Basic properties
| Modulus: | \(5292\) | |
| Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1323}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5292.et
\(\chi_{5292}(41,\cdot)\) \(\chi_{5292}(209,\cdot)\) \(\chi_{5292}(461,\cdot)\) \(\chi_{5292}(545,\cdot)\) \(\chi_{5292}(713,\cdot)\) \(\chi_{5292}(797,\cdot)\) \(\chi_{5292}(965,\cdot)\) \(\chi_{5292}(1049,\cdot)\) \(\chi_{5292}(1217,\cdot)\) \(\chi_{5292}(1301,\cdot)\) \(\chi_{5292}(1553,\cdot)\) \(\chi_{5292}(1721,\cdot)\) \(\chi_{5292}(1805,\cdot)\) \(\chi_{5292}(1973,\cdot)\) \(\chi_{5292}(2225,\cdot)\) \(\chi_{5292}(2309,\cdot)\) \(\chi_{5292}(2477,\cdot)\) \(\chi_{5292}(2561,\cdot)\) \(\chi_{5292}(2729,\cdot)\) \(\chi_{5292}(2813,\cdot)\) \(\chi_{5292}(2981,\cdot)\) \(\chi_{5292}(3065,\cdot)\) \(\chi_{5292}(3317,\cdot)\) \(\chi_{5292}(3485,\cdot)\) \(\chi_{5292}(3569,\cdot)\) \(\chi_{5292}(3737,\cdot)\) \(\chi_{5292}(3989,\cdot)\) \(\chi_{5292}(4073,\cdot)\) \(\chi_{5292}(4241,\cdot)\) \(\chi_{5292}(4325,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((2647,785,1081)\) → \((1,e\left(\frac{17}{18}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5292 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{47}{126}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{2}{21}\right)\) |