Basic properties
Modulus: | \(3549\) | |
Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.eh
\(\chi_{3549}(5,\cdot)\) \(\chi_{3549}(47,\cdot)\) \(\chi_{3549}(122,\cdot)\) \(\chi_{3549}(164,\cdot)\) \(\chi_{3549}(278,\cdot)\) \(\chi_{3549}(320,\cdot)\) \(\chi_{3549}(395,\cdot)\) \(\chi_{3549}(551,\cdot)\) \(\chi_{3549}(593,\cdot)\) \(\chi_{3549}(668,\cdot)\) \(\chi_{3549}(710,\cdot)\) \(\chi_{3549}(824,\cdot)\) \(\chi_{3549}(866,\cdot)\) \(\chi_{3549}(941,\cdot)\) \(\chi_{3549}(983,\cdot)\) \(\chi_{3549}(1097,\cdot)\) \(\chi_{3549}(1139,\cdot)\) \(\chi_{3549}(1214,\cdot)\) \(\chi_{3549}(1256,\cdot)\) \(\chi_{3549}(1370,\cdot)\) \(\chi_{3549}(1412,\cdot)\) \(\chi_{3549}(1487,\cdot)\) \(\chi_{3549}(1529,\cdot)\) \(\chi_{3549}(1643,\cdot)\) \(\chi_{3549}(1685,\cdot)\) \(\chi_{3549}(1802,\cdot)\) \(\chi_{3549}(1916,\cdot)\) \(\chi_{3549}(2033,\cdot)\) \(\chi_{3549}(2075,\cdot)\) \(\chi_{3549}(2189,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{43}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(941, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{52}\right)\) |