Basic properties
Modulus: | \(1441\) | |
Conductor: | \(131\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(65\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{131}(125,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1441.bl
\(\chi_{1441}(12,\cdot)\) \(\chi_{1441}(34,\cdot)\) \(\chi_{1441}(100,\cdot)\) \(\chi_{1441}(144,\cdot)\) \(\chi_{1441}(166,\cdot)\) \(\chi_{1441}(177,\cdot)\) \(\chi_{1441}(232,\cdot)\) \(\chi_{1441}(254,\cdot)\) \(\chi_{1441}(265,\cdot)\) \(\chi_{1441}(287,\cdot)\) \(\chi_{1441}(298,\cdot)\) \(\chi_{1441}(353,\cdot)\) \(\chi_{1441}(364,\cdot)\) \(\chi_{1441}(397,\cdot)\) \(\chi_{1441}(408,\cdot)\) \(\chi_{1441}(441,\cdot)\) \(\chi_{1441}(452,\cdot)\) \(\chi_{1441}(474,\cdot)\) \(\chi_{1441}(507,\cdot)\) \(\chi_{1441}(518,\cdot)\) \(\chi_{1441}(529,\cdot)\) \(\chi_{1441}(540,\cdot)\) \(\chi_{1441}(551,\cdot)\) \(\chi_{1441}(562,\cdot)\) \(\chi_{1441}(573,\cdot)\) \(\chi_{1441}(683,\cdot)\) \(\chi_{1441}(749,\cdot)\) \(\chi_{1441}(760,\cdot)\) \(\chi_{1441}(793,\cdot)\) \(\chi_{1441}(903,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\((1311,133)\) → \((1,e\left(\frac{4}{65}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(518, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) |