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.gc
\(\chi_{9680}(147,\cdot)\) \(\chi_{9680}(203,\cdot)\) \(\chi_{9680}(443,\cdot)\) \(\chi_{9680}(467,\cdot)\) \(\chi_{9680}(603,\cdot)\) \(\chi_{9680}(707,\cdot)\) \(\chi_{9680}(763,\cdot)\) \(\chi_{9680}(867,\cdot)\) \(\chi_{9680}(1027,\cdot)\) \(\chi_{9680}(1083,\cdot)\) \(\chi_{9680}(1323,\cdot)\) \(\chi_{9680}(1347,\cdot)\) \(\chi_{9680}(1483,\cdot)\) \(\chi_{9680}(1587,\cdot)\) \(\chi_{9680}(1643,\cdot)\) \(\chi_{9680}(1747,\cdot)\) \(\chi_{9680}(1907,\cdot)\) \(\chi_{9680}(2203,\cdot)\) \(\chi_{9680}(2227,\cdot)\) \(\chi_{9680}(2363,\cdot)\) \(\chi_{9680}(2467,\cdot)\) \(\chi_{9680}(2523,\cdot)\) \(\chi_{9680}(2627,\cdot)\) \(\chi_{9680}(2787,\cdot)\) \(\chi_{9680}(2843,\cdot)\) \(\chi_{9680}(3083,\cdot)\) \(\chi_{9680}(3107,\cdot)\) \(\chi_{9680}(3243,\cdot)\) \(\chi_{9680}(3347,\cdot)\) \(\chi_{9680}(3403,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((-1,-i,i,e\left(\frac{51}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 9680 }(147, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{151}{220}\right)\) | \(e\left(\frac{47}{220}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{113}{220}\right)\) |