Basic properties
Modulus: | \(927\) | |
Conductor: | \(927\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | 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.bg
\(\chi_{927}(11,\cdot)\) \(\chi_{927}(65,\cdot)\) \(\chi_{927}(77,\cdot)\) \(\chi_{927}(173,\cdot)\) \(\chi_{927}(191,\cdot)\) \(\chi_{927}(212,\cdot)\) \(\chi_{927}(218,\cdot)\) \(\chi_{927}(227,\cdot)\) \(\chi_{927}(284,\cdot)\) \(\chi_{927}(293,\cdot)\) \(\chi_{927}(329,\cdot)\) \(\chi_{927}(362,\cdot)\) \(\chi_{927}(380,\cdot)\) \(\chi_{927}(383,\cdot)\) \(\chi_{927}(410,\cdot)\) \(\chi_{927}(452,\cdot)\) \(\chi_{927}(455,\cdot)\) \(\chi_{927}(479,\cdot)\) \(\chi_{927}(560,\cdot)\) \(\chi_{927}(563,\cdot)\) \(\chi_{927}(590,\cdot)\) \(\chi_{927}(599,\cdot)\) \(\chi_{927}(614,\cdot)\) \(\chi_{927}(623,\cdot)\) \(\chi_{927}(653,\cdot)\) \(\chi_{927}(662,\cdot)\) \(\chi_{927}(680,\cdot)\) \(\chi_{927}(704,\cdot)\) \(\chi_{927}(806,\cdot)\) \(\chi_{927}(875,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((722,829)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{61}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 927 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{102}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{55}{102}\right)\) | \(e\left(\frac{47}{51}\right)\) |