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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1157.ca
\(\chi_{1157}(23,\cdot)\) \(\chi_{1157}(30,\cdot)\) \(\chi_{1157}(43,\cdot)\) \(\chi_{1157}(56,\cdot)\) \(\chi_{1157}(62,\cdot)\) \(\chi_{1157}(75,\cdot)\) \(\chi_{1157}(82,\cdot)\) \(\chi_{1157}(95,\cdot)\) \(\chi_{1157}(108,\cdot)\) \(\chi_{1157}(127,\cdot)\) \(\chi_{1157}(140,\cdot)\) \(\chi_{1157}(147,\cdot)\) \(\chi_{1157}(192,\cdot)\) \(\chi_{1157}(205,\cdot)\) \(\chi_{1157}(238,\cdot)\) \(\chi_{1157}(244,\cdot)\) \(\chi_{1157}(264,\cdot)\) \(\chi_{1157}(270,\cdot)\) \(\chi_{1157}(290,\cdot)\) \(\chi_{1157}(296,\cdot)\) \(\chi_{1157}(329,\cdot)\) \(\chi_{1157}(342,\cdot)\) \(\chi_{1157}(387,\cdot)\) \(\chi_{1157}(394,\cdot)\) \(\chi_{1157}(407,\cdot)\) \(\chi_{1157}(426,\cdot)\) \(\chi_{1157}(439,\cdot)\) \(\chi_{1157}(452,\cdot)\) \(\chi_{1157}(459,\cdot)\) \(\chi_{1157}(472,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{264})$ |
Fixed field: | Number field defined by a degree 264 polynomial (not computed) |
Values on generators
\((535,92)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{39}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1157 }(1005, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{29}{264}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{97}{264}\right)\) | \(e\left(\frac{193}{264}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{103}{132}\right)\) | \(e\left(\frac{13}{33}\right)\) |