Basic properties
Modulus: | \(1089\) | |
Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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.bf
\(\chi_{1089}(5,\cdot)\) \(\chi_{1089}(14,\cdot)\) \(\chi_{1089}(20,\cdot)\) \(\chi_{1089}(38,\cdot)\) \(\chi_{1089}(47,\cdot)\) \(\chi_{1089}(59,\cdot)\) \(\chi_{1089}(86,\cdot)\) \(\chi_{1089}(92,\cdot)\) \(\chi_{1089}(104,\cdot)\) \(\chi_{1089}(113,\cdot)\) \(\chi_{1089}(119,\cdot)\) \(\chi_{1089}(137,\cdot)\) \(\chi_{1089}(146,\cdot)\) \(\chi_{1089}(158,\cdot)\) \(\chi_{1089}(185,\cdot)\) \(\chi_{1089}(191,\cdot)\) \(\chi_{1089}(203,\cdot)\) \(\chi_{1089}(212,\cdot)\) \(\chi_{1089}(218,\cdot)\) \(\chi_{1089}(236,\cdot)\) \(\chi_{1089}(257,\cdot)\) \(\chi_{1089}(284,\cdot)\) \(\chi_{1089}(290,\cdot)\) \(\chi_{1089}(302,\cdot)\) \(\chi_{1089}(311,\cdot)\) \(\chi_{1089}(317,\cdot)\) \(\chi_{1089}(335,\cdot)\) \(\chi_{1089}(344,\cdot)\) \(\chi_{1089}(356,\cdot)\) \(\chi_{1089}(383,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,244)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{34}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 1089 }(1004, a) \) | \(-1\) | \(1\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{301}{330}\right)\) | \(e\left(\frac{109}{165}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{87}{110}\right)\) |