Basic properties
| Modulus: | \(6776\) | |
| Conductor: | \(6776\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | 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 6776.em
\(\chi_{6776}(59,\cdot)\) \(\chi_{6776}(75,\cdot)\) \(\chi_{6776}(115,\cdot)\) \(\chi_{6776}(339,\cdot)\) \(\chi_{6776}(355,\cdot)\) \(\chi_{6776}(411,\cdot)\) \(\chi_{6776}(467,\cdot)\) \(\chi_{6776}(619,\cdot)\) \(\chi_{6776}(675,\cdot)\) \(\chi_{6776}(691,\cdot)\) \(\chi_{6776}(731,\cdot)\) \(\chi_{6776}(955,\cdot)\) \(\chi_{6776}(1027,\cdot)\) \(\chi_{6776}(1083,\cdot)\) \(\chi_{6776}(1235,\cdot)\) \(\chi_{6776}(1307,\cdot)\) \(\chi_{6776}(1347,\cdot)\) \(\chi_{6776}(1571,\cdot)\) \(\chi_{6776}(1587,\cdot)\) \(\chi_{6776}(1643,\cdot)\) \(\chi_{6776}(1699,\cdot)\) \(\chi_{6776}(1851,\cdot)\) \(\chi_{6776}(1907,\cdot)\) \(\chi_{6776}(1923,\cdot)\) \(\chi_{6776}(2203,\cdot)\) \(\chi_{6776}(2315,\cdot)\) \(\chi_{6776}(2467,\cdot)\) \(\chi_{6776}(2523,\cdot)\) \(\chi_{6776}(2539,\cdot)\) \(\chi_{6776}(2579,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((1695,3389,969,3753)\) → \((-1,-1,e\left(\frac{1}{6}\right),e\left(\frac{16}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 6776 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{142}{165}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{139}{330}\right)\) | \(e\left(\frac{323}{330}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{3}{10}\right)\) |