Basic properties
| Modulus: | \(9200\) | |
| Conductor: | \(4600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4600}(3981,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9200.er
\(\chi_{9200}(41,\cdot)\) \(\chi_{9200}(121,\cdot)\) \(\chi_{9200}(361,\cdot)\) \(\chi_{9200}(441,\cdot)\) \(\chi_{9200}(761,\cdot)\) \(\chi_{9200}(841,\cdot)\) \(\chi_{9200}(1481,\cdot)\) \(\chi_{9200}(1641,\cdot)\) \(\chi_{9200}(1881,\cdot)\) \(\chi_{9200}(1961,\cdot)\) \(\chi_{9200}(2281,\cdot)\) \(\chi_{9200}(2441,\cdot)\) \(\chi_{9200}(2681,\cdot)\) \(\chi_{9200}(2841,\cdot)\) \(\chi_{9200}(3321,\cdot)\) \(\chi_{9200}(3481,\cdot)\) \(\chi_{9200}(3721,\cdot)\) \(\chi_{9200}(4041,\cdot)\) \(\chi_{9200}(4121,\cdot)\) \(\chi_{9200}(4281,\cdot)\) \(\chi_{9200}(4441,\cdot)\) \(\chi_{9200}(4521,\cdot)\) \(\chi_{9200}(4681,\cdot)\) \(\chi_{9200}(5161,\cdot)\) \(\chi_{9200}(5321,\cdot)\) \(\chi_{9200}(5561,\cdot)\) \(\chi_{9200}(5641,\cdot)\) \(\chi_{9200}(5881,\cdot)\) \(\chi_{9200}(5961,\cdot)\) \(\chi_{9200}(6121,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,6901,2577,1201)\) → \((1,-1,e\left(\frac{2}{5}\right),e\left(\frac{1}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 9200 }(6281, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{103}{110}\right)\) |