Basic properties
| Modulus: | \(9680\) | |
| Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{605}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9680.ey
\(\chi_{9680}(49,\cdot)\) \(\chi_{9680}(289,\cdot)\) \(\chi_{9680}(449,\cdot)\) \(\chi_{9680}(609,\cdot)\) \(\chi_{9680}(929,\cdot)\) \(\chi_{9680}(1169,\cdot)\) \(\chi_{9680}(1329,\cdot)\) \(\chi_{9680}(1489,\cdot)\) \(\chi_{9680}(1809,\cdot)\) \(\chi_{9680}(2049,\cdot)\) \(\chi_{9680}(2209,\cdot)\) \(\chi_{9680}(2369,\cdot)\) \(\chi_{9680}(2929,\cdot)\) \(\chi_{9680}(3089,\cdot)\) \(\chi_{9680}(3249,\cdot)\) \(\chi_{9680}(3569,\cdot)\) \(\chi_{9680}(3809,\cdot)\) \(\chi_{9680}(3969,\cdot)\) \(\chi_{9680}(4129,\cdot)\) \(\chi_{9680}(4449,\cdot)\) \(\chi_{9680}(4689,\cdot)\) \(\chi_{9680}(5009,\cdot)\) \(\chi_{9680}(5329,\cdot)\) \(\chi_{9680}(5729,\cdot)\) \(\chi_{9680}(6209,\cdot)\) \(\chi_{9680}(6449,\cdot)\) \(\chi_{9680}(6609,\cdot)\) \(\chi_{9680}(6769,\cdot)\) \(\chi_{9680}(7089,\cdot)\) \(\chi_{9680}(7329,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((1,1,-1,e\left(\frac{7}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 9680 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{55}\right)\) |