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.bh
\(\chi_{1441}(20,\cdot)\) \(\chi_{1441}(48,\cdot)\) \(\chi_{1441}(49,\cdot)\) \(\chi_{1441}(91,\cdot)\) \(\chi_{1441}(108,\cdot)\) \(\chi_{1441}(136,\cdot)\) \(\chi_{1441}(152,\cdot)\) \(\chi_{1441}(158,\cdot)\) \(\chi_{1441}(169,\cdot)\) \(\chi_{1441}(278,\cdot)\) \(\chi_{1441}(295,\cdot)\) \(\chi_{1441}(306,\cdot)\) \(\chi_{1441}(356,\cdot)\) \(\chi_{1441}(379,\cdot)\) \(\chi_{1441}(400,\cdot)\) \(\chi_{1441}(467,\cdot)\) \(\chi_{1441}(498,\cdot)\) \(\chi_{1441}(537,\cdot)\) \(\chi_{1441}(565,\cdot)\) \(\chi_{1441}(647,\cdot)\) \(\chi_{1441}(653,\cdot)\) \(\chi_{1441}(719,\cdot)\) \(\chi_{1441}(764,\cdot)\) \(\chi_{1441}(795,\cdot)\) \(\chi_{1441}(801,\cdot)\) \(\chi_{1441}(841,\cdot)\) \(\chi_{1441}(861,\cdot)\) \(\chi_{1441}(863,\cdot)\) \(\chi_{1441}(867,\cdot)\) \(\chi_{1441}(900,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\((1311,133)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{59}{65}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(801, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) |