Basic properties
| Modulus: | \(9680\) | |
| Conductor: | \(4840\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4840}(2589,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9680.et
\(\chi_{9680}(169,\cdot)\) \(\chi_{9680}(489,\cdot)\) \(\chi_{9680}(889,\cdot)\) \(\chi_{9680}(1369,\cdot)\) \(\chi_{9680}(1609,\cdot)\) \(\chi_{9680}(1769,\cdot)\) \(\chi_{9680}(1929,\cdot)\) \(\chi_{9680}(2249,\cdot)\) \(\chi_{9680}(2489,\cdot)\) \(\chi_{9680}(2649,\cdot)\) \(\chi_{9680}(2809,\cdot)\) \(\chi_{9680}(3129,\cdot)\) \(\chi_{9680}(3369,\cdot)\) \(\chi_{9680}(3529,\cdot)\) \(\chi_{9680}(3689,\cdot)\) \(\chi_{9680}(4009,\cdot)\) \(\chi_{9680}(4249,\cdot)\) \(\chi_{9680}(4409,\cdot)\) \(\chi_{9680}(4569,\cdot)\) \(\chi_{9680}(4889,\cdot)\) \(\chi_{9680}(5129,\cdot)\) \(\chi_{9680}(5289,\cdot)\) \(\chi_{9680}(5449,\cdot)\) \(\chi_{9680}(5769,\cdot)\) \(\chi_{9680}(6009,\cdot)\) \(\chi_{9680}(6169,\cdot)\) \(\chi_{9680}(6329,\cdot)\) \(\chi_{9680}(6649,\cdot)\) \(\chi_{9680}(6889,\cdot)\) \(\chi_{9680}(7049,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((1,-1,-1,e\left(\frac{46}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 9680 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{79}{110}\right)\) |