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.bb
\(\chi_{927}(13,\cdot)\) \(\chi_{927}(34,\cdot)\) \(\chi_{927}(61,\cdot)\) \(\chi_{927}(76,\cdot)\) \(\chi_{927}(79,\cdot)\) \(\chi_{927}(112,\cdot)\) \(\chi_{927}(133,\cdot)\) \(\chi_{927}(169,\cdot)\) \(\chi_{927}(175,\cdot)\) \(\chi_{927}(184,\cdot)\) \(\chi_{927}(196,\cdot)\) \(\chi_{927}(214,\cdot)\) \(\chi_{927}(220,\cdot)\) \(\chi_{927}(229,\cdot)\) \(\chi_{927}(322,\cdot)\) \(\chi_{927}(373,\cdot)\) \(\chi_{927}(385,\cdot)\) \(\chi_{927}(409,\cdot)\) \(\chi_{927}(421,\cdot)\) \(\chi_{927}(484,\cdot)\) \(\chi_{927}(493,\cdot)\) \(\chi_{927}(529,\cdot)\) \(\chi_{927}(538,\cdot)\) \(\chi_{927}(652,\cdot)\) \(\chi_{927}(679,\cdot)\) \(\chi_{927}(682,\cdot)\) \(\chi_{927}(697,\cdot)\) \(\chi_{927}(718,\cdot)\) \(\chi_{927}(751,\cdot)\) \(\chi_{927}(787,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((722,829)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{5}{17}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 927 }(214, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{22}{51}\right)\) |