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.dz
\(\chi_{9075}(41,\cdot)\) \(\chi_{9075}(431,\cdot)\) \(\chi_{9075}(446,\cdot)\) \(\chi_{9075}(866,\cdot)\) \(\chi_{9075}(986,\cdot)\) \(\chi_{9075}(1256,\cdot)\) \(\chi_{9075}(1271,\cdot)\) \(\chi_{9075}(1811,\cdot)\) \(\chi_{9075}(2081,\cdot)\) \(\chi_{9075}(2096,\cdot)\) \(\chi_{9075}(2516,\cdot)\) \(\chi_{9075}(2636,\cdot)\) \(\chi_{9075}(2906,\cdot)\) \(\chi_{9075}(2921,\cdot)\) \(\chi_{9075}(3341,\cdot)\) \(\chi_{9075}(3461,\cdot)\) \(\chi_{9075}(3731,\cdot)\) \(\chi_{9075}(3746,\cdot)\) \(\chi_{9075}(4166,\cdot)\) \(\chi_{9075}(4286,\cdot)\) \(\chi_{9075}(4556,\cdot)\) \(\chi_{9075}(4991,\cdot)\) \(\chi_{9075}(5111,\cdot)\) \(\chi_{9075}(5381,\cdot)\) \(\chi_{9075}(5396,\cdot)\) \(\chi_{9075}(5816,\cdot)\) \(\chi_{9075}(5936,\cdot)\) \(\chi_{9075}(6206,\cdot)\) \(\chi_{9075}(6221,\cdot)\) \(\chi_{9075}(6641,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{23}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{37}{110}\right)\) |