Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(688,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.do
\(\chi_{6027}(319,\cdot)\) \(\chi_{6027}(583,\cdot)\) \(\chi_{6027}(688,\cdot)\) \(\chi_{6027}(1075,\cdot)\) \(\chi_{6027}(1180,\cdot)\) \(\chi_{6027}(1444,\cdot)\) \(\chi_{6027}(1936,\cdot)\) \(\chi_{6027}(2041,\cdot)\) \(\chi_{6027}(2305,\cdot)\) \(\chi_{6027}(2410,\cdot)\) \(\chi_{6027}(2797,\cdot)\) \(\chi_{6027}(2902,\cdot)\) \(\chi_{6027}(3271,\cdot)\) \(\chi_{6027}(3658,\cdot)\) \(\chi_{6027}(3763,\cdot)\) \(\chi_{6027}(4027,\cdot)\) \(\chi_{6027}(4132,\cdot)\) \(\chi_{6027}(4519,\cdot)\) \(\chi_{6027}(4888,\cdot)\) \(\chi_{6027}(4993,\cdot)\) \(\chi_{6027}(5380,\cdot)\) \(\chi_{6027}(5485,\cdot)\) \(\chi_{6027}(5749,\cdot)\) \(\chi_{6027}(5854,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{13}{21}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(688, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{11}{12}\right)\) |