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 \(\chi_{1336}(443,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bc
\(\chi_{8016}(55,\cdot)\) \(\chi_{8016}(103,\cdot)\) \(\chi_{8016}(151,\cdot)\) \(\chi_{8016}(247,\cdot)\) \(\chi_{8016}(439,\cdot)\) \(\chi_{8016}(487,\cdot)\) \(\chi_{8016}(535,\cdot)\) \(\chi_{8016}(583,\cdot)\) \(\chi_{8016}(727,\cdot)\) \(\chi_{8016}(823,\cdot)\) \(\chi_{8016}(1015,\cdot)\) \(\chi_{8016}(1111,\cdot)\) \(\chi_{8016}(1255,\cdot)\) \(\chi_{8016}(1303,\cdot)\) \(\chi_{8016}(1351,\cdot)\) \(\chi_{8016}(1447,\cdot)\) \(\chi_{8016}(1495,\cdot)\) \(\chi_{8016}(1543,\cdot)\) \(\chi_{8016}(1639,\cdot)\) \(\chi_{8016}(1687,\cdot)\) \(\chi_{8016}(1783,\cdot)\) \(\chi_{8016}(1831,\cdot)\) \(\chi_{8016}(1927,\cdot)\) \(\chi_{8016}(1975,\cdot)\) \(\chi_{8016}(2071,\cdot)\) \(\chi_{8016}(2167,\cdot)\) \(\chi_{8016}(2263,\cdot)\) \(\chi_{8016}(2311,\cdot)\) \(\chi_{8016}(2407,\cdot)\) \(\chi_{8016}(2455,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((-1,-1,1,e\left(\frac{107}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 8016 }(1111, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{83}\right)\) | \(e\left(\frac{93}{166}\right)\) | \(e\left(\frac{4}{83}\right)\) | \(e\left(\frac{74}{83}\right)\) | \(e\left(\frac{27}{166}\right)\) | \(e\left(\frac{32}{83}\right)\) | \(e\left(\frac{26}{83}\right)\) | \(e\left(\frac{24}{83}\right)\) | \(e\left(\frac{31}{166}\right)\) | \(e\left(\frac{85}{166}\right)\) |