Basic properties
| Modulus: | \(6776\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(113,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6776.dd
\(\chi_{6776}(113,\cdot)\) \(\chi_{6776}(169,\cdot)\) \(\chi_{6776}(225,\cdot)\) \(\chi_{6776}(449,\cdot)\) \(\chi_{6776}(785,\cdot)\) \(\chi_{6776}(841,\cdot)\) \(\chi_{6776}(1065,\cdot)\) \(\chi_{6776}(1345,\cdot)\) \(\chi_{6776}(1401,\cdot)\) \(\chi_{6776}(1457,\cdot)\) \(\chi_{6776}(1681,\cdot)\) \(\chi_{6776}(1961,\cdot)\) \(\chi_{6776}(2073,\cdot)\) \(\chi_{6776}(2297,\cdot)\) \(\chi_{6776}(2577,\cdot)\) \(\chi_{6776}(2633,\cdot)\) \(\chi_{6776}(3193,\cdot)\) \(\chi_{6776}(3249,\cdot)\) \(\chi_{6776}(3305,\cdot)\) \(\chi_{6776}(3529,\cdot)\) \(\chi_{6776}(3809,\cdot)\) \(\chi_{6776}(3865,\cdot)\) \(\chi_{6776}(3921,\cdot)\) \(\chi_{6776}(4145,\cdot)\) \(\chi_{6776}(4425,\cdot)\) \(\chi_{6776}(4481,\cdot)\) \(\chi_{6776}(4537,\cdot)\) \(\chi_{6776}(4761,\cdot)\) \(\chi_{6776}(5041,\cdot)\) \(\chi_{6776}(5097,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((1695,3389,969,3753)\) → \((1,1,1,e\left(\frac{29}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 6776 }(113, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{1}{5}\right)\) |