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.fj
\(\chi_{9200}(123,\cdot)\) \(\chi_{9200}(147,\cdot)\) \(\chi_{9200}(363,\cdot)\) \(\chi_{9200}(547,\cdot)\) \(\chi_{9200}(627,\cdot)\) \(\chi_{9200}(683,\cdot)\) \(\chi_{9200}(763,\cdot)\) \(\chi_{9200}(867,\cdot)\) \(\chi_{9200}(923,\cdot)\) \(\chi_{9200}(947,\cdot)\) \(\chi_{9200}(1083,\cdot)\) \(\chi_{9200}(1163,\cdot)\) \(\chi_{9200}(1267,\cdot)\) \(\chi_{9200}(1323,\cdot)\) \(\chi_{9200}(1347,\cdot)\) \(\chi_{9200}(1803,\cdot)\) \(\chi_{9200}(1963,\cdot)\) \(\chi_{9200}(1987,\cdot)\) \(\chi_{9200}(2147,\cdot)\) \(\chi_{9200}(2203,\cdot)\) \(\chi_{9200}(2283,\cdot)\) \(\chi_{9200}(2387,\cdot)\) \(\chi_{9200}(2467,\cdot)\) \(\chi_{9200}(2523,\cdot)\) \(\chi_{9200}(2603,\cdot)\) \(\chi_{9200}(2763,\cdot)\) \(\chi_{9200}(2787,\cdot)\) \(\chi_{9200}(2923,\cdot)\) \(\chi_{9200}(2947,\cdot)\) \(\chi_{9200}(3003,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,6901,2577,1201)\) → \((-1,-i,e\left(\frac{13}{20}\right),e\left(\frac{1}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 9200 }(1267, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{103}{220}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{19}{220}\right)\) | \(e\left(\frac{179}{220}\right)\) | \(e\left(\frac{161}{220}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{41}{220}\right)\) |