Basic properties
| Modulus: | \(6776\) | |
| Conductor: | \(968\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{968}(211,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6776.dv
\(\chi_{6776}(211,\cdot)\) \(\chi_{6776}(435,\cdot)\) \(\chi_{6776}(491,\cdot)\) \(\chi_{6776}(547,\cdot)\) \(\chi_{6776}(827,\cdot)\) \(\chi_{6776}(1051,\cdot)\) \(\chi_{6776}(1107,\cdot)\) \(\chi_{6776}(1163,\cdot)\) \(\chi_{6776}(1723,\cdot)\) \(\chi_{6776}(1779,\cdot)\) \(\chi_{6776}(2059,\cdot)\) \(\chi_{6776}(2283,\cdot)\) \(\chi_{6776}(2395,\cdot)\) \(\chi_{6776}(2675,\cdot)\) \(\chi_{6776}(2899,\cdot)\) \(\chi_{6776}(2955,\cdot)\) \(\chi_{6776}(3011,\cdot)\) \(\chi_{6776}(3291,\cdot)\) \(\chi_{6776}(3515,\cdot)\) \(\chi_{6776}(3571,\cdot)\) \(\chi_{6776}(3907,\cdot)\) \(\chi_{6776}(4131,\cdot)\) \(\chi_{6776}(4187,\cdot)\) \(\chi_{6776}(4243,\cdot)\) \(\chi_{6776}(4523,\cdot)\) \(\chi_{6776}(4747,\cdot)\) \(\chi_{6776}(4803,\cdot)\) \(\chi_{6776}(4859,\cdot)\) \(\chi_{6776}(5139,\cdot)\) \(\chi_{6776}(5363,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1695,3389,969,3753)\) → \((-1,-1,1,e\left(\frac{31}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 6776 }(211, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{2}{5}\right)\) |