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.bq
\(\chi_{1441}(21,\cdot)\) \(\chi_{1441}(43,\cdot)\) \(\chi_{1441}(65,\cdot)\) \(\chi_{1441}(109,\cdot)\) \(\chi_{1441}(142,\cdot)\) \(\chi_{1441}(164,\cdot)\) \(\chi_{1441}(175,\cdot)\) \(\chi_{1441}(186,\cdot)\) \(\chi_{1441}(208,\cdot)\) \(\chi_{1441}(252,\cdot)\) \(\chi_{1441}(274,\cdot)\) \(\chi_{1441}(296,\cdot)\) \(\chi_{1441}(362,\cdot)\) \(\chi_{1441}(406,\cdot)\) \(\chi_{1441}(428,\cdot)\) \(\chi_{1441}(439,\cdot)\) \(\chi_{1441}(494,\cdot)\) \(\chi_{1441}(516,\cdot)\) \(\chi_{1441}(527,\cdot)\) \(\chi_{1441}(549,\cdot)\) \(\chi_{1441}(560,\cdot)\) \(\chi_{1441}(615,\cdot)\) \(\chi_{1441}(626,\cdot)\) \(\chi_{1441}(659,\cdot)\) \(\chi_{1441}(670,\cdot)\) \(\chi_{1441}(703,\cdot)\) \(\chi_{1441}(714,\cdot)\) \(\chi_{1441}(736,\cdot)\) \(\chi_{1441}(769,\cdot)\) \(\chi_{1441}(780,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((-1,e\left(\frac{38}{65}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(703, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{33}{130}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{17}{65}\right)\) |