Basic properties
| Modulus: | \(6171\) | |
| Conductor: | \(2057\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2057}(100,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6171.cd
\(\chi_{6171}(100,\cdot)\) \(\chi_{6171}(298,\cdot)\) \(\chi_{6171}(331,\cdot)\) \(\chi_{6171}(529,\cdot)\) \(\chi_{6171}(661,\cdot)\) \(\chi_{6171}(859,\cdot)\) \(\chi_{6171}(892,\cdot)\) \(\chi_{6171}(1222,\cdot)\) \(\chi_{6171}(1420,\cdot)\) \(\chi_{6171}(1651,\cdot)\) \(\chi_{6171}(1783,\cdot)\) \(\chi_{6171}(1981,\cdot)\) \(\chi_{6171}(2014,\cdot)\) \(\chi_{6171}(2212,\cdot)\) \(\chi_{6171}(2344,\cdot)\) \(\chi_{6171}(2575,\cdot)\) \(\chi_{6171}(2773,\cdot)\) \(\chi_{6171}(3103,\cdot)\) \(\chi_{6171}(3136,\cdot)\) \(\chi_{6171}(3334,\cdot)\) \(\chi_{6171}(3466,\cdot)\) \(\chi_{6171}(3664,\cdot)\) \(\chi_{6171}(3697,\cdot)\) \(\chi_{6171}(3895,\cdot)\) \(\chi_{6171}(4027,\cdot)\) \(\chi_{6171}(4225,\cdot)\) \(\chi_{6171}(4258,\cdot)\) \(\chi_{6171}(4456,\cdot)\) \(\chi_{6171}(4588,\cdot)\) \(\chi_{6171}(4786,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((4115,970,2179)\) → \((1,e\left(\frac{4}{11}\right),e\left(\frac{3}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 6171 }(100, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{25}{88}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{19}{44}\right)\) |