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.bc
\(\chi_{927}(40,\cdot)\) \(\chi_{927}(43,\cdot)\) \(\chi_{927}(67,\cdot)\) \(\chi_{927}(148,\cdot)\) \(\chi_{927}(151,\cdot)\) \(\chi_{927}(178,\cdot)\) \(\chi_{927}(187,\cdot)\) \(\chi_{927}(202,\cdot)\) \(\chi_{927}(211,\cdot)\) \(\chi_{927}(241,\cdot)\) \(\chi_{927}(250,\cdot)\) \(\chi_{927}(268,\cdot)\) \(\chi_{927}(292,\cdot)\) \(\chi_{927}(394,\cdot)\) \(\chi_{927}(463,\cdot)\) \(\chi_{927}(466,\cdot)\) \(\chi_{927}(508,\cdot)\) \(\chi_{927}(526,\cdot)\) \(\chi_{927}(580,\cdot)\) \(\chi_{927}(592,\cdot)\) \(\chi_{927}(688,\cdot)\) \(\chi_{927}(706,\cdot)\) \(\chi_{927}(727,\cdot)\) \(\chi_{927}(733,\cdot)\) \(\chi_{927}(742,\cdot)\) \(\chi_{927}(799,\cdot)\) \(\chi_{927}(808,\cdot)\) \(\chi_{927}(844,\cdot)\) \(\chi_{927}(877,\cdot)\) \(\chi_{927}(895,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((722,829)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{77}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 927 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{73}{102}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{29}{51}\right)\) | \(e\left(\frac{9}{17}\right)\) |