Basic properties
| Modulus: | \(6019\) | |
| Conductor: | \(6019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(924\) | 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.em
\(\chi_{6019}(11,\cdot)\) \(\chi_{6019}(19,\cdot)\) \(\chi_{6019}(24,\cdot)\) \(\chi_{6019}(54,\cdot)\) \(\chi_{6019}(76,\cdot)\) \(\chi_{6019}(102,\cdot)\) \(\chi_{6019}(137,\cdot)\) \(\chi_{6019}(141,\cdot)\) \(\chi_{6019}(171,\cdot)\) \(\chi_{6019}(176,\cdot)\) \(\chi_{6019}(210,\cdot)\) \(\chi_{6019}(223,\cdot)\) \(\chi_{6019}(258,\cdot)\) \(\chi_{6019}(310,\cdot)\) \(\chi_{6019}(323,\cdot)\) \(\chi_{6019}(332,\cdot)\) \(\chi_{6019}(349,\cdot)\) \(\chi_{6019}(353,\cdot)\) \(\chi_{6019}(384,\cdot)\) \(\chi_{6019}(396,\cdot)\) \(\chi_{6019}(466,\cdot)\) \(\chi_{6019}(483,\cdot)\) \(\chi_{6019}(500,\cdot)\) \(\chi_{6019}(509,\cdot)\) \(\chi_{6019}(526,\cdot)\) \(\chi_{6019}(548,\cdot)\) \(\chi_{6019}(661,\cdot)\) \(\chi_{6019}(665,\cdot)\) \(\chi_{6019}(670,\cdot)\) \(\chi_{6019}(678,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{924})$ |
| Fixed field: | Number field defined by a degree 924 polynomial (not computed) |
Values on generators
\((2316,1392)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{43}{462}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6019 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{691}{924}\right)\) | \(e\left(\frac{197}{462}\right)\) | \(e\left(\frac{229}{462}\right)\) | \(e\left(\frac{817}{924}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{607}{924}\right)\) | \(e\left(\frac{75}{308}\right)\) | \(e\left(\frac{197}{231}\right)\) | \(e\left(\frac{146}{231}\right)\) | \(e\left(\frac{79}{924}\right)\) |