Basic properties
| Modulus: | \(6043\) | |
| Conductor: | \(6043\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(53\) | 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 6043.g
\(\chi_{6043}(64,\cdot)\) \(\chi_{6043}(454,\cdot)\) \(\chi_{6043}(654,\cdot)\) \(\chi_{6043}(809,\cdot)\) \(\chi_{6043}(811,\cdot)\) \(\chi_{6043}(817,\cdot)\) \(\chi_{6043}(1194,\cdot)\) \(\chi_{6043}(1329,\cdot)\) \(\chi_{6043}(1429,\cdot)\) \(\chi_{6043}(1454,\cdot)\) \(\chi_{6043}(1639,\cdot)\) \(\chi_{6043}(1685,\cdot)\) \(\chi_{6043}(1735,\cdot)\) \(\chi_{6043}(1837,\cdot)\) \(\chi_{6043}(1848,\cdot)\) \(\chi_{6043}(2100,\cdot)\) \(\chi_{6043}(2164,\cdot)\) \(\chi_{6043}(2165,\cdot)\) \(\chi_{6043}(2266,\cdot)\) \(\chi_{6043}(2295,\cdot)\) \(\chi_{6043}(2411,\cdot)\) \(\chi_{6043}(2534,\cdot)\) \(\chi_{6043}(2575,\cdot)\) \(\chi_{6043}(2751,\cdot)\) \(\chi_{6043}(2759,\cdot)\) \(\chi_{6043}(3229,\cdot)\) \(\chi_{6043}(3345,\cdot)\) \(\chi_{6043}(3432,\cdot)\) \(\chi_{6043}(3433,\cdot)\) \(\chi_{6043}(3455,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{53})$ |
| Fixed field: | Number field defined by a degree 53 polynomial |
Values on generators
\(5\) → \(e\left(\frac{20}{53}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6043 }(2165, a) \) | \(1\) | \(1\) | \(e\left(\frac{24}{53}\right)\) | \(e\left(\frac{16}{53}\right)\) | \(e\left(\frac{48}{53}\right)\) | \(e\left(\frac{20}{53}\right)\) | \(e\left(\frac{40}{53}\right)\) | \(e\left(\frac{11}{53}\right)\) | \(e\left(\frac{19}{53}\right)\) | \(e\left(\frac{32}{53}\right)\) | \(e\left(\frac{44}{53}\right)\) | \(1\) |