Basic properties
Modulus: | \(6027\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(280\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2009}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.em
\(\chi_{6027}(13,\cdot)\) \(\chi_{6027}(34,\cdot)\) \(\chi_{6027}(76,\cdot)\) \(\chi_{6027}(181,\cdot)\) \(\chi_{6027}(265,\cdot)\) \(\chi_{6027}(475,\cdot)\) \(\chi_{6027}(559,\cdot)\) \(\chi_{6027}(580,\cdot)\) \(\chi_{6027}(622,\cdot)\) \(\chi_{6027}(643,\cdot)\) \(\chi_{6027}(727,\cdot)\) \(\chi_{6027}(790,\cdot)\) \(\chi_{6027}(874,\cdot)\) \(\chi_{6027}(895,\cdot)\) \(\chi_{6027}(937,\cdot)\) \(\chi_{6027}(958,\cdot)\) \(\chi_{6027}(1042,\cdot)\) \(\chi_{6027}(1252,\cdot)\) \(\chi_{6027}(1336,\cdot)\) \(\chi_{6027}(1441,\cdot)\) \(\chi_{6027}(1483,\cdot)\) \(\chi_{6027}(1504,\cdot)\) \(\chi_{6027}(1546,\cdot)\) \(\chi_{6027}(1588,\cdot)\) \(\chi_{6027}(1651,\cdot)\) \(\chi_{6027}(1693,\cdot)\) \(\chi_{6027}(1735,\cdot)\) \(\chi_{6027}(1756,\cdot)\) \(\chi_{6027}(1798,\cdot)\) \(\chi_{6027}(1819,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{280})$ |
Fixed field: | Number field defined by a degree 280 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{11}{14}\right),e\left(\frac{31}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{267}{280}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{19}{40}\right)\) |