Basic properties
Modulus: | \(1441\) | |
Conductor: | \(1441\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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.bu
\(\chi_{1441}(46,\cdot)\) \(\chi_{1441}(74,\cdot)\) \(\chi_{1441}(94,\cdot)\) \(\chi_{1441}(101,\cdot)\) \(\chi_{1441}(138,\cdot)\) \(\chi_{1441}(222,\cdot)\) \(\chi_{1441}(282,\cdot)\) \(\chi_{1441}(303,\cdot)\) \(\chi_{1441}(370,\cdot)\) \(\chi_{1441}(371,\cdot)\) \(\chi_{1441}(391,\cdot)\) \(\chi_{1441}(409,\cdot)\) \(\chi_{1441}(414,\cdot)\) \(\chi_{1441}(448,\cdot)\) \(\chi_{1441}(457,\cdot)\) \(\chi_{1441}(470,\cdot)\) \(\chi_{1441}(514,\cdot)\) \(\chi_{1441}(557,\cdot)\) \(\chi_{1441}(568,\cdot)\) \(\chi_{1441}(629,\cdot)\) \(\chi_{1441}(666,\cdot)\) \(\chi_{1441}(690,\cdot)\) \(\chi_{1441}(789,\cdot)\) \(\chi_{1441}(799,\cdot)\) \(\chi_{1441}(811,\cdot)\) \(\chi_{1441}(909,\cdot)\) \(\chi_{1441}(921,\cdot)\) \(\chi_{1441}(926,\cdot)\) \(\chi_{1441}(976,\cdot)\) \(\chi_{1441}(992,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{31}{65}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(1097, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{130}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{67}{130}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{43}{130}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{19}{65}\right)\) |