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.bn
\(\chi_{927}(2,\cdot)\) \(\chi_{927}(29,\cdot)\) \(\chi_{927}(32,\cdot)\) \(\chi_{927}(50,\cdot)\) \(\chi_{927}(83,\cdot)\) \(\chi_{927}(119,\cdot)\) \(\chi_{927}(128,\cdot)\) \(\chi_{927}(185,\cdot)\) \(\chi_{927}(194,\cdot)\) \(\chi_{927}(200,\cdot)\) \(\chi_{927}(221,\cdot)\) \(\chi_{927}(239,\cdot)\) \(\chi_{927}(335,\cdot)\) \(\chi_{927}(347,\cdot)\) \(\chi_{927}(401,\cdot)\) \(\chi_{927}(419,\cdot)\) \(\chi_{927}(461,\cdot)\) \(\chi_{927}(464,\cdot)\) \(\chi_{927}(533,\cdot)\) \(\chi_{927}(635,\cdot)\) \(\chi_{927}(659,\cdot)\) \(\chi_{927}(677,\cdot)\) \(\chi_{927}(686,\cdot)\) \(\chi_{927}(716,\cdot)\) \(\chi_{927}(725,\cdot)\) \(\chi_{927}(740,\cdot)\) \(\chi_{927}(749,\cdot)\) \(\chi_{927}(776,\cdot)\) \(\chi_{927}(779,\cdot)\) \(\chi_{927}(860,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((722,829)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{19}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 927 }(83, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{91}{102}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{73}{102}\right)\) | \(e\left(\frac{4}{17}\right)\) |