Basic properties
| Modulus: | \(9075\) | |
| Conductor: | \(3025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3025}(784,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.fk
\(\chi_{9075}(379,\cdot)\) \(\chi_{9075}(394,\cdot)\) \(\chi_{9075}(664,\cdot)\) \(\chi_{9075}(784,\cdot)\) \(\chi_{9075}(1204,\cdot)\) \(\chi_{9075}(1489,\cdot)\) \(\chi_{9075}(1609,\cdot)\) \(\chi_{9075}(2029,\cdot)\) \(\chi_{9075}(2044,\cdot)\) \(\chi_{9075}(2314,\cdot)\) \(\chi_{9075}(2434,\cdot)\) \(\chi_{9075}(2854,\cdot)\) \(\chi_{9075}(2869,\cdot)\) \(\chi_{9075}(3139,\cdot)\) \(\chi_{9075}(3259,\cdot)\) \(\chi_{9075}(3679,\cdot)\) \(\chi_{9075}(3694,\cdot)\) \(\chi_{9075}(3964,\cdot)\) \(\chi_{9075}(4084,\cdot)\) \(\chi_{9075}(4519,\cdot)\) \(\chi_{9075}(4789,\cdot)\) \(\chi_{9075}(4909,\cdot)\) \(\chi_{9075}(5329,\cdot)\) \(\chi_{9075}(5344,\cdot)\) \(\chi_{9075}(5614,\cdot)\) \(\chi_{9075}(5734,\cdot)\) \(\chi_{9075}(6154,\cdot)\) \(\chi_{9075}(6169,\cdot)\) \(\chi_{9075}(6439,\cdot)\) \(\chi_{9075}(6559,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{9}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(784, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{17}{110}\right)\) |