Basic properties
| Modulus: | \(5292\) | |
| Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1323}(85,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5292.ec
\(\chi_{5292}(85,\cdot)\) \(\chi_{5292}(169,\cdot)\) \(\chi_{5292}(337,\cdot)\) \(\chi_{5292}(421,\cdot)\) \(\chi_{5292}(673,\cdot)\) \(\chi_{5292}(841,\cdot)\) \(\chi_{5292}(925,\cdot)\) \(\chi_{5292}(1093,\cdot)\) \(\chi_{5292}(1345,\cdot)\) \(\chi_{5292}(1429,\cdot)\) \(\chi_{5292}(1597,\cdot)\) \(\chi_{5292}(1681,\cdot)\) \(\chi_{5292}(1849,\cdot)\) \(\chi_{5292}(1933,\cdot)\) \(\chi_{5292}(2101,\cdot)\) \(\chi_{5292}(2185,\cdot)\) \(\chi_{5292}(2437,\cdot)\) \(\chi_{5292}(2605,\cdot)\) \(\chi_{5292}(2689,\cdot)\) \(\chi_{5292}(2857,\cdot)\) \(\chi_{5292}(3109,\cdot)\) \(\chi_{5292}(3193,\cdot)\) \(\chi_{5292}(3361,\cdot)\) \(\chi_{5292}(3445,\cdot)\) \(\chi_{5292}(3613,\cdot)\) \(\chi_{5292}(3697,\cdot)\) \(\chi_{5292}(3865,\cdot)\) \(\chi_{5292}(3949,\cdot)\) \(\chi_{5292}(4201,\cdot)\) \(\chi_{5292}(4369,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((2647,785,1081)\) → \((1,e\left(\frac{1}{9}\right),e\left(\frac{2}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5292 }(85, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{17}{21}\right)\) |