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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.cy
\(\chi_{3549}(17,\cdot)\) \(\chi_{3549}(257,\cdot)\) \(\chi_{3549}(290,\cdot)\) \(\chi_{3549}(563,\cdot)\) \(\chi_{3549}(803,\cdot)\) \(\chi_{3549}(836,\cdot)\) \(\chi_{3549}(1076,\cdot)\) \(\chi_{3549}(1109,\cdot)\) \(\chi_{3549}(1349,\cdot)\) \(\chi_{3549}(1382,\cdot)\) \(\chi_{3549}(1622,\cdot)\) \(\chi_{3549}(1655,\cdot)\) \(\chi_{3549}(1895,\cdot)\) \(\chi_{3549}(1928,\cdot)\) \(\chi_{3549}(2168,\cdot)\) \(\chi_{3549}(2201,\cdot)\) \(\chi_{3549}(2441,\cdot)\) \(\chi_{3549}(2474,\cdot)\) \(\chi_{3549}(2714,\cdot)\) \(\chi_{3549}(2747,\cdot)\) \(\chi_{3549}(2987,\cdot)\) \(\chi_{3549}(3260,\cdot)\) \(\chi_{3549}(3293,\cdot)\) \(\chi_{3549}(3533,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{77}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(803, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{67}{78}\right)\) |