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.ga
\(\chi_{9200}(3,\cdot)\) \(\chi_{9200}(27,\cdot)\) \(\chi_{9200}(163,\cdot)\) \(\chi_{9200}(187,\cdot)\) \(\chi_{9200}(347,\cdot)\) \(\chi_{9200}(403,\cdot)\) \(\chi_{9200}(427,\cdot)\) \(\chi_{9200}(587,\cdot)\) \(\chi_{9200}(883,\cdot)\) \(\chi_{9200}(1067,\cdot)\) \(\chi_{9200}(1227,\cdot)\) \(\chi_{9200}(1283,\cdot)\) \(\chi_{9200}(1363,\cdot)\) \(\chi_{9200}(1467,\cdot)\) \(\chi_{9200}(1547,\cdot)\) \(\chi_{9200}(1603,\cdot)\) \(\chi_{9200}(1683,\cdot)\) \(\chi_{9200}(1787,\cdot)\) \(\chi_{9200}(1867,\cdot)\) \(\chi_{9200}(2003,\cdot)\) \(\chi_{9200}(2027,\cdot)\) \(\chi_{9200}(2083,\cdot)\) \(\chi_{9200}(2187,\cdot)\) \(\chi_{9200}(2267,\cdot)\) \(\chi_{9200}(2427,\cdot)\) \(\chi_{9200}(2723,\cdot)\) \(\chi_{9200}(2883,\cdot)\) \(\chi_{9200}(3067,\cdot)\) \(\chi_{9200}(3123,\cdot)\) \(\chi_{9200}(3203,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,6901,2577,1201)\) → \((-1,-i,e\left(\frac{7}{20}\right),e\left(\frac{8}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 9200 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{87}{220}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{141}{220}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{89}{220}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{9}{220}\right)\) |