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 \(\chi_{1183}(1081,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.eb
\(\chi_{3549}(115,\cdot)\) \(\chi_{3549}(124,\cdot)\) \(\chi_{3549}(262,\cdot)\) \(\chi_{3549}(292,\cdot)\) \(\chi_{3549}(388,\cdot)\) \(\chi_{3549}(397,\cdot)\) \(\chi_{3549}(535,\cdot)\) \(\chi_{3549}(565,\cdot)\) \(\chi_{3549}(661,\cdot)\) \(\chi_{3549}(670,\cdot)\) \(\chi_{3549}(808,\cdot)\) \(\chi_{3549}(838,\cdot)\) \(\chi_{3549}(943,\cdot)\) \(\chi_{3549}(1081,\cdot)\) \(\chi_{3549}(1111,\cdot)\) \(\chi_{3549}(1207,\cdot)\) \(\chi_{3549}(1216,\cdot)\) \(\chi_{3549}(1354,\cdot)\) \(\chi_{3549}(1384,\cdot)\) \(\chi_{3549}(1480,\cdot)\) \(\chi_{3549}(1489,\cdot)\) \(\chi_{3549}(1627,\cdot)\) \(\chi_{3549}(1657,\cdot)\) \(\chi_{3549}(1753,\cdot)\) \(\chi_{3549}(1762,\cdot)\) \(\chi_{3549}(1900,\cdot)\) \(\chi_{3549}(1930,\cdot)\) \(\chi_{3549}(2026,\cdot)\) \(\chi_{3549}(2035,\cdot)\) \(\chi_{3549}(2173,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1184,1522,3382)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{37}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(1081, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(i\) | \(e\left(\frac{17}{156}\right)\) |