Basic properties
Modulus: | \(1089\) | |
Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1089.be
\(\chi_{1089}(7,\cdot)\) \(\chi_{1089}(13,\cdot)\) \(\chi_{1089}(52,\cdot)\) \(\chi_{1089}(61,\cdot)\) \(\chi_{1089}(79,\cdot)\) \(\chi_{1089}(85,\cdot)\) \(\chi_{1089}(106,\cdot)\) \(\chi_{1089}(139,\cdot)\) \(\chi_{1089}(151,\cdot)\) \(\chi_{1089}(160,\cdot)\) \(\chi_{1089}(178,\cdot)\) \(\chi_{1089}(184,\cdot)\) \(\chi_{1089}(193,\cdot)\) \(\chi_{1089}(205,\cdot)\) \(\chi_{1089}(211,\cdot)\) \(\chi_{1089}(238,\cdot)\) \(\chi_{1089}(250,\cdot)\) \(\chi_{1089}(259,\cdot)\) \(\chi_{1089}(277,\cdot)\) \(\chi_{1089}(283,\cdot)\) \(\chi_{1089}(292,\cdot)\) \(\chi_{1089}(304,\cdot)\) \(\chi_{1089}(310,\cdot)\) \(\chi_{1089}(337,\cdot)\) \(\chi_{1089}(349,\cdot)\) \(\chi_{1089}(358,\cdot)\) \(\chi_{1089}(376,\cdot)\) \(\chi_{1089}(382,\cdot)\) \(\chi_{1089}(391,\cdot)\) \(\chi_{1089}(409,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,244)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{3}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 1089 }(250, a) \) | \(-1\) | \(1\) | \(e\left(\frac{229}{330}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{58}{165}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{29}{330}\right)\) | \(e\left(\frac{91}{165}\right)\) | \(e\left(\frac{128}{165}\right)\) | \(e\left(\frac{37}{110}\right)\) |