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.fh
\(\chi_{9680}(237,\cdot)\) \(\chi_{9680}(293,\cdot)\) \(\chi_{9680}(453,\cdot)\) \(\chi_{9680}(557,\cdot)\) \(\chi_{9680}(613,\cdot)\) \(\chi_{9680}(853,\cdot)\) \(\chi_{9680}(877,\cdot)\) \(\chi_{9680}(1117,\cdot)\) \(\chi_{9680}(1173,\cdot)\) \(\chi_{9680}(1333,\cdot)\) \(\chi_{9680}(1437,\cdot)\) \(\chi_{9680}(1493,\cdot)\) \(\chi_{9680}(1597,\cdot)\) \(\chi_{9680}(1733,\cdot)\) \(\chi_{9680}(1757,\cdot)\) \(\chi_{9680}(1997,\cdot)\) \(\chi_{9680}(2053,\cdot)\) \(\chi_{9680}(2213,\cdot)\) \(\chi_{9680}(2317,\cdot)\) \(\chi_{9680}(2373,\cdot)\) \(\chi_{9680}(2477,\cdot)\) \(\chi_{9680}(2613,\cdot)\) \(\chi_{9680}(2637,\cdot)\) \(\chi_{9680}(2933,\cdot)\) \(\chi_{9680}(3093,\cdot)\) \(\chi_{9680}(3197,\cdot)\) \(\chi_{9680}(3253,\cdot)\) \(\chi_{9680}(3357,\cdot)\) \(\chi_{9680}(3493,\cdot)\) \(\chi_{9680}(3517,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((1,-i,i,e\left(\frac{37}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 9680 }(557, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{23}{220}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{161}{220}\right)\) | \(e\left(\frac{147}{220}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{103}{220}\right)\) |