Basic properties
| Modulus: | \(6776\) | |
| Conductor: | \(3388\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3388}(223,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6776.dt
\(\chi_{6776}(223,\cdot)\) \(\chi_{6776}(279,\cdot)\) \(\chi_{6776}(335,\cdot)\) \(\chi_{6776}(559,\cdot)\) \(\chi_{6776}(839,\cdot)\) \(\chi_{6776}(895,\cdot)\) \(\chi_{6776}(951,\cdot)\) \(\chi_{6776}(1175,\cdot)\) \(\chi_{6776}(1511,\cdot)\) \(\chi_{6776}(1567,\cdot)\) \(\chi_{6776}(1791,\cdot)\) \(\chi_{6776}(2071,\cdot)\) \(\chi_{6776}(2127,\cdot)\) \(\chi_{6776}(2183,\cdot)\) \(\chi_{6776}(2407,\cdot)\) \(\chi_{6776}(2687,\cdot)\) \(\chi_{6776}(2799,\cdot)\) \(\chi_{6776}(3023,\cdot)\) \(\chi_{6776}(3303,\cdot)\) \(\chi_{6776}(3359,\cdot)\) \(\chi_{6776}(3919,\cdot)\) \(\chi_{6776}(3975,\cdot)\) \(\chi_{6776}(4031,\cdot)\) \(\chi_{6776}(4255,\cdot)\) \(\chi_{6776}(4535,\cdot)\) \(\chi_{6776}(4591,\cdot)\) \(\chi_{6776}(4647,\cdot)\) \(\chi_{6776}(4871,\cdot)\) \(\chi_{6776}(5151,\cdot)\) \(\chi_{6776}(5207,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1695,3389,969,3753)\) → \((-1,1,-1,e\left(\frac{14}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 6776 }(223, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{1}{5}\right)\) |