Basic properties
| Modulus: | \(4928\) | |
| 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 \(\chi_{704}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4928.fh
\(\chi_{4928}(211,\cdot)\) \(\chi_{4928}(435,\cdot)\) \(\chi_{4928}(491,\cdot)\) \(\chi_{4928}(547,\cdot)\) \(\chi_{4928}(827,\cdot)\) \(\chi_{4928}(1051,\cdot)\) \(\chi_{4928}(1107,\cdot)\) \(\chi_{4928}(1163,\cdot)\) \(\chi_{4928}(1443,\cdot)\) \(\chi_{4928}(1667,\cdot)\) \(\chi_{4928}(1723,\cdot)\) \(\chi_{4928}(1779,\cdot)\) \(\chi_{4928}(2059,\cdot)\) \(\chi_{4928}(2283,\cdot)\) \(\chi_{4928}(2339,\cdot)\) \(\chi_{4928}(2395,\cdot)\) \(\chi_{4928}(2675,\cdot)\) \(\chi_{4928}(2899,\cdot)\) \(\chi_{4928}(2955,\cdot)\) \(\chi_{4928}(3011,\cdot)\) \(\chi_{4928}(3291,\cdot)\) \(\chi_{4928}(3515,\cdot)\) \(\chi_{4928}(3571,\cdot)\) \(\chi_{4928}(3627,\cdot)\) \(\chi_{4928}(3907,\cdot)\) \(\chi_{4928}(4131,\cdot)\) \(\chi_{4928}(4187,\cdot)\) \(\chi_{4928}(4243,\cdot)\) \(\chi_{4928}(4523,\cdot)\) \(\chi_{4928}(4747,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4159,1541,2817,3137)\) → \((-1,e\left(\frac{7}{16}\right),1,e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 4928 }(4243, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{51}{80}\right)\) |