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.ex
\(\chi_{2793}(2,\cdot)\) \(\chi_{2793}(32,\cdot)\) \(\chi_{2793}(53,\cdot)\) \(\chi_{2793}(200,\cdot)\) \(\chi_{2793}(212,\cdot)\) \(\chi_{2793}(401,\cdot)\) \(\chi_{2793}(431,\cdot)\) \(\chi_{2793}(452,\cdot)\) \(\chi_{2793}(527,\cdot)\) \(\chi_{2793}(599,\cdot)\) \(\chi_{2793}(611,\cdot)\) \(\chi_{2793}(800,\cdot)\) \(\chi_{2793}(830,\cdot)\) \(\chi_{2793}(926,\cdot)\) \(\chi_{2793}(1199,\cdot)\) \(\chi_{2793}(1229,\cdot)\) \(\chi_{2793}(1250,\cdot)\) \(\chi_{2793}(1325,\cdot)\) \(\chi_{2793}(1397,\cdot)\) \(\chi_{2793}(1409,\cdot)\) \(\chi_{2793}(1628,\cdot)\) \(\chi_{2793}(1649,\cdot)\) \(\chi_{2793}(1724,\cdot)\) \(\chi_{2793}(1796,\cdot)\) \(\chi_{2793}(1808,\cdot)\) \(\chi_{2793}(1997,\cdot)\) \(\chi_{2793}(2048,\cdot)\) \(\chi_{2793}(2123,\cdot)\) \(\chi_{2793}(2195,\cdot)\) \(\chi_{2793}(2207,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((932,2110,2206)\) → \((-1,e\left(\frac{20}{21}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 2793 }(452, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{9}{14}\right)\) |