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.bi
\(\chi_{927}(95,\cdot)\) \(\chi_{927}(113,\cdot)\) \(\chi_{927}(140,\cdot)\) \(\chi_{927}(176,\cdot)\) \(\chi_{927}(209,\cdot)\) \(\chi_{927}(230,\cdot)\) \(\chi_{927}(245,\cdot)\) \(\chi_{927}(248,\cdot)\) \(\chi_{927}(275,\cdot)\) \(\chi_{927}(389,\cdot)\) \(\chi_{927}(398,\cdot)\) \(\chi_{927}(434,\cdot)\) \(\chi_{927}(443,\cdot)\) \(\chi_{927}(506,\cdot)\) \(\chi_{927}(518,\cdot)\) \(\chi_{927}(542,\cdot)\) \(\chi_{927}(554,\cdot)\) \(\chi_{927}(605,\cdot)\) \(\chi_{927}(698,\cdot)\) \(\chi_{927}(707,\cdot)\) \(\chi_{927}(713,\cdot)\) \(\chi_{927}(731,\cdot)\) \(\chi_{927}(743,\cdot)\) \(\chi_{927}(752,\cdot)\) \(\chi_{927}(758,\cdot)\) \(\chi_{927}(794,\cdot)\) \(\chi_{927}(815,\cdot)\) \(\chi_{927}(848,\cdot)\) \(\chi_{927}(851,\cdot)\) \(\chi_{927}(866,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((722,829)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{23}{34}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 927 }(230, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{65}{102}\right)\) | \(e\left(\frac{20}{51}\right)\) |