Basic properties
Modulus: | \(1441\) | |
Conductor: | \(1441\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(130\) | 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 1441.cd
\(\chi_{1441}(26,\cdot)\) \(\chi_{1441}(124,\cdot)\) \(\chi_{1441}(137,\cdot)\) \(\chi_{1441}(141,\cdot)\) \(\chi_{1441}(148,\cdot)\) \(\chi_{1441}(168,\cdot)\) \(\chi_{1441}(181,\cdot)\) \(\chi_{1441}(185,\cdot)\) \(\chi_{1441}(207,\cdot)\) \(\chi_{1441}(246,\cdot)\) \(\chi_{1441}(247,\cdot)\) \(\chi_{1441}(284,\cdot)\) \(\chi_{1441}(355,\cdot)\) \(\chi_{1441}(366,\cdot)\) \(\chi_{1441}(388,\cdot)\) \(\chi_{1441}(401,\cdot)\) \(\chi_{1441}(433,\cdot)\) \(\chi_{1441}(476,\cdot)\) \(\chi_{1441}(511,\cdot)\) \(\chi_{1441}(553,\cdot)\) \(\chi_{1441}(554,\cdot)\) \(\chi_{1441}(581,\cdot)\) \(\chi_{1441}(609,\cdot)\) \(\chi_{1441}(619,\cdot)\) \(\chi_{1441}(669,\cdot)\) \(\chi_{1441}(686,\cdot)\) \(\chi_{1441}(742,\cdot)\) \(\chi_{1441}(752,\cdot)\) \(\chi_{1441}(753,\cdot)\) \(\chi_{1441}(774,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{107}{130}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(581, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{89}{130}\right)\) | \(e\left(\frac{59}{65}\right)\) |