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.eb
\(\chi_{9075}(164,\cdot)\) \(\chi_{9075}(329,\cdot)\) \(\chi_{9075}(494,\cdot)\) \(\chi_{9075}(659,\cdot)\) \(\chi_{9075}(989,\cdot)\) \(\chi_{9075}(1154,\cdot)\) \(\chi_{9075}(1319,\cdot)\) \(\chi_{9075}(1484,\cdot)\) \(\chi_{9075}(1979,\cdot)\) \(\chi_{9075}(2144,\cdot)\) \(\chi_{9075}(2309,\cdot)\) \(\chi_{9075}(2639,\cdot)\) \(\chi_{9075}(2804,\cdot)\) \(\chi_{9075}(2969,\cdot)\) \(\chi_{9075}(3134,\cdot)\) \(\chi_{9075}(3464,\cdot)\) \(\chi_{9075}(3794,\cdot)\) \(\chi_{9075}(3959,\cdot)\) \(\chi_{9075}(4289,\cdot)\) \(\chi_{9075}(4454,\cdot)\) \(\chi_{9075}(4619,\cdot)\) \(\chi_{9075}(4784,\cdot)\) \(\chi_{9075}(5114,\cdot)\) \(\chi_{9075}(5279,\cdot)\) \(\chi_{9075}(5609,\cdot)\) \(\chi_{9075}(5939,\cdot)\) \(\chi_{9075}(6104,\cdot)\) \(\chi_{9075}(6269,\cdot)\) \(\chi_{9075}(6434,\cdot)\) \(\chi_{9075}(6764,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{5}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(164, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{39}{55}\right)\) |