Basic properties
Modulus: | \(6027\) | |
Conductor: | \(6027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | 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.cz
\(\chi_{6027}(260,\cdot)\) \(\chi_{6027}(407,\cdot)\) \(\chi_{6027}(659,\cdot)\) \(\chi_{6027}(806,\cdot)\) \(\chi_{6027}(1121,\cdot)\) \(\chi_{6027}(1268,\cdot)\) \(\chi_{6027}(1982,\cdot)\) \(\chi_{6027}(2129,\cdot)\) \(\chi_{6027}(2381,\cdot)\) \(\chi_{6027}(2528,\cdot)\) \(\chi_{6027}(3242,\cdot)\) \(\chi_{6027}(3389,\cdot)\) \(\chi_{6027}(3704,\cdot)\) \(\chi_{6027}(3851,\cdot)\) \(\chi_{6027}(4103,\cdot)\) \(\chi_{6027}(4250,\cdot)\) \(\chi_{6027}(4565,\cdot)\) \(\chi_{6027}(4712,\cdot)\) \(\chi_{6027}(4964,\cdot)\) \(\chi_{6027}(5111,\cdot)\) \(\chi_{6027}(5426,\cdot)\) \(\chi_{6027}(5573,\cdot)\) \(\chi_{6027}(5825,\cdot)\) \(\chi_{6027}(5972,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{1}{7}\right),e\left(\frac{5}{8}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(1121, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{5}{8}\right)\) |