Basic properties
Modulus: | \(4140\) | |
Conductor: | \(4140\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 4140.dm
\(\chi_{4140}(83,\cdot)\) \(\chi_{4140}(203,\cdot)\) \(\chi_{4140}(227,\cdot)\) \(\chi_{4140}(263,\cdot)\) \(\chi_{4140}(383,\cdot)\) \(\chi_{4140}(527,\cdot)\) \(\chi_{4140}(563,\cdot)\) \(\chi_{4140}(707,\cdot)\) \(\chi_{4140}(743,\cdot)\) \(\chi_{4140}(803,\cdot)\) \(\chi_{4140}(983,\cdot)\) \(\chi_{4140}(1247,\cdot)\) \(\chi_{4140}(1307,\cdot)\) \(\chi_{4140}(1463,\cdot)\) \(\chi_{4140}(1487,\cdot)\) \(\chi_{4140}(1523,\cdot)\) \(\chi_{4140}(1607,\cdot)\) \(\chi_{4140}(1643,\cdot)\) \(\chi_{4140}(1667,\cdot)\) \(\chi_{4140}(1847,\cdot)\) \(\chi_{4140}(1883,\cdot)\) \(\chi_{4140}(2183,\cdot)\) \(\chi_{4140}(2363,\cdot)\) \(\chi_{4140}(2567,\cdot)\) \(\chi_{4140}(2687,\cdot)\) \(\chi_{4140}(2747,\cdot)\) \(\chi_{4140}(2867,\cdot)\) \(\chi_{4140}(2903,\cdot)\) \(\chi_{4140}(2963,\cdot)\) \(\chi_{4140}(3047,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2071,461,1657,3961)\) → \((-1,e\left(\frac{5}{6}\right),i,e\left(\frac{7}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 4140 }(707, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{115}{132}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{23}{132}\right)\) |