Basic properties
Modulus: | \(8016\) | |
Conductor: | \(4008\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4008}(2843,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bf
\(\chi_{8016}(215,\cdot)\) \(\chi_{8016}(263,\cdot)\) \(\chi_{8016}(311,\cdot)\) \(\chi_{8016}(359,\cdot)\) \(\chi_{8016}(455,\cdot)\) \(\chi_{8016}(503,\cdot)\) \(\chi_{8016}(551,\cdot)\) \(\chi_{8016}(599,\cdot)\) \(\chi_{8016}(695,\cdot)\) \(\chi_{8016}(743,\cdot)\) \(\chi_{8016}(839,\cdot)\) \(\chi_{8016}(935,\cdot)\) \(\chi_{8016}(1031,\cdot)\) \(\chi_{8016}(1079,\cdot)\) \(\chi_{8016}(1175,\cdot)\) \(\chi_{8016}(1223,\cdot)\) \(\chi_{8016}(1319,\cdot)\) \(\chi_{8016}(1367,\cdot)\) \(\chi_{8016}(1463,\cdot)\) \(\chi_{8016}(1511,\cdot)\) \(\chi_{8016}(1559,\cdot)\) \(\chi_{8016}(1655,\cdot)\) \(\chi_{8016}(1703,\cdot)\) \(\chi_{8016}(1751,\cdot)\) \(\chi_{8016}(1895,\cdot)\) \(\chi_{8016}(1991,\cdot)\) \(\chi_{8016}(2183,\cdot)\) \(\chi_{8016}(2279,\cdot)\) \(\chi_{8016}(2423,\cdot)\) \(\chi_{8016}(2471,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((-1,-1,-1,e\left(\frac{40}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 8016 }(839, a) \) | \(1\) | \(1\) | \(e\left(\frac{40}{83}\right)\) | \(e\left(\frac{61}{166}\right)\) | \(e\left(\frac{165}{166}\right)\) | \(e\left(\frac{23}{166}\right)\) | \(e\left(\frac{7}{166}\right)\) | \(e\left(\frac{79}{83}\right)\) | \(e\left(\frac{59}{83}\right)\) | \(e\left(\frac{80}{83}\right)\) | \(e\left(\frac{24}{83}\right)\) | \(e\left(\frac{145}{166}\right)\) |