Basic properties
Modulus: | \(3549\) | |
Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{169}(140,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.dm
\(\chi_{3549}(43,\cdot)\) \(\chi_{3549}(127,\cdot)\) \(\chi_{3549}(400,\cdot)\) \(\chi_{3549}(589,\cdot)\) \(\chi_{3549}(673,\cdot)\) \(\chi_{3549}(862,\cdot)\) \(\chi_{3549}(946,\cdot)\) \(\chi_{3549}(1135,\cdot)\) \(\chi_{3549}(1219,\cdot)\) \(\chi_{3549}(1408,\cdot)\) \(\chi_{3549}(1492,\cdot)\) \(\chi_{3549}(1681,\cdot)\) \(\chi_{3549}(1765,\cdot)\) \(\chi_{3549}(1954,\cdot)\) \(\chi_{3549}(2038,\cdot)\) \(\chi_{3549}(2227,\cdot)\) \(\chi_{3549}(2311,\cdot)\) \(\chi_{3549}(2500,\cdot)\) \(\chi_{3549}(2584,\cdot)\) \(\chi_{3549}(2773,\cdot)\) \(\chi_{3549}(2857,\cdot)\) \(\chi_{3549}(3046,\cdot)\) \(\chi_{3549}(3130,\cdot)\) \(\chi_{3549}(3319,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((1,1,e\left(\frac{59}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(1492, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{25}{78}\right)\) |