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.bw
\(\chi_{1441}(115,\cdot)\) \(\chi_{1441}(213,\cdot)\) \(\chi_{1441}(234,\cdot)\) \(\chi_{1441}(251,\cdot)\) \(\chi_{1441}(302,\cdot)\) \(\chi_{1441}(334,\cdot)\) \(\chi_{1441}(389,\cdot)\) \(\chi_{1441}(399,\cdot)\) \(\chi_{1441}(410,\cdot)\) \(\chi_{1441}(423,\cdot)\) \(\chi_{1441}(443,\cdot)\) \(\chi_{1441}(460,\cdot)\) \(\chi_{1441}(478,\cdot)\) \(\chi_{1441}(499,\cdot)\) \(\chi_{1441}(509,\cdot)\) \(\chi_{1441}(521,\cdot)\) \(\chi_{1441}(526,\cdot)\) \(\chi_{1441}(555,\cdot)\) \(\chi_{1441}(614,\cdot)\) \(\chi_{1441}(620,\cdot)\) \(\chi_{1441}(621,\cdot)\) \(\chi_{1441}(643,\cdot)\) \(\chi_{1441}(663,\cdot)\) \(\chi_{1441}(773,\cdot)\) \(\chi_{1441}(779,\cdot)\) \(\chi_{1441}(796,\cdot)\) \(\chi_{1441}(823,\cdot)\) \(\chi_{1441}(840,\cdot)\) \(\chi_{1441}(852,\cdot)\) \(\chi_{1441}(862,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{111}{130}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(1043, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{130}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{47}{130}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{12}{65}\right)\) |