Basic properties
| Modulus: | \(9680\) | |
| Conductor: | \(9680\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | 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 9680.fz
\(\chi_{9680}(19,\cdot)\) \(\chi_{9680}(139,\cdot)\) \(\chi_{9680}(259,\cdot)\) \(\chi_{9680}(299,\cdot)\) \(\chi_{9680}(459,\cdot)\) \(\chi_{9680}(579,\cdot)\) \(\chi_{9680}(739,\cdot)\) \(\chi_{9680}(899,\cdot)\) \(\chi_{9680}(1019,\cdot)\) \(\chi_{9680}(1139,\cdot)\) \(\chi_{9680}(1179,\cdot)\) \(\chi_{9680}(1339,\cdot)\) \(\chi_{9680}(1459,\cdot)\) \(\chi_{9680}(1579,\cdot)\) \(\chi_{9680}(1619,\cdot)\) \(\chi_{9680}(1779,\cdot)\) \(\chi_{9680}(1899,\cdot)\) \(\chi_{9680}(2019,\cdot)\) \(\chi_{9680}(2059,\cdot)\) \(\chi_{9680}(2219,\cdot)\) \(\chi_{9680}(2459,\cdot)\) \(\chi_{9680}(2499,\cdot)\) \(\chi_{9680}(2779,\cdot)\) \(\chi_{9680}(2899,\cdot)\) \(\chi_{9680}(2939,\cdot)\) \(\chi_{9680}(3099,\cdot)\) \(\chi_{9680}(3219,\cdot)\) \(\chi_{9680}(3339,\cdot)\) \(\chi_{9680}(3539,\cdot)\) \(\chi_{9680}(3659,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((-1,-i,-1,e\left(\frac{83}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 9680 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{83}{220}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{17}{220}\right)\) |