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.fw
\(\chi_{9680}(69,\cdot)\) \(\chi_{9680}(229,\cdot)\) \(\chi_{9680}(389,\cdot)\) \(\chi_{9680}(509,\cdot)\) \(\chi_{9680}(669,\cdot)\) \(\chi_{9680}(709,\cdot)\) \(\chi_{9680}(829,\cdot)\) \(\chi_{9680}(949,\cdot)\) \(\chi_{9680}(1109,\cdot)\) \(\chi_{9680}(1149,\cdot)\) \(\chi_{9680}(1269,\cdot)\) \(\chi_{9680}(1389,\cdot)\) \(\chi_{9680}(1549,\cdot)\) \(\chi_{9680}(1589,\cdot)\) \(\chi_{9680}(1709,\cdot)\) \(\chi_{9680}(1829,\cdot)\) \(\chi_{9680}(1989,\cdot)\) \(\chi_{9680}(2029,\cdot)\) \(\chi_{9680}(2149,\cdot)\) \(\chi_{9680}(2269,\cdot)\) \(\chi_{9680}(2469,\cdot)\) \(\chi_{9680}(2589,\cdot)\) \(\chi_{9680}(2709,\cdot)\) \(\chi_{9680}(2869,\cdot)\) \(\chi_{9680}(2909,\cdot)\) \(\chi_{9680}(3029,\cdot)\) \(\chi_{9680}(3309,\cdot)\) \(\chi_{9680}(3349,\cdot)\) \(\chi_{9680}(3589,\cdot)\) \(\chi_{9680}(3749,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((1,-i,-1,e\left(\frac{32}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 9680 }(2029, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{113}{220}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{119}{220}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{31}{220}\right)\) |