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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1089.bd
\(\chi_{1089}(2,\cdot)\) \(\chi_{1089}(29,\cdot)\) \(\chi_{1089}(41,\cdot)\) \(\chi_{1089}(50,\cdot)\) \(\chi_{1089}(68,\cdot)\) \(\chi_{1089}(74,\cdot)\) \(\chi_{1089}(83,\cdot)\) \(\chi_{1089}(95,\cdot)\) \(\chi_{1089}(101,\cdot)\) \(\chi_{1089}(128,\cdot)\) \(\chi_{1089}(140,\cdot)\) \(\chi_{1089}(149,\cdot)\) \(\chi_{1089}(167,\cdot)\) \(\chi_{1089}(173,\cdot)\) \(\chi_{1089}(182,\cdot)\) \(\chi_{1089}(194,\cdot)\) \(\chi_{1089}(200,\cdot)\) \(\chi_{1089}(227,\cdot)\) \(\chi_{1089}(248,\cdot)\) \(\chi_{1089}(266,\cdot)\) \(\chi_{1089}(272,\cdot)\) \(\chi_{1089}(281,\cdot)\) \(\chi_{1089}(293,\cdot)\) \(\chi_{1089}(299,\cdot)\) \(\chi_{1089}(326,\cdot)\) \(\chi_{1089}(338,\cdot)\) \(\chi_{1089}(347,\cdot)\) \(\chi_{1089}(365,\cdot)\) \(\chi_{1089}(371,\cdot)\) \(\chi_{1089}(380,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,244)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{37}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 1089 }(194, a) \) | \(1\) | \(1\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{211}{330}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{112}{165}\right)\) | \(e\left(\frac{54}{55}\right)\) |