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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.dq
\(\chi_{6027}(173,\cdot)\) \(\chi_{6027}(278,\cdot)\) \(\chi_{6027}(542,\cdot)\) \(\chi_{6027}(647,\cdot)\) \(\chi_{6027}(1034,\cdot)\) \(\chi_{6027}(1139,\cdot)\) \(\chi_{6027}(1508,\cdot)\) \(\chi_{6027}(1895,\cdot)\) \(\chi_{6027}(2000,\cdot)\) \(\chi_{6027}(2264,\cdot)\) \(\chi_{6027}(2369,\cdot)\) \(\chi_{6027}(2756,\cdot)\) \(\chi_{6027}(3125,\cdot)\) \(\chi_{6027}(3230,\cdot)\) \(\chi_{6027}(3617,\cdot)\) \(\chi_{6027}(3722,\cdot)\) \(\chi_{6027}(3986,\cdot)\) \(\chi_{6027}(4091,\cdot)\) \(\chi_{6027}(4583,\cdot)\) \(\chi_{6027}(4847,\cdot)\) \(\chi_{6027}(4952,\cdot)\) \(\chi_{6027}(5339,\cdot)\) \(\chi_{6027}(5444,\cdot)\) \(\chi_{6027}(5708,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{29}{42}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(5444, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) |