Basic properties
| Modulus: | \(927\) | |
| Conductor: | \(927\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(51\) | 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.y
\(\chi_{927}(4,\cdot)\) \(\chi_{927}(16,\cdot)\) \(\chi_{927}(25,\cdot)\) \(\chi_{927}(58,\cdot)\) \(\chi_{927}(97,\cdot)\) \(\chi_{927}(139,\cdot)\) \(\chi_{927}(166,\cdot)\) \(\chi_{927}(232,\cdot)\) \(\chi_{927}(238,\cdot)\) \(\chi_{927}(256,\cdot)\) \(\chi_{927}(358,\cdot)\) \(\chi_{927}(391,\cdot)\) \(\chi_{927}(400,\cdot)\) \(\chi_{927}(427,\cdot)\) \(\chi_{927}(430,\cdot)\) \(\chi_{927}(445,\cdot)\) \(\chi_{927}(553,\cdot)\) \(\chi_{927}(556,\cdot)\) \(\chi_{927}(574,\cdot)\) \(\chi_{927}(583,\cdot)\) \(\chi_{927}(607,\cdot)\) \(\chi_{927}(625,\cdot)\) \(\chi_{927}(637,\cdot)\) \(\chi_{927}(646,\cdot)\) \(\chi_{927}(670,\cdot)\) \(\chi_{927}(673,\cdot)\) \(\chi_{927}(781,\cdot)\) \(\chi_{927}(826,\cdot)\) \(\chi_{927}(841,\cdot)\) \(\chi_{927}(853,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((722,829)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{32}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 927 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) |