Basic properties
| Modulus: | \(2793\) | |
| Conductor: | \(2793\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 2793.es
\(\chi_{2793}(86,\cdot)\) \(\chi_{2793}(242,\cdot)\) \(\chi_{2793}(317,\cdot)\) \(\chi_{2793}(326,\cdot)\) \(\chi_{2793}(338,\cdot)\) \(\chi_{2793}(485,\cdot)\) \(\chi_{2793}(515,\cdot)\) \(\chi_{2793}(641,\cdot)\) \(\chi_{2793}(725,\cdot)\) \(\chi_{2793}(737,\cdot)\) \(\chi_{2793}(884,\cdot)\) \(\chi_{2793}(914,\cdot)\) \(\chi_{2793}(1040,\cdot)\) \(\chi_{2793}(1115,\cdot)\) \(\chi_{2793}(1124,\cdot)\) \(\chi_{2793}(1136,\cdot)\) \(\chi_{2793}(1283,\cdot)\) \(\chi_{2793}(1313,\cdot)\) \(\chi_{2793}(1514,\cdot)\) \(\chi_{2793}(1523,\cdot)\) \(\chi_{2793}(1535,\cdot)\) \(\chi_{2793}(1682,\cdot)\) \(\chi_{2793}(1712,\cdot)\) \(\chi_{2793}(1838,\cdot)\) \(\chi_{2793}(1913,\cdot)\) \(\chi_{2793}(1922,\cdot)\) \(\chi_{2793}(1934,\cdot)\) \(\chi_{2793}(2081,\cdot)\) \(\chi_{2793}(2111,\cdot)\) \(\chi_{2793}(2237,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((932,2110,2206)\) → \((-1,e\left(\frac{1}{21}\right),e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 2793 }(1283, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{125}{126}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{37}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{5}{14}\right)\) |