Basic properties
Modulus: | \(3549\) | |
Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{507}(398,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.cw
\(\chi_{3549}(8,\cdot)\) \(\chi_{3549}(281,\cdot)\) \(\chi_{3549}(512,\cdot)\) \(\chi_{3549}(554,\cdot)\) \(\chi_{3549}(785,\cdot)\) \(\chi_{3549}(827,\cdot)\) \(\chi_{3549}(1058,\cdot)\) \(\chi_{3549}(1100,\cdot)\) \(\chi_{3549}(1331,\cdot)\) \(\chi_{3549}(1373,\cdot)\) \(\chi_{3549}(1604,\cdot)\) \(\chi_{3549}(1646,\cdot)\) \(\chi_{3549}(1877,\cdot)\) \(\chi_{3549}(1919,\cdot)\) \(\chi_{3549}(2150,\cdot)\) \(\chi_{3549}(2192,\cdot)\) \(\chi_{3549}(2423,\cdot)\) \(\chi_{3549}(2696,\cdot)\) \(\chi_{3549}(2738,\cdot)\) \(\chi_{3549}(2969,\cdot)\) \(\chi_{3549}(3011,\cdot)\) \(\chi_{3549}(3242,\cdot)\) \(\chi_{3549}(3284,\cdot)\) \(\chi_{3549}(3515,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,1,e\left(\frac{45}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(1919, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(i\) | \(e\left(\frac{1}{52}\right)\) |