Basic properties
Modulus: | \(6027\) | |
Conductor: | \(861\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{861}(317,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.dw
\(\chi_{6027}(116,\cdot)\) \(\chi_{6027}(263,\cdot)\) \(\chi_{6027}(275,\cdot)\) \(\chi_{6027}(422,\cdot)\) \(\chi_{6027}(557,\cdot)\) \(\chi_{6027}(704,\cdot)\) \(\chi_{6027}(716,\cdot)\) \(\chi_{6027}(1010,\cdot)\) \(\chi_{6027}(1586,\cdot)\) \(\chi_{6027}(1733,\cdot)\) \(\chi_{6027}(1880,\cdot)\) \(\chi_{6027}(1892,\cdot)\) \(\chi_{6027}(2039,\cdot)\) \(\chi_{6027}(2186,\cdot)\) \(\chi_{6027}(2762,\cdot)\) \(\chi_{6027}(3056,\cdot)\) \(\chi_{6027}(3068,\cdot)\) \(\chi_{6027}(3215,\cdot)\) \(\chi_{6027}(3350,\cdot)\) \(\chi_{6027}(3497,\cdot)\) \(\chi_{6027}(3509,\cdot)\) \(\chi_{6027}(3656,\cdot)\) \(\chi_{6027}(3791,\cdot)\) \(\chi_{6027}(4085,\cdot)\) \(\chi_{6027}(4538,\cdot)\) \(\chi_{6027}(4685,\cdot)\) \(\chi_{6027}(4832,\cdot)\) \(\chi_{6027}(4967,\cdot)\) \(\chi_{6027}(5114,\cdot)\) \(\chi_{6027}(5261,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{23}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(2039, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{101}{120}\right)\) |