Basic properties
Modulus: | \(1183\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 1183.ch
\(\chi_{1183}(24,\cdot)\) \(\chi_{1183}(33,\cdot)\) \(\chi_{1183}(110,\cdot)\) \(\chi_{1183}(115,\cdot)\) \(\chi_{1183}(124,\cdot)\) \(\chi_{1183}(171,\cdot)\) \(\chi_{1183}(201,\cdot)\) \(\chi_{1183}(206,\cdot)\) \(\chi_{1183}(215,\cdot)\) \(\chi_{1183}(262,\cdot)\) \(\chi_{1183}(292,\cdot)\) \(\chi_{1183}(297,\cdot)\) \(\chi_{1183}(306,\cdot)\) \(\chi_{1183}(353,\cdot)\) \(\chi_{1183}(383,\cdot)\) \(\chi_{1183}(388,\cdot)\) \(\chi_{1183}(397,\cdot)\) \(\chi_{1183}(444,\cdot)\) \(\chi_{1183}(474,\cdot)\) \(\chi_{1183}(479,\cdot)\) \(\chi_{1183}(535,\cdot)\) \(\chi_{1183}(565,\cdot)\) \(\chi_{1183}(570,\cdot)\) \(\chi_{1183}(579,\cdot)\) \(\chi_{1183}(626,\cdot)\) \(\chi_{1183}(656,\cdot)\) \(\chi_{1183}(661,\cdot)\) \(\chi_{1183}(670,\cdot)\) \(\chi_{1183}(717,\cdot)\) \(\chi_{1183}(747,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((339,1016)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{103}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1183 }(1025, a) \) | \(1\) | \(1\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{1}{39}\right)\) |