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.dd
\(\chi_{3549}(263,\cdot)\) \(\chi_{3549}(464,\cdot)\) \(\chi_{3549}(536,\cdot)\) \(\chi_{3549}(737,\cdot)\) \(\chi_{3549}(809,\cdot)\) \(\chi_{3549}(1010,\cdot)\) \(\chi_{3549}(1082,\cdot)\) \(\chi_{3549}(1283,\cdot)\) \(\chi_{3549}(1355,\cdot)\) \(\chi_{3549}(1556,\cdot)\) \(\chi_{3549}(1628,\cdot)\) \(\chi_{3549}(1829,\cdot)\) \(\chi_{3549}(1901,\cdot)\) \(\chi_{3549}(2102,\cdot)\) \(\chi_{3549}(2375,\cdot)\) \(\chi_{3549}(2447,\cdot)\) \(\chi_{3549}(2648,\cdot)\) \(\chi_{3549}(2720,\cdot)\) \(\chi_{3549}(2921,\cdot)\) \(\chi_{3549}(2993,\cdot)\) \(\chi_{3549}(3194,\cdot)\) \(\chi_{3549}(3266,\cdot)\) \(\chi_{3549}(3467,\cdot)\) \(\chi_{3549}(3539,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{7}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(2447, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(1\) | \(e\left(\frac{37}{78}\right)\) |