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.ca
\(\chi_{1441}(10,\cdot)\) \(\chi_{1441}(54,\cdot)\) \(\chi_{1441}(76,\cdot)\) \(\chi_{1441}(87,\cdot)\) \(\chi_{1441}(98,\cdot)\) \(\chi_{1441}(120,\cdot)\) \(\chi_{1441}(153,\cdot)\) \(\chi_{1441}(197,\cdot)\) \(\chi_{1441}(219,\cdot)\) \(\chi_{1441}(241,\cdot)\) \(\chi_{1441}(285,\cdot)\) \(\chi_{1441}(318,\cdot)\) \(\chi_{1441}(329,\cdot)\) \(\chi_{1441}(373,\cdot)\) \(\chi_{1441}(384,\cdot)\) \(\chi_{1441}(395,\cdot)\) \(\chi_{1441}(450,\cdot)\) \(\chi_{1441}(483,\cdot)\) \(\chi_{1441}(538,\cdot)\) \(\chi_{1441}(648,\cdot)\) \(\chi_{1441}(681,\cdot)\) \(\chi_{1441}(692,\cdot)\) \(\chi_{1441}(758,\cdot)\) \(\chi_{1441}(868,\cdot)\) \(\chi_{1441}(879,\cdot)\) \(\chi_{1441}(890,\cdot)\) \(\chi_{1441}(901,\cdot)\) \(\chi_{1441}(912,\cdot)\) \(\chi_{1441}(923,\cdot)\) \(\chi_{1441}(934,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((-1,e\left(\frac{111}{130}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(912, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{61}{130}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) |