Basic properties
Modulus: | \(3484\) | |
Conductor: | \(871\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{871}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3484.em
\(\chi_{3484}(33,\cdot)\) \(\chi_{3484}(189,\cdot)\) \(\chi_{3484}(449,\cdot)\) \(\chi_{3484}(609,\cdot)\) \(\chi_{3484}(613,\cdot)\) \(\chi_{3484}(773,\cdot)\) \(\chi_{3484}(821,\cdot)\) \(\chi_{3484}(825,\cdot)\) \(\chi_{3484}(869,\cdot)\) \(\chi_{3484}(925,\cdot)\) \(\chi_{3484}(977,\cdot)\) \(\chi_{3484}(1241,\cdot)\) \(\chi_{3484}(1289,\cdot)\) \(\chi_{3484}(1333,\cdot)\) \(\chi_{3484}(1389,\cdot)\) \(\chi_{3484}(1493,\cdot)\) \(\chi_{3484}(1497,\cdot)\) \(\chi_{3484}(1813,\cdot)\) \(\chi_{3484}(1865,\cdot)\) \(\chi_{3484}(1969,\cdot)\) \(\chi_{3484}(2113,\cdot)\) \(\chi_{3484}(2165,\cdot)\) \(\chi_{3484}(2177,\cdot)\) \(\chi_{3484}(2221,\cdot)\) \(\chi_{3484}(2333,\cdot)\) \(\chi_{3484}(2429,\cdot)\) \(\chi_{3484}(2485,\cdot)\) \(\chi_{3484}(2533,\cdot)\) \(\chi_{3484}(2581,\cdot)\) \(\chi_{3484}(2585,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1743,1341,3017)\) → \((1,e\left(\frac{11}{12}\right),e\left(\frac{16}{33}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 3484 }(33, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{13}{132}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{49}{66}\right)\) |