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.bl
\(\chi_{927}(22,\cdot)\) \(\chi_{927}(31,\cdot)\) \(\chi_{927}(94,\cdot)\) \(\chi_{927}(106,\cdot)\) \(\chi_{927}(130,\cdot)\) \(\chi_{927}(142,\cdot)\) \(\chi_{927}(193,\cdot)\) \(\chi_{927}(286,\cdot)\) \(\chi_{927}(295,\cdot)\) \(\chi_{927}(301,\cdot)\) \(\chi_{927}(319,\cdot)\) \(\chi_{927}(331,\cdot)\) \(\chi_{927}(340,\cdot)\) \(\chi_{927}(346,\cdot)\) \(\chi_{927}(382,\cdot)\) \(\chi_{927}(403,\cdot)\) \(\chi_{927}(436,\cdot)\) \(\chi_{927}(439,\cdot)\) \(\chi_{927}(454,\cdot)\) \(\chi_{927}(481,\cdot)\) \(\chi_{927}(502,\cdot)\) \(\chi_{927}(610,\cdot)\) \(\chi_{927}(628,\cdot)\) \(\chi_{927}(655,\cdot)\) \(\chi_{927}(691,\cdot)\) \(\chi_{927}(724,\cdot)\) \(\chi_{927}(745,\cdot)\) \(\chi_{927}(760,\cdot)\) \(\chi_{927}(763,\cdot)\) \(\chi_{927}(790,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((722,829)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{29}{34}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 927 }(763, a) \) | \(-1\) | \(1\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{71}{102}\right)\) | \(e\left(\frac{38}{51}\right)\) | \(e\left(\frac{14}{51}\right)\) | \(e\left(\frac{40}{51}\right)\) |