Basic properties
| Modulus: | \(6019\) | |
| Conductor: | \(6019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | 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.dm
\(\chi_{6019}(93,\cdot)\) \(\chi_{6019}(284,\cdot)\) \(\chi_{6019}(331,\cdot)\) \(\chi_{6019}(804,\cdot)\) \(\chi_{6019}(890,\cdot)\) \(\chi_{6019}(1016,\cdot)\) \(\chi_{6019}(1246,\cdot)\) \(\chi_{6019}(1294,\cdot)\) \(\chi_{6019}(1350,\cdot)\) \(\chi_{6019}(1658,\cdot)\) \(\chi_{6019}(1775,\cdot)\) \(\chi_{6019}(2086,\cdot)\) \(\chi_{6019}(2182,\cdot)\) \(\chi_{6019}(2463,\cdot)\) \(\chi_{6019}(2485,\cdot)\) \(\chi_{6019}(2550,\cdot)\) \(\chi_{6019}(2646,\cdot)\) \(\chi_{6019}(2684,\cdot)\) \(\chi_{6019}(2710,\cdot)\) \(\chi_{6019}(2784,\cdot)\) \(\chi_{6019}(2871,\cdot)\) \(\chi_{6019}(3113,\cdot)\) \(\chi_{6019}(3205,\cdot)\) \(\chi_{6019}(3525,\cdot)\) \(\chi_{6019}(3794,\cdot)\) \(\chi_{6019}(4045,\cdot)\) \(\chi_{6019}(4401,\cdot)\) \(\chi_{6019}(4487,\cdot)\) \(\chi_{6019}(4591,\cdot)\) \(\chi_{6019}(4778,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2316,1392)\) → \((e\left(\frac{1}{12}\right),e\left(\frac{53}{66}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6019 }(93, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{103}{132}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{5}{44}\right)\) |