Basic properties
Modulus: | \(3549\) | |
Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | 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 3549.el
\(\chi_{3549}(11,\cdot)\) \(\chi_{3549}(149,\cdot)\) \(\chi_{3549}(158,\cdot)\) \(\chi_{3549}(254,\cdot)\) \(\chi_{3549}(284,\cdot)\) \(\chi_{3549}(422,\cdot)\) \(\chi_{3549}(431,\cdot)\) \(\chi_{3549}(527,\cdot)\) \(\chi_{3549}(557,\cdot)\) \(\chi_{3549}(704,\cdot)\) \(\chi_{3549}(800,\cdot)\) \(\chi_{3549}(830,\cdot)\) \(\chi_{3549}(968,\cdot)\) \(\chi_{3549}(977,\cdot)\) \(\chi_{3549}(1073,\cdot)\) \(\chi_{3549}(1241,\cdot)\) \(\chi_{3549}(1250,\cdot)\) \(\chi_{3549}(1346,\cdot)\) \(\chi_{3549}(1376,\cdot)\) \(\chi_{3549}(1514,\cdot)\) \(\chi_{3549}(1523,\cdot)\) \(\chi_{3549}(1619,\cdot)\) \(\chi_{3549}(1649,\cdot)\) \(\chi_{3549}(1787,\cdot)\) \(\chi_{3549}(1796,\cdot)\) \(\chi_{3549}(1892,\cdot)\) \(\chi_{3549}(1922,\cdot)\) \(\chi_{3549}(2060,\cdot)\) \(\chi_{3549}(2069,\cdot)\) \(\chi_{3549}(2165,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{17}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(1787, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{156}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(-i\) | \(e\left(\frac{109}{156}\right)\) |