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.ds
\(\chi_{3549}(179,\cdot)\) \(\chi_{3549}(212,\cdot)\) \(\chi_{3549}(452,\cdot)\) \(\chi_{3549}(725,\cdot)\) \(\chi_{3549}(758,\cdot)\) \(\chi_{3549}(998,\cdot)\) \(\chi_{3549}(1031,\cdot)\) \(\chi_{3549}(1271,\cdot)\) \(\chi_{3549}(1304,\cdot)\) \(\chi_{3549}(1577,\cdot)\) \(\chi_{3549}(1817,\cdot)\) \(\chi_{3549}(1850,\cdot)\) \(\chi_{3549}(2090,\cdot)\) \(\chi_{3549}(2123,\cdot)\) \(\chi_{3549}(2363,\cdot)\) \(\chi_{3549}(2396,\cdot)\) \(\chi_{3549}(2636,\cdot)\) \(\chi_{3549}(2669,\cdot)\) \(\chi_{3549}(2909,\cdot)\) \(\chi_{3549}(2942,\cdot)\) \(\chi_{3549}(3182,\cdot)\) \(\chi_{3549}(3215,\cdot)\) \(\chi_{3549}(3455,\cdot)\) \(\chi_{3549}(3488,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{19}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(2669, a) \) | \(-1\) | \(1\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(-1\) | \(e\left(\frac{7}{39}\right)\) |