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.di
\(\chi_{3549}(131,\cdot)\) \(\chi_{3549}(248,\cdot)\) \(\chi_{3549}(404,\cdot)\) \(\chi_{3549}(521,\cdot)\) \(\chi_{3549}(794,\cdot)\) \(\chi_{3549}(950,\cdot)\) \(\chi_{3549}(1067,\cdot)\) \(\chi_{3549}(1223,\cdot)\) \(\chi_{3549}(1340,\cdot)\) \(\chi_{3549}(1496,\cdot)\) \(\chi_{3549}(1613,\cdot)\) \(\chi_{3549}(1769,\cdot)\) \(\chi_{3549}(1886,\cdot)\) \(\chi_{3549}(2042,\cdot)\) \(\chi_{3549}(2159,\cdot)\) \(\chi_{3549}(2315,\cdot)\) \(\chi_{3549}(2432,\cdot)\) \(\chi_{3549}(2588,\cdot)\) \(\chi_{3549}(2861,\cdot)\) \(\chi_{3549}(2978,\cdot)\) \(\chi_{3549}(3134,\cdot)\) \(\chi_{3549}(3251,\cdot)\) \(\chi_{3549}(3407,\cdot)\) \(\chi_{3549}(3524,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{8}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(1496, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{10}{13}\right)\) |