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.bn
\(\chi_{1441}(7,\cdot)\) \(\chi_{1441}(13,\cdot)\) \(\chi_{1441}(123,\cdot)\) \(\chi_{1441}(140,\cdot)\) \(\chi_{1441}(172,\cdot)\) \(\chi_{1441}(206,\cdot)\) \(\chi_{1441}(248,\cdot)\) \(\chi_{1441}(260,\cdot)\) \(\chi_{1441}(277,\cdot)\) \(\chi_{1441}(305,\cdot)\) \(\chi_{1441}(326,\cdot)\) \(\chi_{1441}(327,\cdot)\) \(\chi_{1441}(336,\cdot)\) \(\chi_{1441}(343,\cdot)\) \(\chi_{1441}(376,\cdot)\) \(\chi_{1441}(387,\cdot)\) \(\chi_{1441}(535,\cdot)\) \(\chi_{1441}(536,\cdot)\) \(\chi_{1441}(552,\cdot)\) \(\chi_{1441}(558,\cdot)\) \(\chi_{1441}(624,\cdot)\) \(\chi_{1441}(633,\cdot)\) \(\chi_{1441}(701,\cdot)\) \(\chi_{1441}(710,\cdot)\) \(\chi_{1441}(732,\cdot)\) \(\chi_{1441}(756,\cdot)\) \(\chi_{1441}(776,\cdot)\) \(\chi_{1441}(877,\cdot)\) \(\chi_{1441}(937,\cdot)\) \(\chi_{1441}(952,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{47}{65}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(624, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{130}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{67}{130}\right)\) | \(e\left(\frac{9}{130}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{33}{65}\right)\) |