Basic properties
| Modulus: | \(6336\) | |
| Conductor: | \(2112\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2112}(179,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6336.fh
\(\chi_{6336}(179,\cdot)\) \(\chi_{6336}(251,\cdot)\) \(\chi_{6336}(323,\cdot)\) \(\chi_{6336}(467,\cdot)\) \(\chi_{6336}(971,\cdot)\) \(\chi_{6336}(1043,\cdot)\) \(\chi_{6336}(1115,\cdot)\) \(\chi_{6336}(1259,\cdot)\) \(\chi_{6336}(1763,\cdot)\) \(\chi_{6336}(1835,\cdot)\) \(\chi_{6336}(1907,\cdot)\) \(\chi_{6336}(2051,\cdot)\) \(\chi_{6336}(2555,\cdot)\) \(\chi_{6336}(2627,\cdot)\) \(\chi_{6336}(2699,\cdot)\) \(\chi_{6336}(2843,\cdot)\) \(\chi_{6336}(3347,\cdot)\) \(\chi_{6336}(3419,\cdot)\) \(\chi_{6336}(3491,\cdot)\) \(\chi_{6336}(3635,\cdot)\) \(\chi_{6336}(4139,\cdot)\) \(\chi_{6336}(4211,\cdot)\) \(\chi_{6336}(4283,\cdot)\) \(\chi_{6336}(4427,\cdot)\) \(\chi_{6336}(4931,\cdot)\) \(\chi_{6336}(5003,\cdot)\) \(\chi_{6336}(5075,\cdot)\) \(\chi_{6336}(5219,\cdot)\) \(\chi_{6336}(5723,\cdot)\) \(\chi_{6336}(5795,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4159,4357,3521,1729)\) → \((-1,e\left(\frac{15}{16}\right),-1,e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6336 }(179, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{80}\right)\) |