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 \(\chi_{704}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6336.fg
\(\chi_{6336}(19,\cdot)\) \(\chi_{6336}(523,\cdot)\) \(\chi_{6336}(667,\cdot)\) \(\chi_{6336}(739,\cdot)\) \(\chi_{6336}(811,\cdot)\) \(\chi_{6336}(1315,\cdot)\) \(\chi_{6336}(1459,\cdot)\) \(\chi_{6336}(1531,\cdot)\) \(\chi_{6336}(1603,\cdot)\) \(\chi_{6336}(2107,\cdot)\) \(\chi_{6336}(2251,\cdot)\) \(\chi_{6336}(2323,\cdot)\) \(\chi_{6336}(2395,\cdot)\) \(\chi_{6336}(2899,\cdot)\) \(\chi_{6336}(3043,\cdot)\) \(\chi_{6336}(3115,\cdot)\) \(\chi_{6336}(3187,\cdot)\) \(\chi_{6336}(3691,\cdot)\) \(\chi_{6336}(3835,\cdot)\) \(\chi_{6336}(3907,\cdot)\) \(\chi_{6336}(3979,\cdot)\) \(\chi_{6336}(4483,\cdot)\) \(\chi_{6336}(4627,\cdot)\) \(\chi_{6336}(4699,\cdot)\) \(\chi_{6336}(4771,\cdot)\) \(\chi_{6336}(5275,\cdot)\) \(\chi_{6336}(5419,\cdot)\) \(\chi_{6336}(5491,\cdot)\) \(\chi_{6336}(5563,\cdot)\) \(\chi_{6336}(6067,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4159,4357,3521,1729)\) → \((-1,e\left(\frac{7}{16}\right),1,e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6336 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{49}{80}\right)\) |