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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 927.bf
\(\chi_{927}(14,\cdot)\) \(\chi_{927}(23,\cdot)\) \(\chi_{927}(137,\cdot)\) \(\chi_{927}(164,\cdot)\) \(\chi_{927}(167,\cdot)\) \(\chi_{927}(182,\cdot)\) \(\chi_{927}(203,\cdot)\) \(\chi_{927}(236,\cdot)\) \(\chi_{927}(272,\cdot)\) \(\chi_{927}(299,\cdot)\) \(\chi_{927}(317,\cdot)\) \(\chi_{927}(425,\cdot)\) \(\chi_{927}(446,\cdot)\) \(\chi_{927}(473,\cdot)\) \(\chi_{927}(488,\cdot)\) \(\chi_{927}(491,\cdot)\) \(\chi_{927}(524,\cdot)\) \(\chi_{927}(545,\cdot)\) \(\chi_{927}(581,\cdot)\) \(\chi_{927}(587,\cdot)\) \(\chi_{927}(596,\cdot)\) \(\chi_{927}(608,\cdot)\) \(\chi_{927}(626,\cdot)\) \(\chi_{927}(632,\cdot)\) \(\chi_{927}(641,\cdot)\) \(\chi_{927}(734,\cdot)\) \(\chi_{927}(785,\cdot)\) \(\chi_{927}(797,\cdot)\) \(\chi_{927}(821,\cdot)\) \(\chi_{927}(833,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((722,829)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{13}{17}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 927 }(833, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{102}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{95}{102}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{49}{102}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{47}{51}\right)\) |