Basic properties
| Modulus: | \(4928\) | |
| Conductor: | \(4928\) | 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 4928.fg
\(\chi_{4928}(13,\cdot)\) \(\chi_{4928}(237,\cdot)\) \(\chi_{4928}(293,\cdot)\) \(\chi_{4928}(349,\cdot)\) \(\chi_{4928}(629,\cdot)\) \(\chi_{4928}(853,\cdot)\) \(\chi_{4928}(909,\cdot)\) \(\chi_{4928}(965,\cdot)\) \(\chi_{4928}(1245,\cdot)\) \(\chi_{4928}(1469,\cdot)\) \(\chi_{4928}(1525,\cdot)\) \(\chi_{4928}(1581,\cdot)\) \(\chi_{4928}(1861,\cdot)\) \(\chi_{4928}(2085,\cdot)\) \(\chi_{4928}(2141,\cdot)\) \(\chi_{4928}(2197,\cdot)\) \(\chi_{4928}(2477,\cdot)\) \(\chi_{4928}(2701,\cdot)\) \(\chi_{4928}(2757,\cdot)\) \(\chi_{4928}(2813,\cdot)\) \(\chi_{4928}(3093,\cdot)\) \(\chi_{4928}(3317,\cdot)\) \(\chi_{4928}(3373,\cdot)\) \(\chi_{4928}(3429,\cdot)\) \(\chi_{4928}(3709,\cdot)\) \(\chi_{4928}(3933,\cdot)\) \(\chi_{4928}(3989,\cdot)\) \(\chi_{4928}(4045,\cdot)\) \(\chi_{4928}(4325,\cdot)\) \(\chi_{4928}(4549,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4159,1541,2817,3137)\) → \((1,e\left(\frac{15}{16}\right),-1,e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 4928 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{27}{80}\right)\) |