Basic properties
| Modulus: | \(6336\) | |
| 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 6336.fm
\(\chi_{6336}(37,\cdot)\) \(\chi_{6336}(181,\cdot)\) \(\chi_{6336}(685,\cdot)\) \(\chi_{6336}(757,\cdot)\) \(\chi_{6336}(829,\cdot)\) \(\chi_{6336}(973,\cdot)\) \(\chi_{6336}(1477,\cdot)\) \(\chi_{6336}(1549,\cdot)\) \(\chi_{6336}(1621,\cdot)\) \(\chi_{6336}(1765,\cdot)\) \(\chi_{6336}(2269,\cdot)\) \(\chi_{6336}(2341,\cdot)\) \(\chi_{6336}(2413,\cdot)\) \(\chi_{6336}(2557,\cdot)\) \(\chi_{6336}(3061,\cdot)\) \(\chi_{6336}(3133,\cdot)\) \(\chi_{6336}(3205,\cdot)\) \(\chi_{6336}(3349,\cdot)\) \(\chi_{6336}(3853,\cdot)\) \(\chi_{6336}(3925,\cdot)\) \(\chi_{6336}(3997,\cdot)\) \(\chi_{6336}(4141,\cdot)\) \(\chi_{6336}(4645,\cdot)\) \(\chi_{6336}(4717,\cdot)\) \(\chi_{6336}(4789,\cdot)\) \(\chi_{6336}(4933,\cdot)\) \(\chi_{6336}(5437,\cdot)\) \(\chi_{6336}(5509,\cdot)\) \(\chi_{6336}(5581,\cdot)\) \(\chi_{6336}(5725,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4159,4357,3521,1729)\) → \((1,e\left(\frac{9}{16}\right),1,e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6336 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{31}{80}\right)\) |