Basic properties
Modulus: | \(3549\) | |
Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | 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.dk
\(\chi_{3549}(152,\cdot)\) \(\chi_{3549}(185,\cdot)\) \(\chi_{3549}(425,\cdot)\) \(\chi_{3549}(458,\cdot)\) \(\chi_{3549}(731,\cdot)\) \(\chi_{3549}(971,\cdot)\) \(\chi_{3549}(1004,\cdot)\) \(\chi_{3549}(1244,\cdot)\) \(\chi_{3549}(1277,\cdot)\) \(\chi_{3549}(1517,\cdot)\) \(\chi_{3549}(1550,\cdot)\) \(\chi_{3549}(1790,\cdot)\) \(\chi_{3549}(1823,\cdot)\) \(\chi_{3549}(2063,\cdot)\) \(\chi_{3549}(2096,\cdot)\) \(\chi_{3549}(2336,\cdot)\) \(\chi_{3549}(2369,\cdot)\) \(\chi_{3549}(2609,\cdot)\) \(\chi_{3549}(2642,\cdot)\) \(\chi_{3549}(2882,\cdot)\) \(\chi_{3549}(2915,\cdot)\) \(\chi_{3549}(3155,\cdot)\) \(\chi_{3549}(3428,\cdot)\) \(\chi_{3549}(3461,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{11}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(971, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(-1\) | \(e\left(\frac{4}{39}\right)\) |