Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(1585,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.eb
\(\chi_{6027}(208,\cdot)\) \(\chi_{6027}(355,\cdot)\) \(\chi_{6027}(577,\cdot)\) \(\chi_{6027}(670,\cdot)\) \(\chi_{6027}(724,\cdot)\) \(\chi_{6027}(817,\cdot)\) \(\chi_{6027}(1039,\cdot)\) \(\chi_{6027}(1069,\cdot)\) \(\chi_{6027}(1186,\cdot)\) \(\chi_{6027}(1216,\cdot)\) \(\chi_{6027}(1438,\cdot)\) \(\chi_{6027}(1531,\cdot)\) \(\chi_{6027}(1585,\cdot)\) \(\chi_{6027}(1678,\cdot)\) \(\chi_{6027}(1900,\cdot)\) \(\chi_{6027}(2047,\cdot)\) \(\chi_{6027}(2299,\cdot)\) \(\chi_{6027}(2392,\cdot)\) \(\chi_{6027}(2446,\cdot)\) \(\chi_{6027}(2539,\cdot)\) \(\chi_{6027}(2761,\cdot)\) \(\chi_{6027}(2791,\cdot)\) \(\chi_{6027}(2908,\cdot)\) \(\chi_{6027}(2938,\cdot)\) \(\chi_{6027}(3160,\cdot)\) \(\chi_{6027}(3307,\cdot)\) \(\chi_{6027}(3622,\cdot)\) \(\chi_{6027}(3652,\cdot)\) \(\chi_{6027}(3769,\cdot)\) \(\chi_{6027}(3799,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{25}{42}\right),e\left(\frac{1}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(1585, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{31}{168}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{1}{168}\right)\) | \(e\left(\frac{23}{24}\right)\) |