Basic properties
| Modulus: | \(8016\) | |
| 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 \(\chi_{2004}(95,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bd
\(\chi_{8016}(95,\cdot)\) \(\chi_{8016}(143,\cdot)\) \(\chi_{8016}(287,\cdot)\) \(\chi_{8016}(479,\cdot)\) \(\chi_{8016}(527,\cdot)\) \(\chi_{8016}(575,\cdot)\) \(\chi_{8016}(719,\cdot)\) \(\chi_{8016}(1007,\cdot)\) \(\chi_{8016}(1055,\cdot)\) \(\chi_{8016}(1103,\cdot)\) \(\chi_{8016}(1151,\cdot)\) \(\chi_{8016}(1199,\cdot)\) \(\chi_{8016}(1247,\cdot)\) \(\chi_{8016}(1391,\cdot)\) \(\chi_{8016}(1439,\cdot)\) \(\chi_{8016}(1487,\cdot)\) \(\chi_{8016}(1583,\cdot)\) \(\chi_{8016}(1775,\cdot)\) \(\chi_{8016}(1823,\cdot)\) \(\chi_{8016}(1871,\cdot)\) \(\chi_{8016}(1919,\cdot)\) \(\chi_{8016}(2063,\cdot)\) \(\chi_{8016}(2159,\cdot)\) \(\chi_{8016}(2351,\cdot)\) \(\chi_{8016}(2447,\cdot)\) \(\chi_{8016}(2591,\cdot)\) \(\chi_{8016}(2639,\cdot)\) \(\chi_{8016}(2687,\cdot)\) \(\chi_{8016}(2783,\cdot)\) \(\chi_{8016}(2831,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((-1,1,-1,e\left(\frac{59}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 8016 }(95, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{83}\right)\) | \(e\left(\frac{73}{166}\right)\) | \(e\left(\frac{79}{83}\right)\) | \(e\left(\frac{101}{166}\right)\) | \(e\left(\frac{28}{83}\right)\) | \(e\left(\frac{19}{166}\right)\) | \(e\left(\frac{31}{166}\right)\) | \(e\left(\frac{59}{83}\right)\) | \(e\left(\frac{135}{166}\right)\) | \(e\left(\frac{81}{166}\right)\) |