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.dc
\(\chi_{3549}(230,\cdot)\) \(\chi_{3549}(419,\cdot)\) \(\chi_{3549}(503,\cdot)\) \(\chi_{3549}(692,\cdot)\) \(\chi_{3549}(776,\cdot)\) \(\chi_{3549}(965,\cdot)\) \(\chi_{3549}(1049,\cdot)\) \(\chi_{3549}(1238,\cdot)\) \(\chi_{3549}(1322,\cdot)\) \(\chi_{3549}(1511,\cdot)\) \(\chi_{3549}(1595,\cdot)\) \(\chi_{3549}(1784,\cdot)\) \(\chi_{3549}(1868,\cdot)\) \(\chi_{3549}(2057,\cdot)\) \(\chi_{3549}(2141,\cdot)\) \(\chi_{3549}(2330,\cdot)\) \(\chi_{3549}(2414,\cdot)\) \(\chi_{3549}(2603,\cdot)\) \(\chi_{3549}(2687,\cdot)\) \(\chi_{3549}(2876,\cdot)\) \(\chi_{3549}(2960,\cdot)\) \(\chi_{3549}(3149,\cdot)\) \(\chi_{3549}(3422,\cdot)\) \(\chi_{3549}(3506,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,-1,e\left(\frac{23}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(1868, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{39}\right)\) |