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.gc
\(\chi_{9200}(53,\cdot)\) \(\chi_{9200}(237,\cdot)\) \(\chi_{9200}(373,\cdot)\) \(\chi_{9200}(477,\cdot)\) \(\chi_{9200}(613,\cdot)\) \(\chi_{9200}(773,\cdot)\) \(\chi_{9200}(797,\cdot)\) \(\chi_{9200}(1253,\cdot)\) \(\chi_{9200}(1413,\cdot)\) \(\chi_{9200}(1437,\cdot)\) \(\chi_{9200}(1597,\cdot)\) \(\chi_{9200}(1653,\cdot)\) \(\chi_{9200}(1677,\cdot)\) \(\chi_{9200}(1813,\cdot)\) \(\chi_{9200}(1837,\cdot)\) \(\chi_{9200}(1997,\cdot)\) \(\chi_{9200}(2077,\cdot)\) \(\chi_{9200}(2133,\cdot)\) \(\chi_{9200}(2213,\cdot)\) \(\chi_{9200}(2317,\cdot)\) \(\chi_{9200}(2397,\cdot)\) \(\chi_{9200}(2453,\cdot)\) \(\chi_{9200}(2613,\cdot)\) \(\chi_{9200}(2637,\cdot)\) \(\chi_{9200}(2797,\cdot)\) \(\chi_{9200}(3253,\cdot)\) \(\chi_{9200}(3277,\cdot)\) \(\chi_{9200}(3333,\cdot)\) \(\chi_{9200}(3437,\cdot)\) \(\chi_{9200}(3517,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,6901,2577,1201)\) → \((1,i,e\left(\frac{7}{20}\right),e\left(\frac{19}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 9200 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{137}{220}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{131}{220}\right)\) | \(e\left(\frac{1}{220}\right)\) | \(e\left(\frac{149}{220}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{219}{220}\right)\) |