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 \(\chi_{4008}(2411,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bm
\(\chi_{8016}(23,\cdot)\) \(\chi_{8016}(71,\cdot)\) \(\chi_{8016}(119,\cdot)\) \(\chi_{8016}(407,\cdot)\) \(\chi_{8016}(647,\cdot)\) \(\chi_{8016}(791,\cdot)\) \(\chi_{8016}(887,\cdot)\) \(\chi_{8016}(983,\cdot)\) \(\chi_{8016}(1127,\cdot)\) \(\chi_{8016}(1271,\cdot)\) \(\chi_{8016}(1415,\cdot)\) \(\chi_{8016}(1607,\cdot)\) \(\chi_{8016}(1799,\cdot)\) \(\chi_{8016}(1847,\cdot)\) \(\chi_{8016}(1943,\cdot)\) \(\chi_{8016}(2039,\cdot)\) \(\chi_{8016}(2087,\cdot)\) \(\chi_{8016}(2135,\cdot)\) \(\chi_{8016}(2231,\cdot)\) \(\chi_{8016}(2327,\cdot)\) \(\chi_{8016}(2375,\cdot)\) \(\chi_{8016}(2615,\cdot)\) \(\chi_{8016}(2663,\cdot)\) \(\chi_{8016}(2711,\cdot)\) \(\chi_{8016}(2807,\cdot)\) \(\chi_{8016}(2999,\cdot)\) \(\chi_{8016}(3047,\cdot)\) \(\chi_{8016}(3383,\cdot)\) \(\chi_{8016}(3431,\cdot)\) \(\chi_{8016}(3479,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((-1,-1,-1,e\left(\frac{89}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 8016 }(407, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{166}\right)\) | \(e\left(\frac{127}{166}\right)\) | \(e\left(\frac{85}{166}\right)\) | \(e\left(\frac{60}{83}\right)\) | \(e\left(\frac{76}{83}\right)\) | \(e\left(\frac{8}{83}\right)\) | \(e\left(\frac{13}{166}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{35}{83}\right)\) | \(e\left(\frac{125}{166}\right)\) |