Basic properties
| Modulus: | \(9200\) | |
| Conductor: | \(9200\) | 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 9200.fy
\(\chi_{9200}(141,\cdot)\) \(\chi_{9200}(261,\cdot)\) \(\chi_{9200}(381,\cdot)\) \(\chi_{9200}(541,\cdot)\) \(\chi_{9200}(581,\cdot)\) \(\chi_{9200}(821,\cdot)\) \(\chi_{9200}(1021,\cdot)\) \(\chi_{9200}(1061,\cdot)\) \(\chi_{9200}(1181,\cdot)\) \(\chi_{9200}(1221,\cdot)\) \(\chi_{9200}(1421,\cdot)\) \(\chi_{9200}(1461,\cdot)\) \(\chi_{9200}(1741,\cdot)\) \(\chi_{9200}(1821,\cdot)\) \(\chi_{9200}(1941,\cdot)\) \(\chi_{9200}(1981,\cdot)\) \(\chi_{9200}(2141,\cdot)\) \(\chi_{9200}(2221,\cdot)\) \(\chi_{9200}(2341,\cdot)\) \(\chi_{9200}(2381,\cdot)\) \(\chi_{9200}(2421,\cdot)\) \(\chi_{9200}(2661,\cdot)\) \(\chi_{9200}(2741,\cdot)\) \(\chi_{9200}(2861,\cdot)\) \(\chi_{9200}(3021,\cdot)\) \(\chi_{9200}(3061,\cdot)\) \(\chi_{9200}(3141,\cdot)\) \(\chi_{9200}(3261,\cdot)\) \(\chi_{9200}(3341,\cdot)\) \(\chi_{9200}(3581,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,6901,2577,1201)\) → \((1,-i,e\left(\frac{1}{5}\right),e\left(\frac{8}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 9200 }(141, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{220}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{109}{220}\right)\) | \(e\left(\frac{51}{220}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{167}{220}\right)\) | \(e\left(\frac{133}{220}\right)\) | \(e\left(\frac{189}{220}\right)\) | \(e\left(\frac{163}{220}\right)\) |