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.ep
\(\chi_{3549}(59,\cdot)\) \(\chi_{3549}(227,\cdot)\) \(\chi_{3549}(236,\cdot)\) \(\chi_{3549}(332,\cdot)\) \(\chi_{3549}(362,\cdot)\) \(\chi_{3549}(500,\cdot)\) \(\chi_{3549}(509,\cdot)\) \(\chi_{3549}(605,\cdot)\) \(\chi_{3549}(635,\cdot)\) \(\chi_{3549}(773,\cdot)\) \(\chi_{3549}(782,\cdot)\) \(\chi_{3549}(878,\cdot)\) \(\chi_{3549}(908,\cdot)\) \(\chi_{3549}(1046,\cdot)\) \(\chi_{3549}(1055,\cdot)\) \(\chi_{3549}(1151,\cdot)\) \(\chi_{3549}(1181,\cdot)\) \(\chi_{3549}(1319,\cdot)\) \(\chi_{3549}(1328,\cdot)\) \(\chi_{3549}(1424,\cdot)\) \(\chi_{3549}(1454,\cdot)\) \(\chi_{3549}(1592,\cdot)\) \(\chi_{3549}(1697,\cdot)\) \(\chi_{3549}(1727,\cdot)\) \(\chi_{3549}(1865,\cdot)\) \(\chi_{3549}(1874,\cdot)\) \(\chi_{3549}(1970,\cdot)\) \(\chi_{3549}(2000,\cdot)\) \(\chi_{3549}(2138,\cdot)\) \(\chi_{3549}(2147,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{89}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(2684, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{43}{156}\right)\) |