Basic properties
| Modulus: | \(6019\) | |
| Conductor: | \(6019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(231\) | 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 6019.dq
\(\chi_{6019}(9,\cdot)\) \(\chi_{6019}(16,\cdot)\) \(\chi_{6019}(35,\cdot)\) \(\chi_{6019}(81,\cdot)\) \(\chi_{6019}(113,\cdot)\) \(\chi_{6019}(172,\cdot)\) \(\chi_{6019}(185,\cdot)\) \(\chi_{6019}(211,\cdot)\) \(\chi_{6019}(256,\cdot)\) \(\chi_{6019}(289,\cdot)\) \(\chi_{6019}(542,\cdot)\) \(\chi_{6019}(594,\cdot)\) \(\chi_{6019}(731,\cdot)\) \(\chi_{6019}(750,\cdot)\) \(\chi_{6019}(789,\cdot)\) \(\chi_{6019}(822,\cdot)\) \(\chi_{6019}(958,\cdot)\) \(\chi_{6019}(1017,\cdot)\) \(\chi_{6019}(1056,\cdot)\) \(\chi_{6019}(1062,\cdot)\) \(\chi_{6019}(1082,\cdot)\) \(\chi_{6019}(1088,\cdot)\) \(\chi_{6019}(1114,\cdot)\) \(\chi_{6019}(1225,\cdot)\) \(\chi_{6019}(1270,\cdot)\) \(\chi_{6019}(1277,\cdot)\) \(\chi_{6019}(1348,\cdot)\) \(\chi_{6019}(1361,\cdot)\) \(\chi_{6019}(1420,\cdot)\) \(\chi_{6019}(1439,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 231 polynomial (not computed) |
Values on generators
\((2316,1392)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{231}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6019 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{188}{231}\right)\) | \(e\left(\frac{155}{231}\right)\) | \(e\left(\frac{145}{231}\right)\) | \(e\left(\frac{125}{231}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{230}{231}\right)\) | \(e\left(\frac{34}{77}\right)\) | \(e\left(\frac{79}{231}\right)\) | \(e\left(\frac{82}{231}\right)\) | \(e\left(\frac{197}{231}\right)\) |