Basic properties
| Modulus: | \(6012\) | |
| Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(83\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{167}(76,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6012.q
\(\chi_{6012}(181,\cdot)\) \(\chi_{6012}(217,\cdot)\) \(\chi_{6012}(289,\cdot)\) \(\chi_{6012}(361,\cdot)\) \(\chi_{6012}(397,\cdot)\) \(\chi_{6012}(433,\cdot)\) \(\chi_{6012}(505,\cdot)\) \(\chi_{6012}(577,\cdot)\) \(\chi_{6012}(613,\cdot)\) \(\chi_{6012}(757,\cdot)\) \(\chi_{6012}(901,\cdot)\) \(\chi_{6012}(1009,\cdot)\) \(\chi_{6012}(1117,\cdot)\) \(\chi_{6012}(1225,\cdot)\) \(\chi_{6012}(1297,\cdot)\) \(\chi_{6012}(1369,\cdot)\) \(\chi_{6012}(1477,\cdot)\) \(\chi_{6012}(1657,\cdot)\) \(\chi_{6012}(1873,\cdot)\) \(\chi_{6012}(1909,\cdot)\) \(\chi_{6012}(1945,\cdot)\) \(\chi_{6012}(1981,\cdot)\) \(\chi_{6012}(2053,\cdot)\) \(\chi_{6012}(2089,\cdot)\) \(\chi_{6012}(2125,\cdot)\) \(\chi_{6012}(2161,\cdot)\) \(\chi_{6012}(2233,\cdot)\) \(\chi_{6012}(2269,\cdot)\) \(\chi_{6012}(2341,\cdot)\) \(\chi_{6012}(2413,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 83 polynomial |
Values on generators
\((3007,3341,4681)\) → \((1,1,e\left(\frac{69}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6012 }(577, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{83}\right)\) | \(e\left(\frac{8}{83}\right)\) | \(e\left(\frac{23}{83}\right)\) | \(e\left(\frac{52}{83}\right)\) | \(e\left(\frac{5}{83}\right)\) | \(e\left(\frac{18}{83}\right)\) | \(e\left(\frac{25}{83}\right)\) | \(e\left(\frac{55}{83}\right)\) | \(e\left(\frac{58}{83}\right)\) | \(e\left(\frac{68}{83}\right)\) |