Basic properties
| Modulus: | \(6776\) | |
| Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{847}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6776.ed
\(\chi_{6776}(41,\cdot)\) \(\chi_{6776}(321,\cdot)\) \(\chi_{6776}(545,\cdot)\) \(\chi_{6776}(601,\cdot)\) \(\chi_{6776}(657,\cdot)\) \(\chi_{6776}(937,\cdot)\) \(\chi_{6776}(1161,\cdot)\) \(\chi_{6776}(1217,\cdot)\) \(\chi_{6776}(1273,\cdot)\) \(\chi_{6776}(1553,\cdot)\) \(\chi_{6776}(1777,\cdot)\) \(\chi_{6776}(1833,\cdot)\) \(\chi_{6776}(1889,\cdot)\) \(\chi_{6776}(2449,\cdot)\) \(\chi_{6776}(2505,\cdot)\) \(\chi_{6776}(2785,\cdot)\) \(\chi_{6776}(3009,\cdot)\) \(\chi_{6776}(3121,\cdot)\) \(\chi_{6776}(3401,\cdot)\) \(\chi_{6776}(3625,\cdot)\) \(\chi_{6776}(3681,\cdot)\) \(\chi_{6776}(3737,\cdot)\) \(\chi_{6776}(4017,\cdot)\) \(\chi_{6776}(4241,\cdot)\) \(\chi_{6776}(4297,\cdot)\) \(\chi_{6776}(4633,\cdot)\) \(\chi_{6776}(4857,\cdot)\) \(\chi_{6776}(4913,\cdot)\) \(\chi_{6776}(4969,\cdot)\) \(\chi_{6776}(5249,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1695,3389,969,3753)\) → \((1,1,-1,e\left(\frac{23}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 6776 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{7}{10}\right)\) |