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.en
\(\chi_{2793}(5,\cdot)\) \(\chi_{2793}(101,\cdot)\) \(\chi_{2793}(131,\cdot)\) \(\chi_{2793}(320,\cdot)\) \(\chi_{2793}(332,\cdot)\) \(\chi_{2793}(404,\cdot)\) \(\chi_{2793}(479,\cdot)\) \(\chi_{2793}(500,\cdot)\) \(\chi_{2793}(530,\cdot)\) \(\chi_{2793}(719,\cdot)\) \(\chi_{2793}(731,\cdot)\) \(\chi_{2793}(878,\cdot)\) \(\chi_{2793}(899,\cdot)\) \(\chi_{2793}(929,\cdot)\) \(\chi_{2793}(1118,\cdot)\) \(\chi_{2793}(1130,\cdot)\) \(\chi_{2793}(1202,\cdot)\) \(\chi_{2793}(1277,\cdot)\) \(\chi_{2793}(1298,\cdot)\) \(\chi_{2793}(1328,\cdot)\) \(\chi_{2793}(1517,\cdot)\) \(\chi_{2793}(1529,\cdot)\) \(\chi_{2793}(1601,\cdot)\) \(\chi_{2793}(1676,\cdot)\) \(\chi_{2793}(1727,\cdot)\) \(\chi_{2793}(1916,\cdot)\) \(\chi_{2793}(1928,\cdot)\) \(\chi_{2793}(2000,\cdot)\) \(\chi_{2793}(2075,\cdot)\) \(\chi_{2793}(2096,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((932,2110,2206)\) → \((-1,e\left(\frac{11}{42}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 2793 }(1727, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{5}{7}\right)\) |