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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.ea
\(\chi_{3549}(110,\cdot)\) \(\chi_{3549}(206,\cdot)\) \(\chi_{3549}(215,\cdot)\) \(\chi_{3549}(353,\cdot)\) \(\chi_{3549}(383,\cdot)\) \(\chi_{3549}(479,\cdot)\) \(\chi_{3549}(626,\cdot)\) \(\chi_{3549}(656,\cdot)\) \(\chi_{3549}(752,\cdot)\) \(\chi_{3549}(761,\cdot)\) \(\chi_{3549}(899,\cdot)\) \(\chi_{3549}(929,\cdot)\) \(\chi_{3549}(1025,\cdot)\) \(\chi_{3549}(1034,\cdot)\) \(\chi_{3549}(1172,\cdot)\) \(\chi_{3549}(1298,\cdot)\) \(\chi_{3549}(1307,\cdot)\) \(\chi_{3549}(1445,\cdot)\) \(\chi_{3549}(1475,\cdot)\) \(\chi_{3549}(1571,\cdot)\) \(\chi_{3549}(1580,\cdot)\) \(\chi_{3549}(1718,\cdot)\) \(\chi_{3549}(1748,\cdot)\) \(\chi_{3549}(1844,\cdot)\) \(\chi_{3549}(1853,\cdot)\) \(\chi_{3549}(1991,\cdot)\) \(\chi_{3549}(2021,\cdot)\) \(\chi_{3549}(2126,\cdot)\) \(\chi_{3549}(2264,\cdot)\) \(\chi_{3549}(2294,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{127}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(2390, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(-i\) | \(e\left(\frac{149}{156}\right)\) |