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 \(\chi_{4840}(1459,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9680.ez
\(\chi_{9680}(39,\cdot)\) \(\chi_{9680}(359,\cdot)\) \(\chi_{9680}(519,\cdot)\) \(\chi_{9680}(679,\cdot)\) \(\chi_{9680}(919,\cdot)\) \(\chi_{9680}(1239,\cdot)\) \(\chi_{9680}(1399,\cdot)\) \(\chi_{9680}(1559,\cdot)\) \(\chi_{9680}(1799,\cdot)\) \(\chi_{9680}(2119,\cdot)\) \(\chi_{9680}(2279,\cdot)\) \(\chi_{9680}(2439,\cdot)\) \(\chi_{9680}(2679,\cdot)\) \(\chi_{9680}(2999,\cdot)\) \(\chi_{9680}(3159,\cdot)\) \(\chi_{9680}(3319,\cdot)\) \(\chi_{9680}(3559,\cdot)\) \(\chi_{9680}(3879,\cdot)\) \(\chi_{9680}(4039,\cdot)\) \(\chi_{9680}(4199,\cdot)\) \(\chi_{9680}(4439,\cdot)\) \(\chi_{9680}(4919,\cdot)\) \(\chi_{9680}(5319,\cdot)\) \(\chi_{9680}(5639,\cdot)\) \(\chi_{9680}(5959,\cdot)\) \(\chi_{9680}(6199,\cdot)\) \(\chi_{9680}(6519,\cdot)\) \(\chi_{9680}(6679,\cdot)\) \(\chi_{9680}(6839,\cdot)\) \(\chi_{9680}(7079,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((-1,-1,-1,e\left(\frac{7}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 9680 }(3879, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{32}{55}\right)\) |