Basic properties
Modulus: | \(3549\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(486,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.ej
\(\chi_{3549}(31,\cdot)\) \(\chi_{3549}(73,\cdot)\) \(\chi_{3549}(187,\cdot)\) \(\chi_{3549}(229,\cdot)\) \(\chi_{3549}(304,\cdot)\) \(\chi_{3549}(346,\cdot)\) \(\chi_{3549}(460,\cdot)\) \(\chi_{3549}(502,\cdot)\) \(\chi_{3549}(619,\cdot)\) \(\chi_{3549}(733,\cdot)\) \(\chi_{3549}(850,\cdot)\) \(\chi_{3549}(892,\cdot)\) \(\chi_{3549}(1006,\cdot)\) \(\chi_{3549}(1048,\cdot)\) \(\chi_{3549}(1123,\cdot)\) \(\chi_{3549}(1165,\cdot)\) \(\chi_{3549}(1279,\cdot)\) \(\chi_{3549}(1321,\cdot)\) \(\chi_{3549}(1396,\cdot)\) \(\chi_{3549}(1438,\cdot)\) \(\chi_{3549}(1552,\cdot)\) \(\chi_{3549}(1594,\cdot)\) \(\chi_{3549}(1669,\cdot)\) \(\chi_{3549}(1711,\cdot)\) \(\chi_{3549}(1825,\cdot)\) \(\chi_{3549}(1867,\cdot)\) \(\chi_{3549}(1942,\cdot)\) \(\chi_{3549}(1984,\cdot)\) \(\chi_{3549}(2140,\cdot)\) \(\chi_{3549}(2215,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1184,1522,3382)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{51}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(1669, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{15}{52}\right)\) |