Basic properties
Modulus: | \(1441\) | |
Conductor: | \(131\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{131}(40,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1441.bs
\(\chi_{1441}(23,\cdot)\) \(\chi_{1441}(56,\cdot)\) \(\chi_{1441}(67,\cdot)\) \(\chi_{1441}(111,\cdot)\) \(\chi_{1441}(122,\cdot)\) \(\chi_{1441}(133,\cdot)\) \(\chi_{1441}(188,\cdot)\) \(\chi_{1441}(221,\cdot)\) \(\chi_{1441}(276,\cdot)\) \(\chi_{1441}(386,\cdot)\) \(\chi_{1441}(419,\cdot)\) \(\chi_{1441}(430,\cdot)\) \(\chi_{1441}(496,\cdot)\) \(\chi_{1441}(606,\cdot)\) \(\chi_{1441}(617,\cdot)\) \(\chi_{1441}(628,\cdot)\) \(\chi_{1441}(639,\cdot)\) \(\chi_{1441}(650,\cdot)\) \(\chi_{1441}(661,\cdot)\) \(\chi_{1441}(672,\cdot)\) \(\chi_{1441}(705,\cdot)\) \(\chi_{1441}(727,\cdot)\) \(\chi_{1441}(738,\cdot)\) \(\chi_{1441}(771,\cdot)\) \(\chi_{1441}(782,\cdot)\) \(\chi_{1441}(815,\cdot)\) \(\chi_{1441}(826,\cdot)\) \(\chi_{1441}(881,\cdot)\) \(\chi_{1441}(892,\cdot)\) \(\chi_{1441}(914,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((1,e\left(\frac{49}{130}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(826, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{130}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{67}{130}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{93}{130}\right)\) | \(e\left(\frac{58}{65}\right)\) |