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.dy
\(\chi_{3549}(68,\cdot)\) \(\chi_{3549}(269,\cdot)\) \(\chi_{3549}(341,\cdot)\) \(\chi_{3549}(542,\cdot)\) \(\chi_{3549}(614,\cdot)\) \(\chi_{3549}(815,\cdot)\) \(\chi_{3549}(887,\cdot)\) \(\chi_{3549}(1088,\cdot)\) \(\chi_{3549}(1361,\cdot)\) \(\chi_{3549}(1433,\cdot)\) \(\chi_{3549}(1634,\cdot)\) \(\chi_{3549}(1706,\cdot)\) \(\chi_{3549}(1907,\cdot)\) \(\chi_{3549}(1979,\cdot)\) \(\chi_{3549}(2180,\cdot)\) \(\chi_{3549}(2252,\cdot)\) \(\chi_{3549}(2453,\cdot)\) \(\chi_{3549}(2525,\cdot)\) \(\chi_{3549}(2798,\cdot)\) \(\chi_{3549}(2999,\cdot)\) \(\chi_{3549}(3071,\cdot)\) \(\chi_{3549}(3272,\cdot)\) \(\chi_{3549}(3344,\cdot)\) \(\chi_{3549}(3545,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{19}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(887, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{14}{39}\right)\) |