Basic properties
| Modulus: | \(5445\) | |
| Conductor: | \(5445\) | 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 5445.cy
\(\chi_{5445}(43,\cdot)\) \(\chi_{5445}(142,\cdot)\) \(\chi_{5445}(373,\cdot)\) \(\chi_{5445}(472,\cdot)\) \(\chi_{5445}(538,\cdot)\) \(\chi_{5445}(637,\cdot)\) \(\chi_{5445}(868,\cdot)\) \(\chi_{5445}(1033,\cdot)\) \(\chi_{5445}(1132,\cdot)\) \(\chi_{5445}(1363,\cdot)\) \(\chi_{5445}(1462,\cdot)\) \(\chi_{5445}(1528,\cdot)\) \(\chi_{5445}(1627,\cdot)\) \(\chi_{5445}(1858,\cdot)\) \(\chi_{5445}(1957,\cdot)\) \(\chi_{5445}(2023,\cdot)\) \(\chi_{5445}(2122,\cdot)\) \(\chi_{5445}(2353,\cdot)\) \(\chi_{5445}(2452,\cdot)\) \(\chi_{5445}(2518,\cdot)\) \(\chi_{5445}(2617,\cdot)\) \(\chi_{5445}(2848,\cdot)\) \(\chi_{5445}(2947,\cdot)\) \(\chi_{5445}(3013,\cdot)\) \(\chi_{5445}(3112,\cdot)\) \(\chi_{5445}(3343,\cdot)\) \(\chi_{5445}(3442,\cdot)\) \(\chi_{5445}(3607,\cdot)\) \(\chi_{5445}(3838,\cdot)\) \(\chi_{5445}(3937,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3026,4357,3511)\) → \((e\left(\frac{2}{3}\right),-i,e\left(\frac{5}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 5445 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{1}{132}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{71}{132}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{65}{132}\right)\) |