cdot)\) \(\chi_{4800}(1379,\cdot)\) \(\chi_{4800}(1619,\cdot)\) \(\chi_{4800}(1739,\cdot)\) \(\chi_{4800}(1859,\cdot)\) \(\chi_{4800}(1979,\cdot)\) \(\chi_{4800}(2219,\cdot)\) \(\chi_{4800}(2339,\cdot)\) \(\chi_{4800}(2459,\cdot)\) \(\chi_{4800}(2579,\cdot)\) \(\chi_{4800}(2819,\cdot)\) \(\chi_{4800}(2939,\cdot)\) \(\chi_{4800}(3059,\cdot)\) \(\chi_{4800}(3179,\cdot)\) \(\chi_{4800}(3419,\cdot)\) \(\chi_{4800}(3539,\cdot)\) \(\chi_{4800}(3659,\cdot)\) \(\chi_{4800}(3779,\cdot)\) \(\chi_{4800}(4019,\cdot)\) \(\chi_{4800}(4139,\cdot)\) \(\chi_{4800}(4259,\cdot)\) \(\chi_{4800}(4379,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4351,901,1601,577)\) → \((-1,e\left(\frac{1}{16}\right),-1,e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 4800 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{7}{40}\right)\) |