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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.em
\(\chi_{3549}(2,\cdot)\) \(\chi_{3549}(32,\cdot)\) \(\chi_{3549}(128,\cdot)\) \(\chi_{3549}(137,\cdot)\) \(\chi_{3549}(275,\cdot)\) \(\chi_{3549}(305,\cdot)\) \(\chi_{3549}(401,\cdot)\) \(\chi_{3549}(410,\cdot)\) \(\chi_{3549}(548,\cdot)\) \(\chi_{3549}(578,\cdot)\) \(\chi_{3549}(674,\cdot)\) \(\chi_{3549}(683,\cdot)\) \(\chi_{3549}(821,\cdot)\) \(\chi_{3549}(851,\cdot)\) \(\chi_{3549}(947,\cdot)\) \(\chi_{3549}(956,\cdot)\) \(\chi_{3549}(1124,\cdot)\) \(\chi_{3549}(1220,\cdot)\) \(\chi_{3549}(1229,\cdot)\) \(\chi_{3549}(1367,\cdot)\) \(\chi_{3549}(1397,\cdot)\) \(\chi_{3549}(1493,\cdot)\) \(\chi_{3549}(1640,\cdot)\) \(\chi_{3549}(1670,\cdot)\) \(\chi_{3549}(1766,\cdot)\) \(\chi_{3549}(1775,\cdot)\) \(\chi_{3549}(1913,\cdot)\) \(\chi_{3549}(1943,\cdot)\) \(\chi_{3549}(2039,\cdot)\) \(\chi_{3549}(2048,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{131}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(1229, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{115}{156}\right)\) |