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.bx
\(\chi_{1157}(71,\cdot)\) \(\chi_{1157}(72,\cdot)\) \(\chi_{1157}(80,\cdot)\) \(\chi_{1157}(98,\cdot)\) \(\chi_{1157}(106,\cdot)\) \(\chi_{1157}(136,\cdot)\) \(\chi_{1157}(188,\cdot)\) \(\chi_{1157}(249,\cdot)\) \(\chi_{1157}(314,\cdot)\) \(\chi_{1157}(336,\cdot)\) \(\chi_{1157}(366,\cdot)\) \(\chi_{1157}(396,\cdot)\) \(\chi_{1157}(409,\cdot)\) \(\chi_{1157}(440,\cdot)\) \(\chi_{1157}(466,\cdot)\) \(\chi_{1157}(513,\cdot)\) \(\chi_{1157}(514,\cdot)\) \(\chi_{1157}(539,\cdot)\) \(\chi_{1157}(570,\cdot)\) \(\chi_{1157}(574,\cdot)\) \(\chi_{1157}(583,\cdot)\) \(\chi_{1157}(587,\cdot)\) \(\chi_{1157}(618,\cdot)\) \(\chi_{1157}(643,\cdot)\) \(\chi_{1157}(644,\cdot)\) \(\chi_{1157}(691,\cdot)\) \(\chi_{1157}(717,\cdot)\) \(\chi_{1157}(748,\cdot)\) \(\chi_{1157}(761,\cdot)\) \(\chi_{1157}(791,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((535,92)\) → \((e\left(\frac{1}{12}\right),e\left(\frac{3}{44}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1157 }(106, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{53}{132}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{41}{132}\right)\) |