Basic properties
| Modulus: | \(2112\) | |
| Conductor: | \(704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{704}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2112.da
\(\chi_{2112}(37,\cdot)\) \(\chi_{2112}(157,\cdot)\) \(\chi_{2112}(181,\cdot)\) \(\chi_{2112}(229,\cdot)\) \(\chi_{2112}(301,\cdot)\) \(\chi_{2112}(421,\cdot)\) \(\chi_{2112}(445,\cdot)\) \(\chi_{2112}(493,\cdot)\) \(\chi_{2112}(565,\cdot)\) \(\chi_{2112}(685,\cdot)\) \(\chi_{2112}(709,\cdot)\) \(\chi_{2112}(757,\cdot)\) \(\chi_{2112}(829,\cdot)\) \(\chi_{2112}(949,\cdot)\) \(\chi_{2112}(973,\cdot)\) \(\chi_{2112}(1021,\cdot)\) \(\chi_{2112}(1093,\cdot)\) \(\chi_{2112}(1213,\cdot)\) \(\chi_{2112}(1237,\cdot)\) \(\chi_{2112}(1285,\cdot)\) \(\chi_{2112}(1357,\cdot)\) \(\chi_{2112}(1477,\cdot)\) \(\chi_{2112}(1501,\cdot)\) \(\chi_{2112}(1549,\cdot)\) \(\chi_{2112}(1621,\cdot)\) \(\chi_{2112}(1741,\cdot)\) \(\chi_{2112}(1765,\cdot)\) \(\chi_{2112}(1813,\cdot)\) \(\chi_{2112}(1885,\cdot)\) \(\chi_{2112}(2005,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2047,133,1409,1729)\) → \((1,e\left(\frac{9}{16}\right),1,e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2112 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{31}{80}\right)\) |