Basic properties
| Modulus: | \(9075\) | |
| Conductor: | \(9075\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | 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.fn
\(\chi_{9075}(479,\cdot)\) \(\chi_{9075}(689,\cdot)\) \(\chi_{9075}(734,\cdot)\) \(\chi_{9075}(794,\cdot)\) \(\chi_{9075}(1514,\cdot)\) \(\chi_{9075}(1559,\cdot)\) \(\chi_{9075}(1619,\cdot)\) \(\chi_{9075}(2129,\cdot)\) \(\chi_{9075}(2384,\cdot)\) \(\chi_{9075}(2444,\cdot)\) \(\chi_{9075}(2954,\cdot)\) \(\chi_{9075}(3164,\cdot)\) \(\chi_{9075}(3209,\cdot)\) \(\chi_{9075}(3269,\cdot)\) \(\chi_{9075}(3779,\cdot)\) \(\chi_{9075}(3989,\cdot)\) \(\chi_{9075}(4034,\cdot)\) \(\chi_{9075}(4094,\cdot)\) \(\chi_{9075}(4604,\cdot)\) \(\chi_{9075}(4814,\cdot)\) \(\chi_{9075}(4859,\cdot)\) \(\chi_{9075}(4919,\cdot)\) \(\chi_{9075}(5429,\cdot)\) \(\chi_{9075}(5639,\cdot)\) \(\chi_{9075}(5744,\cdot)\) \(\chi_{9075}(6254,\cdot)\) \(\chi_{9075}(6464,\cdot)\) \(\chi_{9075}(6509,\cdot)\) \(\chi_{9075}(6569,\cdot)\) \(\chi_{9075}(7079,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{19}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(479, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{38}{55}\right)\) |