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.bt
\(\chi_{1441}(47,\cdot)\) \(\chi_{1441}(69,\cdot)\) \(\chi_{1441}(71,\cdot)\) \(\chi_{1441}(86,\cdot)\) \(\chi_{1441}(92,\cdot)\) \(\chi_{1441}(163,\cdot)\) \(\chi_{1441}(202,\cdot)\) \(\chi_{1441}(223,\cdot)\) \(\chi_{1441}(280,\cdot)\) \(\chi_{1441}(313,\cdot)\) \(\chi_{1441}(333,\cdot)\) \(\chi_{1441}(411,\cdot)\) \(\chi_{1441}(412,\cdot)\) \(\chi_{1441}(444,\cdot)\) \(\chi_{1441}(542,\cdot)\) \(\chi_{1441}(543,\cdot)\) \(\chi_{1441}(548,\cdot)\) \(\chi_{1441}(575,\cdot)\) \(\chi_{1441}(592,\cdot)\) \(\chi_{1441}(603,\cdot)\) \(\chi_{1441}(610,\cdot)\) \(\chi_{1441}(674,\cdot)\) \(\chi_{1441}(687,\cdot)\) \(\chi_{1441}(702,\cdot)\) \(\chi_{1441}(724,\cdot)\) \(\chi_{1441}(741,\cdot)\) \(\chi_{1441}(818,\cdot)\) \(\chi_{1441}(872,\cdot)\) \(\chi_{1441}(878,\cdot)\) \(\chi_{1441}(949,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{25}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(86, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{89}{130}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) |