Basic properties
| Modulus: | \(8016\) | |
| Conductor: | \(1336\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1336}(1269,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bj
\(\chi_{8016}(25,\cdot)\) \(\chi_{8016}(121,\cdot)\) \(\chi_{8016}(169,\cdot)\) \(\chi_{8016}(217,\cdot)\) \(\chi_{8016}(265,\cdot)\) \(\chi_{8016}(361,\cdot)\) \(\chi_{8016}(409,\cdot)\) \(\chi_{8016}(505,\cdot)\) \(\chi_{8016}(601,\cdot)\) \(\chi_{8016}(697,\cdot)\) \(\chi_{8016}(745,\cdot)\) \(\chi_{8016}(841,\cdot)\) \(\chi_{8016}(889,\cdot)\) \(\chi_{8016}(985,\cdot)\) \(\chi_{8016}(1033,\cdot)\) \(\chi_{8016}(1129,\cdot)\) \(\chi_{8016}(1177,\cdot)\) \(\chi_{8016}(1225,\cdot)\) \(\chi_{8016}(1321,\cdot)\) \(\chi_{8016}(1369,\cdot)\) \(\chi_{8016}(1417,\cdot)\) \(\chi_{8016}(1561,\cdot)\) \(\chi_{8016}(1657,\cdot)\) \(\chi_{8016}(1849,\cdot)\) \(\chi_{8016}(1945,\cdot)\) \(\chi_{8016}(2089,\cdot)\) \(\chi_{8016}(2137,\cdot)\) \(\chi_{8016}(2185,\cdot)\) \(\chi_{8016}(2233,\cdot)\) \(\chi_{8016}(2425,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((1,-1,1,e\left(\frac{41}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 8016 }(601, a) \) | \(1\) | \(1\) | \(e\left(\frac{165}{166}\right)\) | \(e\left(\frac{24}{83}\right)\) | \(e\left(\frac{55}{166}\right)\) | \(e\left(\frac{63}{166}\right)\) | \(e\left(\frac{15}{83}\right)\) | \(e\left(\frac{25}{166}\right)\) | \(e\left(\frac{75}{83}\right)\) | \(e\left(\frac{82}{83}\right)\) | \(e\left(\frac{99}{166}\right)\) | \(e\left(\frac{38}{83}\right)\) |