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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1441.by
\(\chi_{1441}(2,\cdot)\) \(\chi_{1441}(8,\cdot)\) \(\chi_{1441}(90,\cdot)\) \(\chi_{1441}(106,\cdot)\) \(\chi_{1441}(118,\cdot)\) \(\chi_{1441}(128,\cdot)\) \(\chi_{1441}(171,\cdot)\) \(\chi_{1441}(227,\cdot)\) \(\chi_{1441}(255,\cdot)\) \(\chi_{1441}(292,\cdot)\) \(\chi_{1441}(299,\cdot)\) \(\chi_{1441}(347,\cdot)\) \(\chi_{1441}(349,\cdot)\) \(\chi_{1441}(360,\cdot)\) \(\chi_{1441}(403,\cdot)\) \(\chi_{1441}(424,\cdot)\) \(\chi_{1441}(447,\cdot)\) \(\chi_{1441}(469,\cdot)\) \(\chi_{1441}(486,\cdot)\) \(\chi_{1441}(490,\cdot)\) \(\chi_{1441}(497,\cdot)\) \(\chi_{1441}(503,\cdot)\) \(\chi_{1441}(512,\cdot)\) \(\chi_{1441}(519,\cdot)\) \(\chi_{1441}(546,\cdot)\) \(\chi_{1441}(547,\cdot)\) \(\chi_{1441}(607,\cdot)\) \(\chi_{1441}(635,\cdot)\) \(\chi_{1441}(684,\cdot)\) \(\chi_{1441}(721,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{61}{130}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(90, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{97}{130}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{47}{65}\right)\) |