Basic properties
| Modulus: | \(6012\) | |
| Conductor: | \(668\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{668}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6012.t
\(\chi_{6012}(19,\cdot)\) \(\chi_{6012}(127,\cdot)\) \(\chi_{6012}(199,\cdot)\) \(\chi_{6012}(343,\cdot)\) \(\chi_{6012}(415,\cdot)\) \(\chi_{6012}(523,\cdot)\) \(\chi_{6012}(559,\cdot)\) \(\chi_{6012}(595,\cdot)\) \(\chi_{6012}(631,\cdot)\) \(\chi_{6012}(775,\cdot)\) \(\chi_{6012}(847,\cdot)\) \(\chi_{6012}(883,\cdot)\) \(\chi_{6012}(919,\cdot)\) \(\chi_{6012}(1027,\cdot)\) \(\chi_{6012}(1063,\cdot)\) \(\chi_{6012}(1099,\cdot)\) \(\chi_{6012}(1135,\cdot)\) \(\chi_{6012}(1171,\cdot)\) \(\chi_{6012}(1207,\cdot)\) \(\chi_{6012}(1423,\cdot)\) \(\chi_{6012}(1531,\cdot)\) \(\chi_{6012}(1567,\cdot)\) \(\chi_{6012}(1603,\cdot)\) \(\chi_{6012}(1747,\cdot)\) \(\chi_{6012}(1855,\cdot)\) \(\chi_{6012}(1891,\cdot)\) \(\chi_{6012}(1963,\cdot)\) \(\chi_{6012}(1999,\cdot)\) \(\chi_{6012}(2035,\cdot)\) \(\chi_{6012}(2179,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((-1,1,e\left(\frac{29}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6012 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{83}\right)\) | \(e\left(\frac{121}{166}\right)\) | \(e\left(\frac{47}{166}\right)\) | \(e\left(\frac{82}{83}\right)\) | \(e\left(\frac{43}{83}\right)\) | \(e\left(\frac{127}{166}\right)\) | \(e\left(\frac{15}{166}\right)\) | \(e\left(\frac{58}{83}\right)\) | \(e\left(\frac{34}{83}\right)\) | \(e\left(\frac{157}{166}\right)\) |