Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(6027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | 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.ee
\(\chi_{6027}(44,\cdot)\) \(\chi_{6027}(137,\cdot)\) \(\chi_{6027}(191,\cdot)\) \(\chi_{6027}(284,\cdot)\) \(\chi_{6027}(506,\cdot)\) \(\chi_{6027}(536,\cdot)\) \(\chi_{6027}(653,\cdot)\) \(\chi_{6027}(683,\cdot)\) \(\chi_{6027}(905,\cdot)\) \(\chi_{6027}(1052,\cdot)\) \(\chi_{6027}(1367,\cdot)\) \(\chi_{6027}(1397,\cdot)\) \(\chi_{6027}(1514,\cdot)\) \(\chi_{6027}(1544,\cdot)\) \(\chi_{6027}(1766,\cdot)\) \(\chi_{6027}(1859,\cdot)\) \(\chi_{6027}(1913,\cdot)\) \(\chi_{6027}(2006,\cdot)\) \(\chi_{6027}(2228,\cdot)\) \(\chi_{6027}(2258,\cdot)\) \(\chi_{6027}(2375,\cdot)\) \(\chi_{6027}(2405,\cdot)\) \(\chi_{6027}(2720,\cdot)\) \(\chi_{6027}(2867,\cdot)\) \(\chi_{6027}(3089,\cdot)\) \(\chi_{6027}(3119,\cdot)\) \(\chi_{6027}(3236,\cdot)\) \(\chi_{6027}(3266,\cdot)\) \(\chi_{6027}(3488,\cdot)\) \(\chi_{6027}(3581,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{10}{21}\right),e\left(\frac{7}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(653, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{29}{168}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{47}{168}\right)\) | \(e\left(\frac{13}{24}\right)\) |