Basic properties
Modulus: | \(1157\) | |
Conductor: | \(1157\) | 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 1157.bv
\(\chi_{1157}(11,\cdot)\) \(\chi_{1157}(50,\cdot)\) \(\chi_{1157}(85,\cdot)\) \(\chi_{1157}(111,\cdot)\) \(\chi_{1157}(162,\cdot)\) \(\chi_{1157}(176,\cdot)\) \(\chi_{1157}(189,\cdot)\) \(\chi_{1157}(228,\cdot)\) \(\chi_{1157}(292,\cdot)\) \(\chi_{1157}(340,\cdot)\) \(\chi_{1157}(470,\cdot)\) \(\chi_{1157}(518,\cdot)\) \(\chi_{1157}(526,\cdot)\) \(\chi_{1157}(578,\cdot)\) \(\chi_{1157}(591,\cdot)\) \(\chi_{1157}(648,\cdot)\) \(\chi_{1157}(696,\cdot)\) \(\chi_{1157}(704,\cdot)\) \(\chi_{1157}(708,\cdot)\) \(\chi_{1157}(734,\cdot)\) \(\chi_{1157}(756,\cdot)\) \(\chi_{1157}(769,\cdot)\) \(\chi_{1157}(799,\cdot)\) \(\chi_{1157}(812,\cdot)\) \(\chi_{1157}(826,\cdot)\) \(\chi_{1157}(851,\cdot)\) \(\chi_{1157}(882,\cdot)\) \(\chi_{1157}(886,\cdot)\) \(\chi_{1157}(912,\cdot)\) \(\chi_{1157}(934,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((535,92)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{19}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1157 }(1064, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{49}{132}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{83}{132}\right)\) |