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.bm
\(\chi_{1441}(6,\cdot)\) \(\chi_{1441}(17,\cdot)\) \(\chi_{1441}(40,\cdot)\) \(\chi_{1441}(50,\cdot)\) \(\chi_{1441}(57,\cdot)\) \(\chi_{1441}(116,\cdot)\) \(\chi_{1441}(145,\cdot)\) \(\chi_{1441}(161,\cdot)\) \(\chi_{1441}(216,\cdot)\) \(\chi_{1441}(270,\cdot)\) \(\chi_{1441}(293,\cdot)\) \(\chi_{1441}(359,\cdot)\) \(\chi_{1441}(380,\cdot)\) \(\chi_{1441}(381,\cdot)\) \(\chi_{1441}(382,\cdot)\) \(\chi_{1441}(475,\cdot)\) \(\chi_{1441}(590,\cdot)\) \(\chi_{1441}(591,\cdot)\) \(\chi_{1441}(596,\cdot)\) \(\chi_{1441}(611,\cdot)\) \(\chi_{1441}(612,\cdot)\) \(\chi_{1441}(622,\cdot)\) \(\chi_{1441}(651,\cdot)\) \(\chi_{1441}(657,\cdot)\) \(\chi_{1441}(711,\cdot)\) \(\chi_{1441}(745,\cdot)\) \(\chi_{1441}(761,\cdot)\) \(\chi_{1441}(765,\cdot)\) \(\chi_{1441}(777,\cdot)\) \(\chi_{1441}(783,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{83}{130}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(380, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{16}{65}\right)\) |