Basic properties
Modulus: | \(3549\) | |
Conductor: | \(507\) | 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 \(\chi_{507}(50,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.ee
\(\chi_{3549}(50,\cdot)\) \(\chi_{3549}(71,\cdot)\) \(\chi_{3549}(176,\cdot)\) \(\chi_{3549}(197,\cdot)\) \(\chi_{3549}(323,\cdot)\) \(\chi_{3549}(344,\cdot)\) \(\chi_{3549}(449,\cdot)\) \(\chi_{3549}(470,\cdot)\) \(\chi_{3549}(617,\cdot)\) \(\chi_{3549}(722,\cdot)\) \(\chi_{3549}(743,\cdot)\) \(\chi_{3549}(869,\cdot)\) \(\chi_{3549}(890,\cdot)\) \(\chi_{3549}(1016,\cdot)\) \(\chi_{3549}(1142,\cdot)\) \(\chi_{3549}(1163,\cdot)\) \(\chi_{3549}(1268,\cdot)\) \(\chi_{3549}(1289,\cdot)\) \(\chi_{3549}(1415,\cdot)\) \(\chi_{3549}(1436,\cdot)\) \(\chi_{3549}(1541,\cdot)\) \(\chi_{3549}(1562,\cdot)\) \(\chi_{3549}(1688,\cdot)\) \(\chi_{3549}(1814,\cdot)\) \(\chi_{3549}(1835,\cdot)\) \(\chi_{3549}(1961,\cdot)\) \(\chi_{3549}(1982,\cdot)\) \(\chi_{3549}(2087,\cdot)\) \(\chi_{3549}(2234,\cdot)\) \(\chi_{3549}(2255,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1184,1522,3382)\) → \((-1,1,e\left(\frac{19}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(50, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{131}{156}\right)\) |