Basic properties
| Modulus: | \(6012\) | |
| Conductor: | \(2004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2004}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6012.s
\(\chi_{6012}(35,\cdot)\) \(\chi_{6012}(71,\cdot)\) \(\chi_{6012}(143,\cdot)\) \(\chi_{6012}(287,\cdot)\) \(\chi_{6012}(323,\cdot)\) \(\chi_{6012}(575,\cdot)\) \(\chi_{6012}(611,\cdot)\) \(\chi_{6012}(647,\cdot)\) \(\chi_{6012}(683,\cdot)\) \(\chi_{6012}(719,\cdot)\) \(\chi_{6012}(791,\cdot)\) \(\chi_{6012}(827,\cdot)\) \(\chi_{6012}(971,\cdot)\) \(\chi_{6012}(1007,\cdot)\) \(\chi_{6012}(1043,\cdot)\) \(\chi_{6012}(1115,\cdot)\) \(\chi_{6012}(1151,\cdot)\) \(\chi_{6012}(1259,\cdot)\) \(\chi_{6012}(1403,\cdot)\) \(\chi_{6012}(1439,\cdot)\) \(\chi_{6012}(1475,\cdot)\) \(\chi_{6012}(1583,\cdot)\) \(\chi_{6012}(1799,\cdot)\) \(\chi_{6012}(1835,\cdot)\) \(\chi_{6012}(1871,\cdot)\) \(\chi_{6012}(1907,\cdot)\) \(\chi_{6012}(1943,\cdot)\) \(\chi_{6012}(1979,\cdot)\) \(\chi_{6012}(2087,\cdot)\) \(\chi_{6012}(2123,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((-1,-1,e\left(\frac{119}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6012 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{18}{83}\right)\) | \(e\left(\frac{15}{166}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{139}{166}\right)\) | \(e\left(\frac{41}{83}\right)\) | \(e\left(\frac{13}{166}\right)\) | \(e\left(\frac{161}{166}\right)\) | \(e\left(\frac{36}{83}\right)\) | \(e\left(\frac{5}{166}\right)\) | \(e\left(\frac{3}{166}\right)\) |