Basic properties
| Modulus: | \(3549\) | |
| Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | 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.cv
\(\chi_{3549}(83,\cdot)\) \(\chi_{3549}(125,\cdot)\) \(\chi_{3549}(356,\cdot)\) \(\chi_{3549}(398,\cdot)\) \(\chi_{3549}(629,\cdot)\) \(\chi_{3549}(671,\cdot)\) \(\chi_{3549}(902,\cdot)\) \(\chi_{3549}(1175,\cdot)\) \(\chi_{3549}(1217,\cdot)\) \(\chi_{3549}(1448,\cdot)\) \(\chi_{3549}(1490,\cdot)\) \(\chi_{3549}(1721,\cdot)\) \(\chi_{3549}(1763,\cdot)\) \(\chi_{3549}(1994,\cdot)\) \(\chi_{3549}(2036,\cdot)\) \(\chi_{3549}(2309,\cdot)\) \(\chi_{3549}(2540,\cdot)\) \(\chi_{3549}(2582,\cdot)\) \(\chi_{3549}(2813,\cdot)\) \(\chi_{3549}(2855,\cdot)\) \(\chi_{3549}(3086,\cdot)\) \(\chi_{3549}(3128,\cdot)\) \(\chi_{3549}(3359,\cdot)\) \(\chi_{3549}(3401,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,-1,e\left(\frac{3}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(2540, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(i\) | \(e\left(\frac{33}{52}\right)\) |