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.dx
\(\chi_{3549}(74,\cdot)\) \(\chi_{3549}(107,\cdot)\) \(\chi_{3549}(347,\cdot)\) \(\chi_{3549}(380,\cdot)\) \(\chi_{3549}(620,\cdot)\) \(\chi_{3549}(893,\cdot)\) \(\chi_{3549}(926,\cdot)\) \(\chi_{3549}(1166,\cdot)\) \(\chi_{3549}(1199,\cdot)\) \(\chi_{3549}(1439,\cdot)\) \(\chi_{3549}(1472,\cdot)\) \(\chi_{3549}(1745,\cdot)\) \(\chi_{3549}(1985,\cdot)\) \(\chi_{3549}(2018,\cdot)\) \(\chi_{3549}(2258,\cdot)\) \(\chi_{3549}(2291,\cdot)\) \(\chi_{3549}(2531,\cdot)\) \(\chi_{3549}(2564,\cdot)\) \(\chi_{3549}(2804,\cdot)\) \(\chi_{3549}(2837,\cdot)\) \(\chi_{3549}(3077,\cdot)\) \(\chi_{3549}(3110,\cdot)\) \(\chi_{3549}(3350,\cdot)\) \(\chi_{3549}(3383,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{10}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(2564, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{25}{78}\right)\) |