Basic properties
Modulus: | \(3484\) | |
Conductor: | \(871\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{871}(84,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3484.el
\(\chi_{3484}(93,\cdot)\) \(\chi_{3484}(301,\cdot)\) \(\chi_{3484}(345,\cdot)\) \(\chi_{3484}(457,\cdot)\) \(\chi_{3484}(505,\cdot)\) \(\chi_{3484}(553,\cdot)\) \(\chi_{3484}(557,\cdot)\) \(\chi_{3484}(657,\cdot)\) \(\chi_{3484}(709,\cdot)\) \(\chi_{3484}(717,\cdot)\) \(\chi_{3484}(877,\cdot)\) \(\chi_{3484}(973,\cdot)\) \(\chi_{3484}(1021,\cdot)\) \(\chi_{3484}(1137,\cdot)\) \(\chi_{3484}(1229,\cdot)\) \(\chi_{3484}(1545,\cdot)\) \(\chi_{3484}(1597,\cdot)\) \(\chi_{3484}(1601,\cdot)\) \(\chi_{3484}(1657,\cdot)\) \(\chi_{3484}(1701,\cdot)\) \(\chi_{3484}(1761,\cdot)\) \(\chi_{3484}(1909,\cdot)\) \(\chi_{3484}(2065,\cdot)\) \(\chi_{3484}(2217,\cdot)\) \(\chi_{3484}(2325,\cdot)\) \(\chi_{3484}(2381,\cdot)\) \(\chi_{3484}(2433,\cdot)\) \(\chi_{3484}(2477,\cdot)\) \(\chi_{3484}(2489,\cdot)\) \(\chi_{3484}(2697,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1743,1341,3017)\) → \((1,e\left(\frac{5}{12}\right),e\left(\frac{32}{33}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 3484 }(2697, a) \) | \(-1\) | \(1\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{103}{132}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{103}{132}\right)\) | \(e\left(\frac{49}{132}\right)\) | \(e\left(\frac{7}{22}\right)\) |