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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2793.er
\(\chi_{2793}(59,\cdot)\) \(\chi_{2793}(89,\cdot)\) \(\chi_{2793}(110,\cdot)\) \(\chi_{2793}(185,\cdot)\) \(\chi_{2793}(257,\cdot)\) \(\chi_{2793}(269,\cdot)\) \(\chi_{2793}(458,\cdot)\) \(\chi_{2793}(488,\cdot)\) \(\chi_{2793}(584,\cdot)\) \(\chi_{2793}(857,\cdot)\) \(\chi_{2793}(887,\cdot)\) \(\chi_{2793}(908,\cdot)\) \(\chi_{2793}(983,\cdot)\) \(\chi_{2793}(1055,\cdot)\) \(\chi_{2793}(1067,\cdot)\) \(\chi_{2793}(1286,\cdot)\) \(\chi_{2793}(1307,\cdot)\) \(\chi_{2793}(1382,\cdot)\) \(\chi_{2793}(1454,\cdot)\) \(\chi_{2793}(1466,\cdot)\) \(\chi_{2793}(1655,\cdot)\) \(\chi_{2793}(1706,\cdot)\) \(\chi_{2793}(1781,\cdot)\) \(\chi_{2793}(1853,\cdot)\) \(\chi_{2793}(1865,\cdot)\) \(\chi_{2793}(2054,\cdot)\) \(\chi_{2793}(2084,\cdot)\) \(\chi_{2793}(2105,\cdot)\) \(\chi_{2793}(2180,\cdot)\) \(\chi_{2793}(2252,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((932,2110,2206)\) → \((-1,e\left(\frac{41}{42}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 2793 }(1307, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{4}{7}\right)\) |