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.ei
\(\chi_{2793}(23,\cdot)\) \(\chi_{2793}(44,\cdot)\) \(\chi_{2793}(74,\cdot)\) \(\chi_{2793}(347,\cdot)\) \(\chi_{2793}(443,\cdot)\) \(\chi_{2793}(473,\cdot)\) \(\chi_{2793}(662,\cdot)\) \(\chi_{2793}(674,\cdot)\) \(\chi_{2793}(746,\cdot)\) \(\chi_{2793}(821,\cdot)\) \(\chi_{2793}(842,\cdot)\) \(\chi_{2793}(872,\cdot)\) \(\chi_{2793}(1061,\cdot)\) \(\chi_{2793}(1073,\cdot)\) \(\chi_{2793}(1220,\cdot)\) \(\chi_{2793}(1241,\cdot)\) \(\chi_{2793}(1271,\cdot)\) \(\chi_{2793}(1460,\cdot)\) \(\chi_{2793}(1472,\cdot)\) \(\chi_{2793}(1544,\cdot)\) \(\chi_{2793}(1619,\cdot)\) \(\chi_{2793}(1640,\cdot)\) \(\chi_{2793}(1670,\cdot)\) \(\chi_{2793}(1859,\cdot)\) \(\chi_{2793}(1871,\cdot)\) \(\chi_{2793}(1943,\cdot)\) \(\chi_{2793}(2018,\cdot)\) \(\chi_{2793}(2069,\cdot)\) \(\chi_{2793}(2258,\cdot)\) \(\chi_{2793}(2270,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((932,2110,2206)\) → \((-1,e\left(\frac{2}{21}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 2793 }(1943, a) \) | \(-1\) | \(1\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{3}{14}\right)\) |