Basic properties
Modulus: | \(927\) | |
Conductor: | \(927\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(51\) | 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 927.z
\(\chi_{927}(7,\cdot)\) \(\chi_{927}(49,\cdot)\) \(\chi_{927}(52,\cdot)\) \(\chi_{927}(121,\cdot)\) \(\chi_{927}(223,\cdot)\) \(\chi_{927}(247,\cdot)\) \(\chi_{927}(265,\cdot)\) \(\chi_{927}(274,\cdot)\) \(\chi_{927}(304,\cdot)\) \(\chi_{927}(313,\cdot)\) \(\chi_{927}(328,\cdot)\) \(\chi_{927}(337,\cdot)\) \(\chi_{927}(364,\cdot)\) \(\chi_{927}(367,\cdot)\) \(\chi_{927}(448,\cdot)\) \(\chi_{927}(472,\cdot)\) \(\chi_{927}(475,\cdot)\) \(\chi_{927}(517,\cdot)\) \(\chi_{927}(544,\cdot)\) \(\chi_{927}(547,\cdot)\) \(\chi_{927}(565,\cdot)\) \(\chi_{927}(598,\cdot)\) \(\chi_{927}(634,\cdot)\) \(\chi_{927}(643,\cdot)\) \(\chi_{927}(700,\cdot)\) \(\chi_{927}(709,\cdot)\) \(\chi_{927}(715,\cdot)\) \(\chi_{927}(736,\cdot)\) \(\chi_{927}(754,\cdot)\) \(\chi_{927}(850,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((722,829)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{49}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 927 }(265, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{22}{51}\right)\) |