Basic properties
| Modulus: | \(5292\) | |
| Conductor: | \(5292\) | 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 5292.eu
\(\chi_{5292}(11,\cdot)\) \(\chi_{5292}(23,\cdot)\) \(\chi_{5292}(515,\cdot)\) \(\chi_{5292}(527,\cdot)\) \(\chi_{5292}(767,\cdot)\) \(\chi_{5292}(779,\cdot)\) \(\chi_{5292}(1019,\cdot)\) \(\chi_{5292}(1031,\cdot)\) \(\chi_{5292}(1271,\cdot)\) \(\chi_{5292}(1283,\cdot)\) \(\chi_{5292}(1523,\cdot)\) \(\chi_{5292}(1535,\cdot)\) \(\chi_{5292}(1775,\cdot)\) \(\chi_{5292}(1787,\cdot)\) \(\chi_{5292}(2279,\cdot)\) \(\chi_{5292}(2291,\cdot)\) \(\chi_{5292}(2531,\cdot)\) \(\chi_{5292}(2543,\cdot)\) \(\chi_{5292}(2783,\cdot)\) \(\chi_{5292}(2795,\cdot)\) \(\chi_{5292}(3035,\cdot)\) \(\chi_{5292}(3047,\cdot)\) \(\chi_{5292}(3287,\cdot)\) \(\chi_{5292}(3299,\cdot)\) \(\chi_{5292}(3539,\cdot)\) \(\chi_{5292}(3551,\cdot)\) \(\chi_{5292}(4043,\cdot)\) \(\chi_{5292}(4055,\cdot)\) \(\chi_{5292}(4295,\cdot)\) \(\chi_{5292}(4307,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((2647,785,1081)\) → \((-1,e\left(\frac{13}{18}\right),e\left(\frac{20}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5292 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(-1\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{17}{21}\right)\) |