Basic properties
| Modulus: | \(9075\) | |
| Conductor: | \(9075\) | 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 9075.gl
\(\chi_{9075}(113,\cdot)\) \(\chi_{9075}(203,\cdot)\) \(\chi_{9075}(212,\cdot)\) \(\chi_{9075}(317,\cdot)\) \(\chi_{9075}(383,\cdot)\) \(\chi_{9075}(752,\cdot)\) \(\chi_{9075}(797,\cdot)\) \(\chi_{9075}(938,\cdot)\) \(\chi_{9075}(1028,\cdot)\) \(\chi_{9075}(1037,\cdot)\) \(\chi_{9075}(1142,\cdot)\) \(\chi_{9075}(1148,\cdot)\) \(\chi_{9075}(1208,\cdot)\) \(\chi_{9075}(1577,\cdot)\) \(\chi_{9075}(1622,\cdot)\) \(\chi_{9075}(1763,\cdot)\) \(\chi_{9075}(1853,\cdot)\) \(\chi_{9075}(1862,\cdot)\) \(\chi_{9075}(1967,\cdot)\) \(\chi_{9075}(1973,\cdot)\) \(\chi_{9075}(2033,\cdot)\) \(\chi_{9075}(2402,\cdot)\) \(\chi_{9075}(2588,\cdot)\) \(\chi_{9075}(2678,\cdot)\) \(\chi_{9075}(2687,\cdot)\) \(\chi_{9075}(2798,\cdot)\) \(\chi_{9075}(2858,\cdot)\) \(\chi_{9075}(3272,\cdot)\) \(\chi_{9075}(3413,\cdot)\) \(\chi_{9075}(3503,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,e\left(\frac{9}{20}\right),e\left(\frac{19}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(2687, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{147}{220}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{97}{220}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{61}{220}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{139}{220}\right)\) |