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
\((535,92)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{23}{44}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1157 }(1059, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{132}\right)\) | \(e\left(\frac{25}{132}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{109}{132}\right)\) |