Basic properties
Modulus: | \(1089\) | |
Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(165\) | 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 1089.bc
\(\chi_{1089}(4,\cdot)\) \(\chi_{1089}(16,\cdot)\) \(\chi_{1089}(25,\cdot)\) \(\chi_{1089}(31,\cdot)\) \(\chi_{1089}(49,\cdot)\) \(\chi_{1089}(58,\cdot)\) \(\chi_{1089}(70,\cdot)\) \(\chi_{1089}(97,\cdot)\) \(\chi_{1089}(103,\cdot)\) \(\chi_{1089}(115,\cdot)\) \(\chi_{1089}(157,\cdot)\) \(\chi_{1089}(169,\cdot)\) \(\chi_{1089}(196,\cdot)\) \(\chi_{1089}(214,\cdot)\) \(\chi_{1089}(223,\cdot)\) \(\chi_{1089}(229,\cdot)\) \(\chi_{1089}(247,\cdot)\) \(\chi_{1089}(256,\cdot)\) \(\chi_{1089}(268,\cdot)\) \(\chi_{1089}(295,\cdot)\) \(\chi_{1089}(301,\cdot)\) \(\chi_{1089}(313,\cdot)\) \(\chi_{1089}(322,\cdot)\) \(\chi_{1089}(328,\cdot)\) \(\chi_{1089}(346,\cdot)\) \(\chi_{1089}(355,\cdot)\) \(\chi_{1089}(367,\cdot)\) \(\chi_{1089}(394,\cdot)\) \(\chi_{1089}(400,\cdot)\) \(\chi_{1089}(412,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((848,244)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{27}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 1089 }(544, a) \) | \(1\) | \(1\) | \(e\left(\frac{136}{165}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{164}{165}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{41}{165}\right)\) | \(e\left(\frac{98}{165}\right)\) | \(e\left(\frac{49}{165}\right)\) | \(e\left(\frac{3}{55}\right)\) |