Basic properties
Modulus: | \(8027\) | |
Conductor: | \(8027\) | 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 8027.be
\(\chi_{8027}(189,\cdot)\) \(\chi_{8027}(373,\cdot)\) \(\chi_{8027}(674,\cdot)\) \(\chi_{8027}(858,\cdot)\) \(\chi_{8027}(1023,\cdot)\) \(\chi_{8027}(1207,\cdot)\) \(\chi_{8027}(1236,\cdot)\) \(\chi_{8027}(1372,\cdot)\) \(\chi_{8027}(1420,\cdot)\) \(\chi_{8027}(1556,\cdot)\) \(\chi_{8027}(1585,\cdot)\) \(\chi_{8027}(1721,\cdot)\) \(\chi_{8027}(1769,\cdot)\) \(\chi_{8027}(1905,\cdot)\) \(\chi_{8027}(2632,\cdot)\) \(\chi_{8027}(2816,\cdot)\) \(\chi_{8027}(2981,\cdot)\) \(\chi_{8027}(3165,\cdot)\) \(\chi_{8027}(3815,\cdot)\) \(\chi_{8027}(3999,\cdot)\) \(\chi_{8027}(4377,\cdot)\) \(\chi_{8027}(4513,\cdot)\) \(\chi_{8027}(4561,\cdot)\) \(\chi_{8027}(4697,\cdot)\) \(\chi_{8027}(4726,\cdot)\) \(\chi_{8027}(4910,\cdot)\) \(\chi_{8027}(5075,\cdot)\) \(\chi_{8027}(5259,\cdot)\) \(\chi_{8027}(5424,\cdot)\) \(\chi_{8027}(5560,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((e\left(\frac{21}{22}\right),e\left(\frac{5}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(2981, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{7}{132}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) |