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.bj
\(\chi_{927}(70,\cdot)\) \(\chi_{927}(85,\cdot)\) \(\chi_{927}(88,\cdot)\) \(\chi_{927}(115,\cdot)\) \(\chi_{927}(124,\cdot)\) \(\chi_{927}(157,\cdot)\) \(\chi_{927}(259,\cdot)\) \(\chi_{927}(277,\cdot)\) \(\chi_{927}(283,\cdot)\) \(\chi_{927}(349,\cdot)\) \(\chi_{927}(376,\cdot)\) \(\chi_{927}(418,\cdot)\) \(\chi_{927}(457,\cdot)\) \(\chi_{927}(490,\cdot)\) \(\chi_{927}(499,\cdot)\) \(\chi_{927}(511,\cdot)\) \(\chi_{927}(520,\cdot)\) \(\chi_{927}(535,\cdot)\) \(\chi_{927}(589,\cdot)\) \(\chi_{927}(601,\cdot)\) \(\chi_{927}(616,\cdot)\) \(\chi_{927}(661,\cdot)\) \(\chi_{927}(769,\cdot)\) \(\chi_{927}(772,\cdot)\) \(\chi_{927}(796,\cdot)\) \(\chi_{927}(805,\cdot)\) \(\chi_{927}(817,\cdot)\) \(\chi_{927}(835,\cdot)\) \(\chi_{927}(859,\cdot)\) \(\chi_{927}(868,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((722,829)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{11}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 927 }(769, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{79}{102}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{16}{51}\right)\) |