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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.da
\(\chi_{3549}(95,\cdot)\) \(\chi_{3549}(296,\cdot)\) \(\chi_{3549}(368,\cdot)\) \(\chi_{3549}(569,\cdot)\) \(\chi_{3549}(641,\cdot)\) \(\chi_{3549}(842,\cdot)\) \(\chi_{3549}(914,\cdot)\) \(\chi_{3549}(1115,\cdot)\) \(\chi_{3549}(1187,\cdot)\) \(\chi_{3549}(1388,\cdot)\) \(\chi_{3549}(1460,\cdot)\) \(\chi_{3549}(1661,\cdot)\) \(\chi_{3549}(1733,\cdot)\) \(\chi_{3549}(1934,\cdot)\) \(\chi_{3549}(2207,\cdot)\) \(\chi_{3549}(2279,\cdot)\) \(\chi_{3549}(2480,\cdot)\) \(\chi_{3549}(2552,\cdot)\) \(\chi_{3549}(2753,\cdot)\) \(\chi_{3549}(2825,\cdot)\) \(\chi_{3549}(3026,\cdot)\) \(\chi_{3549}(3098,\cdot)\) \(\chi_{3549}(3299,\cdot)\) \(\chi_{3549}(3371,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{43}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(2279, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{22}{39}\right)\) |