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.dk
\(\chi_{4140}(187,\cdot)\) \(\chi_{4140}(223,\cdot)\) \(\chi_{4140}(403,\cdot)\) \(\chi_{4140}(427,\cdot)\) \(\chi_{4140}(463,\cdot)\) \(\chi_{4140}(547,\cdot)\) \(\chi_{4140}(583,\cdot)\) \(\chi_{4140}(607,\cdot)\) \(\chi_{4140}(763,\cdot)\) \(\chi_{4140}(823,\cdot)\) \(\chi_{4140}(1087,\cdot)\) \(\chi_{4140}(1267,\cdot)\) \(\chi_{4140}(1327,\cdot)\) \(\chi_{4140}(1363,\cdot)\) \(\chi_{4140}(1507,\cdot)\) \(\chi_{4140}(1543,\cdot)\) \(\chi_{4140}(1687,\cdot)\) \(\chi_{4140}(1807,\cdot)\) \(\chi_{4140}(1843,\cdot)\) \(\chi_{4140}(1867,\cdot)\) \(\chi_{4140}(1987,\cdot)\) \(\chi_{4140}(2083,\cdot)\) \(\chi_{4140}(2203,\cdot)\) \(\chi_{4140}(2263,\cdot)\) \(\chi_{4140}(2707,\cdot)\) \(\chi_{4140}(2743,\cdot)\) \(\chi_{4140}(2887,\cdot)\) \(\chi_{4140}(2923,\cdot)\) \(\chi_{4140}(2947,\cdot)\) \(\chi_{4140}(2983,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2071,461,1657,3961)\) → \((-1,e\left(\frac{1}{3}\right),i,e\left(\frac{4}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 4140 }(1327, a) \) | \(1\) | \(1\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{67}{132}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{53}{132}\right)\) |