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.bw
\(\chi_{1157}(20,\cdot)\) \(\chi_{1157}(84,\cdot)\) \(\chi_{1157}(110,\cdot)\) \(\chi_{1157}(158,\cdot)\) \(\chi_{1157}(214,\cdot)\) \(\chi_{1157}(227,\cdot)\) \(\chi_{1157}(258,\cdot)\) \(\chi_{1157}(262,\cdot)\) \(\chi_{1157}(284,\cdot)\) \(\chi_{1157}(288,\cdot)\) \(\chi_{1157}(392,\cdot)\) \(\chi_{1157}(405,\cdot)\) \(\chi_{1157}(427,\cdot)\) \(\chi_{1157}(435,\cdot)\) \(\chi_{1157}(436,\cdot)\) \(\chi_{1157}(462,\cdot)\) \(\chi_{1157}(487,\cdot)\) \(\chi_{1157}(492,\cdot)\) \(\chi_{1157}(544,\cdot)\) \(\chi_{1157}(552,\cdot)\) \(\chi_{1157}(605,\cdot)\) \(\chi_{1157}(613,\cdot)\) \(\chi_{1157}(665,\cdot)\) \(\chi_{1157}(670,\cdot)\) \(\chi_{1157}(695,\cdot)\) \(\chi_{1157}(721,\cdot)\) \(\chi_{1157}(722,\cdot)\) \(\chi_{1157}(730,\cdot)\) \(\chi_{1157}(752,\cdot)\) \(\chi_{1157}(765,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((535,92)\) → \((e\left(\frac{1}{12}\right),e\left(\frac{21}{44}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1157 }(613, a) \) | \(-1\) | \(1\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{89}{132}\right)\) |