Basic properties
| Modulus: | \(8016\) | |
| 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 \(\chi_{668}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.be
\(\chi_{8016}(31,\cdot)\) \(\chi_{8016}(127,\cdot)\) \(\chi_{8016}(175,\cdot)\) \(\chi_{8016}(223,\cdot)\) \(\chi_{8016}(319,\cdot)\) \(\chi_{8016}(367,\cdot)\) \(\chi_{8016}(415,\cdot)\) \(\chi_{8016}(559,\cdot)\) \(\chi_{8016}(655,\cdot)\) \(\chi_{8016}(847,\cdot)\) \(\chi_{8016}(943,\cdot)\) \(\chi_{8016}(1087,\cdot)\) \(\chi_{8016}(1135,\cdot)\) \(\chi_{8016}(1183,\cdot)\) \(\chi_{8016}(1231,\cdot)\) \(\chi_{8016}(1423,\cdot)\) \(\chi_{8016}(1519,\cdot)\) \(\chi_{8016}(1567,\cdot)\) \(\chi_{8016}(1615,\cdot)\) \(\chi_{8016}(1759,\cdot)\) \(\chi_{8016}(1807,\cdot)\) \(\chi_{8016}(1855,\cdot)\) \(\chi_{8016}(1903,\cdot)\) \(\chi_{8016}(1951,\cdot)\) \(\chi_{8016}(1999,\cdot)\) \(\chi_{8016}(2287,\cdot)\) \(\chi_{8016}(2431,\cdot)\) \(\chi_{8016}(2479,\cdot)\) \(\chi_{8016}(2527,\cdot)\) \(\chi_{8016}(2719,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((-1,1,1,e\left(\frac{45}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 8016 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{45}{83}\right)\) | \(e\left(\frac{79}{166}\right)\) | \(e\left(\frac{113}{166}\right)\) | \(e\left(\frac{70}{83}\right)\) | \(e\left(\frac{61}{83}\right)\) | \(e\left(\frac{157}{166}\right)\) | \(e\left(\frac{29}{166}\right)\) | \(e\left(\frac{7}{83}\right)\) | \(e\left(\frac{27}{83}\right)\) | \(e\left(\frac{49}{166}\right)\) |