Basic properties
| Modulus: | \(6171\) | |
| Conductor: | \(6171\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | 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 6171.cq
\(\chi_{6171}(140,\cdot)\) \(\chi_{6171}(149,\cdot)\) \(\chi_{6171}(200,\cdot)\) \(\chi_{6171}(293,\cdot)\) \(\chi_{6171}(404,\cdot)\) \(\chi_{6171}(446,\cdot)\) \(\chi_{6171}(497,\cdot)\) \(\chi_{6171}(557,\cdot)\) \(\chi_{6171}(701,\cdot)\) \(\chi_{6171}(710,\cdot)\) \(\chi_{6171}(761,\cdot)\) \(\chi_{6171}(854,\cdot)\) \(\chi_{6171}(1007,\cdot)\) \(\chi_{6171}(1058,\cdot)\) \(\chi_{6171}(1118,\cdot)\) \(\chi_{6171}(1262,\cdot)\) \(\chi_{6171}(1271,\cdot)\) \(\chi_{6171}(1415,\cdot)\) \(\chi_{6171}(1526,\cdot)\) \(\chi_{6171}(1568,\cdot)\) \(\chi_{6171}(1619,\cdot)\) \(\chi_{6171}(1679,\cdot)\) \(\chi_{6171}(1823,\cdot)\) \(\chi_{6171}(1832,\cdot)\) \(\chi_{6171}(1883,\cdot)\) \(\chi_{6171}(2087,\cdot)\) \(\chi_{6171}(2129,\cdot)\) \(\chi_{6171}(2180,\cdot)\) \(\chi_{6171}(2240,\cdot)\) \(\chi_{6171}(2384,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((4115,970,2179)\) → \((-1,e\left(\frac{83}{110}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 6171 }(140, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{19}{220}\right)\) | \(e\left(\frac{117}{220}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{63}{220}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{7}{55}\right)\) |