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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5445.da
\(\chi_{5445}(32,\cdot)\) \(\chi_{5445}(263,\cdot)\) \(\chi_{5445}(428,\cdot)\) \(\chi_{5445}(527,\cdot)\) \(\chi_{5445}(758,\cdot)\) \(\chi_{5445}(857,\cdot)\) \(\chi_{5445}(923,\cdot)\) \(\chi_{5445}(1022,\cdot)\) \(\chi_{5445}(1253,\cdot)\) \(\chi_{5445}(1352,\cdot)\) \(\chi_{5445}(1418,\cdot)\) \(\chi_{5445}(1517,\cdot)\) \(\chi_{5445}(1748,\cdot)\) \(\chi_{5445}(1847,\cdot)\) \(\chi_{5445}(1913,\cdot)\) \(\chi_{5445}(2012,\cdot)\) \(\chi_{5445}(2243,\cdot)\) \(\chi_{5445}(2342,\cdot)\) \(\chi_{5445}(2408,\cdot)\) \(\chi_{5445}(2507,\cdot)\) \(\chi_{5445}(2738,\cdot)\) \(\chi_{5445}(2837,\cdot)\) \(\chi_{5445}(3002,\cdot)\) \(\chi_{5445}(3233,\cdot)\) \(\chi_{5445}(3332,\cdot)\) \(\chi_{5445}(3398,\cdot)\) \(\chi_{5445}(3497,\cdot)\) \(\chi_{5445}(3728,\cdot)\) \(\chi_{5445}(3827,\cdot)\) \(\chi_{5445}(3893,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3026,4357,3511)\) → \((e\left(\frac{1}{6}\right),i,e\left(\frac{15}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 5445 }(857, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{125}{132}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{41}{132}\right)\) |