Basic properties
| Modulus: | \(9680\) | |
| Conductor: | \(1936\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1936}(141,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9680.fn
\(\chi_{9680}(141,\cdot)\) \(\chi_{9680}(181,\cdot)\) \(\chi_{9680}(301,\cdot)\) \(\chi_{9680}(421,\cdot)\) \(\chi_{9680}(581,\cdot)\) \(\chi_{9680}(621,\cdot)\) \(\chi_{9680}(741,\cdot)\) \(\chi_{9680}(861,\cdot)\) \(\chi_{9680}(1021,\cdot)\) \(\chi_{9680}(1061,\cdot)\) \(\chi_{9680}(1181,\cdot)\) \(\chi_{9680}(1301,\cdot)\) \(\chi_{9680}(1501,\cdot)\) \(\chi_{9680}(1621,\cdot)\) \(\chi_{9680}(1741,\cdot)\) \(\chi_{9680}(1901,\cdot)\) \(\chi_{9680}(1941,\cdot)\) \(\chi_{9680}(2061,\cdot)\) \(\chi_{9680}(2341,\cdot)\) \(\chi_{9680}(2381,\cdot)\) \(\chi_{9680}(2621,\cdot)\) \(\chi_{9680}(2781,\cdot)\) \(\chi_{9680}(2821,\cdot)\) \(\chi_{9680}(2941,\cdot)\) \(\chi_{9680}(3061,\cdot)\) \(\chi_{9680}(3221,\cdot)\) \(\chi_{9680}(3261,\cdot)\) \(\chi_{9680}(3381,\cdot)\) \(\chi_{9680}(3501,\cdot)\) \(\chi_{9680}(3661,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((1,-i,1,e\left(\frac{38}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 9680 }(141, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{220}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{131}{220}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{219}{220}\right)\) |