Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8281.dh
\(\chi_{8281}(31,\cdot)\) \(\chi_{8281}(411,\cdot)\) \(\chi_{8281}(460,\cdot)\) \(\chi_{8281}(619,\cdot)\) \(\chi_{8281}(668,\cdot)\) \(\chi_{8281}(1048,\cdot)\) \(\chi_{8281}(1097,\cdot)\) \(\chi_{8281}(1256,\cdot)\) \(\chi_{8281}(1305,\cdot)\) \(\chi_{8281}(1685,\cdot)\) \(\chi_{8281}(1734,\cdot)\) \(\chi_{8281}(1893,\cdot)\) \(\chi_{8281}(1942,\cdot)\) \(\chi_{8281}(2322,\cdot)\) \(\chi_{8281}(2371,\cdot)\) \(\chi_{8281}(2530,\cdot)\) \(\chi_{8281}(2579,\cdot)\) \(\chi_{8281}(2959,\cdot)\) \(\chi_{8281}(3008,\cdot)\) \(\chi_{8281}(3167,\cdot)\) \(\chi_{8281}(3216,\cdot)\) \(\chi_{8281}(3596,\cdot)\) \(\chi_{8281}(3645,\cdot)\) \(\chi_{8281}(3804,\cdot)\) \(\chi_{8281}(3853,\cdot)\) \(\chi_{8281}(4233,\cdot)\) \(\chi_{8281}(4282,\cdot)\) \(\chi_{8281}(4441,\cdot)\) \(\chi_{8281}(4490,\cdot)\) \(\chi_{8281}(4870,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1522,3382)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{7}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{31}{39}\right)\) |