Basic properties
| Modulus: | \(1122\) | |
| Conductor: | \(187\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{187}(91,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1122.bk
\(\chi_{1122}(31,\cdot)\) \(\chi_{1122}(37,\cdot)\) \(\chi_{1122}(91,\cdot)\) \(\chi_{1122}(97,\cdot)\) \(\chi_{1122}(163,\cdot)\) \(\chi_{1122}(181,\cdot)\) \(\chi_{1122}(235,\cdot)\) \(\chi_{1122}(295,\cdot)\) \(\chi_{1122}(301,\cdot)\) \(\chi_{1122}(313,\cdot)\) \(\chi_{1122}(367,\cdot)\) \(\chi_{1122}(379,\cdot)\) \(\chi_{1122}(445,\cdot)\) \(\chi_{1122}(487,\cdot)\) \(\chi_{1122}(499,\cdot)\) \(\chi_{1122}(619,\cdot)\) \(\chi_{1122}(643,\cdot)\) \(\chi_{1122}(685,\cdot)\) \(\chi_{1122}(691,\cdot)\) \(\chi_{1122}(709,\cdot)\) \(\chi_{1122}(751,\cdot)\) \(\chi_{1122}(775,\cdot)\) \(\chi_{1122}(823,\cdot)\) \(\chi_{1122}(889,\cdot)\) \(\chi_{1122}(895,\cdot)\) \(\chi_{1122}(907,\cdot)\) \(\chi_{1122}(949,\cdot)\) \(\chi_{1122}(955,\cdot)\) \(\chi_{1122}(1015,\cdot)\) \(\chi_{1122}(1027,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((749,409,1057)\) → \((1,e\left(\frac{4}{5}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 1122 }(91, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{43}{80}\right)\) |