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.fi
\(\chi_{9075}(131,\cdot)\) \(\chi_{9075}(296,\cdot)\) \(\chi_{9075}(461,\cdot)\) \(\chi_{9075}(791,\cdot)\) \(\chi_{9075}(956,\cdot)\) \(\chi_{9075}(1121,\cdot)\) \(\chi_{9075}(1286,\cdot)\) \(\chi_{9075}(1616,\cdot)\) \(\chi_{9075}(1781,\cdot)\) \(\chi_{9075}(1946,\cdot)\) \(\chi_{9075}(2111,\cdot)\) \(\chi_{9075}(2441,\cdot)\) \(\chi_{9075}(2606,\cdot)\) \(\chi_{9075}(2771,\cdot)\) \(\chi_{9075}(2936,\cdot)\) \(\chi_{9075}(3431,\cdot)\) \(\chi_{9075}(3596,\cdot)\) \(\chi_{9075}(3761,\cdot)\) \(\chi_{9075}(4091,\cdot)\) \(\chi_{9075}(4256,\cdot)\) \(\chi_{9075}(4421,\cdot)\) \(\chi_{9075}(4586,\cdot)\) \(\chi_{9075}(4916,\cdot)\) \(\chi_{9075}(5246,\cdot)\) \(\chi_{9075}(5411,\cdot)\) \(\chi_{9075}(5741,\cdot)\) \(\chi_{9075}(5906,\cdot)\) \(\chi_{9075}(6071,\cdot)\) \(\chi_{9075}(6236,\cdot)\) \(\chi_{9075}(6566,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{15}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(131, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{69}{110}\right)\) |