Basic properties
Modulus: | \(1096\) | |
Conductor: | \(1096\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(68\) | 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 1096.z
\(\chi_{1096}(11,\cdot)\) \(\chi_{1096}(19,\cdot)\) \(\chi_{1096}(107,\cdot)\) \(\chi_{1096}(139,\cdot)\) \(\chi_{1096}(235,\cdot)\) \(\chi_{1096}(267,\cdot)\) \(\chi_{1096}(283,\cdot)\) \(\chi_{1096}(291,\cdot)\) \(\chi_{1096}(299,\cdot)\) \(\chi_{1096}(379,\cdot)\) \(\chi_{1096}(403,\cdot)\) \(\chi_{1096}(419,\cdot)\) \(\chi_{1096}(443,\cdot)\) \(\chi_{1096}(523,\cdot)\) \(\chi_{1096}(531,\cdot)\) \(\chi_{1096}(539,\cdot)\) \(\chi_{1096}(555,\cdot)\) \(\chi_{1096}(587,\cdot)\) \(\chi_{1096}(683,\cdot)\) \(\chi_{1096}(715,\cdot)\) \(\chi_{1096}(803,\cdot)\) \(\chi_{1096}(811,\cdot)\) \(\chi_{1096}(883,\cdot)\) \(\chi_{1096}(891,\cdot)\) \(\chi_{1096}(915,\cdot)\) \(\chi_{1096}(923,\cdot)\) \(\chi_{1096}(931,\cdot)\) \(\chi_{1096}(987,\cdot)\) \(\chi_{1096}(995,\cdot)\) \(\chi_{1096}(1003,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{68})$ |
Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((823,549,825)\) → \((-1,-1,e\left(\frac{27}{68}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1096 }(811, a) \) | \(-1\) | \(1\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{19}{68}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{39}{68}\right)\) |