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.dv
\(\chi_{3549}(62,\cdot)\) \(\chi_{3549}(251,\cdot)\) \(\chi_{3549}(335,\cdot)\) \(\chi_{3549}(524,\cdot)\) \(\chi_{3549}(608,\cdot)\) \(\chi_{3549}(797,\cdot)\) \(\chi_{3549}(881,\cdot)\) \(\chi_{3549}(1070,\cdot)\) \(\chi_{3549}(1154,\cdot)\) \(\chi_{3549}(1343,\cdot)\) \(\chi_{3549}(1427,\cdot)\) \(\chi_{3549}(1616,\cdot)\) \(\chi_{3549}(1700,\cdot)\) \(\chi_{3549}(1889,\cdot)\) \(\chi_{3549}(1973,\cdot)\) \(\chi_{3549}(2162,\cdot)\) \(\chi_{3549}(2246,\cdot)\) \(\chi_{3549}(2435,\cdot)\) \(\chi_{3549}(2519,\cdot)\) \(\chi_{3549}(2708,\cdot)\) \(\chi_{3549}(2792,\cdot)\) \(\chi_{3549}(2981,\cdot)\) \(\chi_{3549}(3254,\cdot)\) \(\chi_{3549}(3338,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,-1,e\left(\frac{19}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(2162, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{53}{78}\right)\) |