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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1441.bx
\(\chi_{1441}(29,\cdot)\) \(\chi_{1441}(30,\cdot)\) \(\chi_{1441}(72,\cdot)\) \(\chi_{1441}(85,\cdot)\) \(\chi_{1441}(95,\cdot)\) \(\chi_{1441}(127,\cdot)\) \(\chi_{1441}(162,\cdot)\) \(\chi_{1441}(228,\cdot)\) \(\chi_{1441}(237,\cdot)\) \(\chi_{1441}(250,\cdot)\) \(\chi_{1441}(259,\cdot)\) \(\chi_{1441}(358,\cdot)\) \(\chi_{1441}(365,\cdot)\) \(\chi_{1441}(459,\cdot)\) \(\chi_{1441}(481,\cdot)\) \(\chi_{1441}(513,\cdot)\) \(\chi_{1441}(530,\cdot)\) \(\chi_{1441}(534,\cdot)\) \(\chi_{1441}(541,\cdot)\) \(\chi_{1441}(574,\cdot)\) \(\chi_{1441}(578,\cdot)\) \(\chi_{1441}(580,\cdot)\) \(\chi_{1441}(600,\cdot)\) \(\chi_{1441}(640,\cdot)\) \(\chi_{1441}(646,\cdot)\) \(\chi_{1441}(677,\cdot)\) \(\chi_{1441}(722,\cdot)\) \(\chi_{1441}(788,\cdot)\) \(\chi_{1441}(794,\cdot)\) \(\chi_{1441}(876,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{43}{130}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(541, a) \) | \(1\) | \(1\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{59}{130}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) |