Basic properties
Modulus: | \(6027\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2009}(799,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.dx
\(\chi_{6027}(43,\cdot)\) \(\chi_{6027}(169,\cdot)\) \(\chi_{6027}(484,\cdot)\) \(\chi_{6027}(610,\cdot)\) \(\chi_{6027}(799,\cdot)\) \(\chi_{6027}(841,\cdot)\) \(\chi_{6027}(904,\cdot)\) \(\chi_{6027}(1156,\cdot)\) \(\chi_{6027}(1345,\cdot)\) \(\chi_{6027}(1597,\cdot)\) \(\chi_{6027}(1660,\cdot)\) \(\chi_{6027}(1702,\cdot)\) \(\chi_{6027}(1891,\cdot)\) \(\chi_{6027}(2017,\cdot)\) \(\chi_{6027}(2332,\cdot)\) \(\chi_{6027}(2458,\cdot)\) \(\chi_{6027}(2521,\cdot)\) \(\chi_{6027}(2563,\cdot)\) \(\chi_{6027}(2626,\cdot)\) \(\chi_{6027}(2752,\cdot)\) \(\chi_{6027}(2878,\cdot)\) \(\chi_{6027}(3067,\cdot)\) \(\chi_{6027}(3193,\cdot)\) \(\chi_{6027}(3319,\cdot)\) \(\chi_{6027}(3424,\cdot)\) \(\chi_{6027}(3487,\cdot)\) \(\chi_{6027}(3613,\cdot)\) \(\chi_{6027}(3739,\cdot)\) \(\chi_{6027}(3928,\cdot)\) \(\chi_{6027}(4054,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{140})$ |
Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{5}{7}\right),e\left(\frac{17}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(799, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{17}{140}\right)\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{13}{20}\right)\) |