Basic properties
| Modulus: | \(927\) | |
| Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{103}(28,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 927.ba
\(\chi_{927}(19,\cdot)\) \(\chi_{927}(28,\cdot)\) \(\chi_{927}(55,\cdot)\) \(\chi_{927}(82,\cdot)\) \(\chi_{927}(91,\cdot)\) \(\chi_{927}(118,\cdot)\) \(\chi_{927}(136,\cdot)\) \(\chi_{927}(163,\cdot)\) \(\chi_{927}(208,\cdot)\) \(\chi_{927}(235,\cdot)\) \(\chi_{927}(244,\cdot)\) \(\chi_{927}(289,\cdot)\) \(\chi_{927}(298,\cdot)\) \(\chi_{927}(316,\cdot)\) \(\chi_{927}(325,\cdot)\) \(\chi_{927}(334,\cdot)\) \(\chi_{927}(361,\cdot)\) \(\chi_{927}(406,\cdot)\) \(\chi_{927}(532,\cdot)\) \(\chi_{927}(541,\cdot)\) \(\chi_{927}(613,\cdot)\) \(\chi_{927}(622,\cdot)\) \(\chi_{927}(667,\cdot)\) \(\chi_{927}(676,\cdot)\) \(\chi_{927}(739,\cdot)\) \(\chi_{927}(757,\cdot)\) \(\chi_{927}(784,\cdot)\) \(\chi_{927}(856,\cdot)\) \(\chi_{927}(865,\cdot)\) \(\chi_{927}(874,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((722,829)\) → \((1,e\left(\frac{46}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 927 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{38}{51}\right)\) |