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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1157.bz
\(\chi_{1157}(9,\cdot)\) \(\chi_{1157}(42,\cdot)\) \(\chi_{1157}(68,\cdot)\) \(\chi_{1157}(94,\cdot)\) \(\chi_{1157}(107,\cdot)\) \(\chi_{1157}(198,\cdot)\) \(\chi_{1157}(250,\cdot)\) \(\chi_{1157}(276,\cdot)\) \(\chi_{1157}(347,\cdot)\) \(\chi_{1157}(373,\cdot)\) \(\chi_{1157}(425,\cdot)\) \(\chi_{1157}(516,\cdot)\) \(\chi_{1157}(529,\cdot)\) \(\chi_{1157}(555,\cdot)\) \(\chi_{1157}(581,\cdot)\) \(\chi_{1157}(614,\cdot)\) \(\chi_{1157}(633,\cdot)\) \(\chi_{1157}(640,\cdot)\) \(\chi_{1157}(659,\cdot)\) \(\chi_{1157}(672,\cdot)\) \(\chi_{1157}(692,\cdot)\) \(\chi_{1157}(783,\cdot)\) \(\chi_{1157}(796,\cdot)\) \(\chi_{1157}(822,\cdot)\) \(\chi_{1157}(841,\cdot)\) \(\chi_{1157}(848,\cdot)\) \(\chi_{1157}(854,\cdot)\) \(\chi_{1157}(880,\cdot)\) \(\chi_{1157}(900,\cdot)\) \(\chi_{1157}(926,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((535,92)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{41}{44}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1157 }(822, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{35}{132}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{67}{132}\right)\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{20}{33}\right)\) |