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 \(\chi_{1183}(678,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.ei
\(\chi_{3549}(76,\cdot)\) \(\chi_{3549}(97,\cdot)\) \(\chi_{3549}(202,\cdot)\) \(\chi_{3549}(223,\cdot)\) \(\chi_{3549}(349,\cdot)\) \(\chi_{3549}(370,\cdot)\) \(\chi_{3549}(475,\cdot)\) \(\chi_{3549}(496,\cdot)\) \(\chi_{3549}(622,\cdot)\) \(\chi_{3549}(643,\cdot)\) \(\chi_{3549}(748,\cdot)\) \(\chi_{3549}(769,\cdot)\) \(\chi_{3549}(895,\cdot)\) \(\chi_{3549}(916,\cdot)\) \(\chi_{3549}(1021,\cdot)\) \(\chi_{3549}(1042,\cdot)\) \(\chi_{3549}(1168,\cdot)\) \(\chi_{3549}(1189,\cdot)\) \(\chi_{3549}(1294,\cdot)\) \(\chi_{3549}(1315,\cdot)\) \(\chi_{3549}(1462,\cdot)\) \(\chi_{3549}(1567,\cdot)\) \(\chi_{3549}(1588,\cdot)\) \(\chi_{3549}(1714,\cdot)\) \(\chi_{3549}(1735,\cdot)\) \(\chi_{3549}(1861,\cdot)\) \(\chi_{3549}(1987,\cdot)\) \(\chi_{3549}(2008,\cdot)\) \(\chi_{3549}(2113,\cdot)\) \(\chi_{3549}(2134,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1184,1522,3382)\) → \((1,-1,e\left(\frac{1}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(1861, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{89}{156}\right)\) |