Basic properties
| Modulus: | \(6534\) | |
| Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(165\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1089}(400,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6534.bl
\(\chi_{6534}(37,\cdot)\) \(\chi_{6534}(91,\cdot)\) \(\chi_{6534}(181,\cdot)\) \(\chi_{6534}(235,\cdot)\) \(\chi_{6534}(289,\cdot)\) \(\chi_{6534}(361,\cdot)\) \(\chi_{6534}(559,\cdot)\) \(\chi_{6534}(577,\cdot)\) \(\chi_{6534}(631,\cdot)\) \(\chi_{6534}(685,\cdot)\) \(\chi_{6534}(775,\cdot)\) \(\chi_{6534}(829,\cdot)\) \(\chi_{6534}(883,\cdot)\) \(\chi_{6534}(955,\cdot)\) \(\chi_{6534}(1153,\cdot)\) \(\chi_{6534}(1171,\cdot)\) \(\chi_{6534}(1225,\cdot)\) \(\chi_{6534}(1279,\cdot)\) \(\chi_{6534}(1369,\cdot)\) \(\chi_{6534}(1423,\cdot)\) \(\chi_{6534}(1477,\cdot)\) \(\chi_{6534}(1549,\cdot)\) \(\chi_{6534}(1747,\cdot)\) \(\chi_{6534}(1765,\cdot)\) \(\chi_{6534}(1819,\cdot)\) \(\chi_{6534}(1873,\cdot)\) \(\chi_{6534}(2071,\cdot)\) \(\chi_{6534}(2143,\cdot)\) \(\chi_{6534}(2341,\cdot)\) \(\chi_{6534}(2359,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((6293,3511)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{21}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6534 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{136}{165}\right)\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{51}{55}\right)\) |