Basic properties
Modulus: | \(6027\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2009}(1063,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.dc
\(\chi_{6027}(55,\cdot)\) \(\chi_{6027}(202,\cdot)\) \(\chi_{6027}(454,\cdot)\) \(\chi_{6027}(601,\cdot)\) \(\chi_{6027}(916,\cdot)\) \(\chi_{6027}(1063,\cdot)\) \(\chi_{6027}(1315,\cdot)\) \(\chi_{6027}(1462,\cdot)\) \(\chi_{6027}(1777,\cdot)\) \(\chi_{6027}(1924,\cdot)\) \(\chi_{6027}(2176,\cdot)\) \(\chi_{6027}(2323,\cdot)\) \(\chi_{6027}(2638,\cdot)\) \(\chi_{6027}(2785,\cdot)\) \(\chi_{6027}(3499,\cdot)\) \(\chi_{6027}(3646,\cdot)\) \(\chi_{6027}(3898,\cdot)\) \(\chi_{6027}(4045,\cdot)\) \(\chi_{6027}(4759,\cdot)\) \(\chi_{6027}(4906,\cdot)\) \(\chi_{6027}(5221,\cdot)\) \(\chi_{6027}(5368,\cdot)\) \(\chi_{6027}(5620,\cdot)\) \(\chi_{6027}(5767,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{3}{14}\right),e\left(\frac{7}{8}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(1063, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{3}{8}\right)\) |