Basic properties
| Modulus: | \(3549\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(10,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.dj
\(\chi_{3549}(10,\cdot)\) \(\chi_{3549}(82,\cdot)\) \(\chi_{3549}(283,\cdot)\) \(\chi_{3549}(355,\cdot)\) \(\chi_{3549}(556,\cdot)\) \(\chi_{3549}(628,\cdot)\) \(\chi_{3549}(829,\cdot)\) \(\chi_{3549}(901,\cdot)\) \(\chi_{3549}(1102,\cdot)\) \(\chi_{3549}(1174,\cdot)\) \(\chi_{3549}(1447,\cdot)\) \(\chi_{3549}(1648,\cdot)\) \(\chi_{3549}(1720,\cdot)\) \(\chi_{3549}(1921,\cdot)\) \(\chi_{3549}(1993,\cdot)\) \(\chi_{3549}(2194,\cdot)\) \(\chi_{3549}(2266,\cdot)\) \(\chi_{3549}(2467,\cdot)\) \(\chi_{3549}(2539,\cdot)\) \(\chi_{3549}(2740,\cdot)\) \(\chi_{3549}(2812,\cdot)\) \(\chi_{3549}(3013,\cdot)\) \(\chi_{3549}(3085,\cdot)\) \(\chi_{3549}(3286,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{5}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(1\) | \(e\left(\frac{8}{39}\right)\) |