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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1183.cc
\(\chi_{1183}(5,\cdot)\) \(\chi_{1183}(31,\cdot)\) \(\chi_{1183}(47,\cdot)\) \(\chi_{1183}(73,\cdot)\) \(\chi_{1183}(96,\cdot)\) \(\chi_{1183}(122,\cdot)\) \(\chi_{1183}(138,\cdot)\) \(\chi_{1183}(164,\cdot)\) \(\chi_{1183}(187,\cdot)\) \(\chi_{1183}(213,\cdot)\) \(\chi_{1183}(229,\cdot)\) \(\chi_{1183}(255,\cdot)\) \(\chi_{1183}(278,\cdot)\) \(\chi_{1183}(304,\cdot)\) \(\chi_{1183}(320,\cdot)\) \(\chi_{1183}(346,\cdot)\) \(\chi_{1183}(369,\cdot)\) \(\chi_{1183}(395,\cdot)\) \(\chi_{1183}(411,\cdot)\) \(\chi_{1183}(460,\cdot)\) \(\chi_{1183}(486,\cdot)\) \(\chi_{1183}(502,\cdot)\) \(\chi_{1183}(528,\cdot)\) \(\chi_{1183}(551,\cdot)\) \(\chi_{1183}(593,\cdot)\) \(\chi_{1183}(619,\cdot)\) \(\chi_{1183}(642,\cdot)\) \(\chi_{1183}(668,\cdot)\) \(\chi_{1183}(684,\cdot)\) \(\chi_{1183}(710,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((339,1016)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{27}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1183 }(1006, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{23}{39}\right)\) |