Basic properties
Modulus: | \(1157\) | |
Conductor: | \(1157\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(264\) | 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.cc
\(\chi_{1157}(7,\cdot)\) \(\chi_{1157}(15,\cdot)\) \(\chi_{1157}(19,\cdot)\) \(\chi_{1157}(24,\cdot)\) \(\chi_{1157}(33,\cdot)\) \(\chi_{1157}(46,\cdot)\) \(\chi_{1157}(54,\cdot)\) \(\chi_{1157}(58,\cdot)\) \(\chi_{1157}(119,\cdot)\) \(\chi_{1157}(137,\cdot)\) \(\chi_{1157}(149,\cdot)\) \(\chi_{1157}(150,\cdot)\) \(\chi_{1157}(154,\cdot)\) \(\chi_{1157}(197,\cdot)\) \(\chi_{1157}(202,\cdot)\) \(\chi_{1157}(206,\cdot)\) \(\chi_{1157}(219,\cdot)\) \(\chi_{1157}(236,\cdot)\) \(\chi_{1157}(240,\cdot)\) \(\chi_{1157}(305,\cdot)\) \(\chi_{1157}(310,\cdot)\) \(\chi_{1157}(318,\cdot)\) \(\chi_{1157}(323,\cdot)\) \(\chi_{1157}(327,\cdot)\) \(\chi_{1157}(332,\cdot)\) \(\chi_{1157}(349,\cdot)\) \(\chi_{1157}(362,\cdot)\) \(\chi_{1157}(383,\cdot)\) \(\chi_{1157}(384,\cdot)\) \(\chi_{1157}(397,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{264})$ |
Fixed field: | Number field defined by a degree 264 polynomial (not computed) |
Values on generators
\((535,92)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{25}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1157 }(206, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{163}{264}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{197}{264}\right)\) | \(e\left(\frac{113}{264}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{35}{132}\right)\) | \(e\left(\frac{125}{132}\right)\) |