Basic properties
Modulus: | \(1441\) | |
Conductor: | \(1441\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(65\) | 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 1441.bj
\(\chi_{1441}(3,\cdot)\) \(\chi_{1441}(5,\cdot)\) \(\chi_{1441}(9,\cdot)\) \(\chi_{1441}(15,\cdot)\) \(\chi_{1441}(25,\cdot)\) \(\chi_{1441}(27,\cdot)\) \(\chi_{1441}(38,\cdot)\) \(\chi_{1441}(75,\cdot)\) \(\chi_{1441}(81,\cdot)\) \(\chi_{1441}(114,\cdot)\) \(\chi_{1441}(125,\cdot)\) \(\chi_{1441}(135,\cdot)\) \(\chi_{1441}(174,\cdot)\) \(\chi_{1441}(190,\cdot)\) \(\chi_{1441}(196,\cdot)\) \(\chi_{1441}(225,\cdot)\) \(\chi_{1441}(269,\cdot)\) \(\chi_{1441}(290,\cdot)\) \(\chi_{1441}(311,\cdot)\) \(\chi_{1441}(405,\cdot)\) \(\chi_{1441}(427,\cdot)\) \(\chi_{1441}(434,\cdot)\) \(\chi_{1441}(493,\cdot)\) \(\chi_{1441}(522,\cdot)\) \(\chi_{1441}(570,\cdot)\) \(\chi_{1441}(588,\cdot)\) \(\chi_{1441}(625,\cdot)\) \(\chi_{1441}(641,\cdot)\) \(\chi_{1441}(675,\cdot)\) \(\chi_{1441}(729,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\((1311,133)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{3}{65}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(588, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{27}{65}\right)\) |