Basic properties
Modulus: | \(3549\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(935,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.dg
\(\chi_{3549}(25,\cdot)\) \(\chi_{3549}(142,\cdot)\) \(\chi_{3549}(298,\cdot)\) \(\chi_{3549}(415,\cdot)\) \(\chi_{3549}(571,\cdot)\) \(\chi_{3549}(688,\cdot)\) \(\chi_{3549}(961,\cdot)\) \(\chi_{3549}(1117,\cdot)\) \(\chi_{3549}(1234,\cdot)\) \(\chi_{3549}(1390,\cdot)\) \(\chi_{3549}(1507,\cdot)\) \(\chi_{3549}(1663,\cdot)\) \(\chi_{3549}(1780,\cdot)\) \(\chi_{3549}(1936,\cdot)\) \(\chi_{3549}(2053,\cdot)\) \(\chi_{3549}(2209,\cdot)\) \(\chi_{3549}(2326,\cdot)\) \(\chi_{3549}(2482,\cdot)\) \(\chi_{3549}(2599,\cdot)\) \(\chi_{3549}(2755,\cdot)\) \(\chi_{3549}(3028,\cdot)\) \(\chi_{3549}(3145,\cdot)\) \(\chi_{3549}(3301,\cdot)\) \(\chi_{3549}(3418,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{17}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(3301, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{26}\right)\) |