Basic properties
Modulus: | \(6027\) | |
Conductor: | \(6027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.dr
\(\chi_{6027}(32,\cdot)\) \(\chi_{6027}(296,\cdot)\) \(\chi_{6027}(401,\cdot)\) \(\chi_{6027}(788,\cdot)\) \(\chi_{6027}(893,\cdot)\) \(\chi_{6027}(1262,\cdot)\) \(\chi_{6027}(1649,\cdot)\) \(\chi_{6027}(1754,\cdot)\) \(\chi_{6027}(2018,\cdot)\) \(\chi_{6027}(2123,\cdot)\) \(\chi_{6027}(2510,\cdot)\) \(\chi_{6027}(2879,\cdot)\) \(\chi_{6027}(2984,\cdot)\) \(\chi_{6027}(3371,\cdot)\) \(\chi_{6027}(3476,\cdot)\) \(\chi_{6027}(3740,\cdot)\) \(\chi_{6027}(3845,\cdot)\) \(\chi_{6027}(4337,\cdot)\) \(\chi_{6027}(4601,\cdot)\) \(\chi_{6027}(4706,\cdot)\) \(\chi_{6027}(5093,\cdot)\) \(\chi_{6027}(5198,\cdot)\) \(\chi_{6027}(5462,\cdot)\) \(\chi_{6027}(5954,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{2}{21}\right),i)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(32, a) \) | \(-1\) | \(1\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{7}{12}\right)\) |