Basic properties
Modulus: | \(8016\) | |
Conductor: | \(501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{501}(407,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bb
\(\chi_{8016}(17,\cdot)\) \(\chi_{8016}(113,\cdot)\) \(\chi_{8016}(161,\cdot)\) \(\chi_{8016}(257,\cdot)\) \(\chi_{8016}(305,\cdot)\) \(\chi_{8016}(401,\cdot)\) \(\chi_{8016}(497,\cdot)\) \(\chi_{8016}(593,\cdot)\) \(\chi_{8016}(641,\cdot)\) \(\chi_{8016}(737,\cdot)\) \(\chi_{8016}(785,\cdot)\) \(\chi_{8016}(833,\cdot)\) \(\chi_{8016}(881,\cdot)\) \(\chi_{8016}(977,\cdot)\) \(\chi_{8016}(1025,\cdot)\) \(\chi_{8016}(1073,\cdot)\) \(\chi_{8016}(1121,\cdot)\) \(\chi_{8016}(1409,\cdot)\) \(\chi_{8016}(1649,\cdot)\) \(\chi_{8016}(1793,\cdot)\) \(\chi_{8016}(1889,\cdot)\) \(\chi_{8016}(1985,\cdot)\) \(\chi_{8016}(2129,\cdot)\) \(\chi_{8016}(2273,\cdot)\) \(\chi_{8016}(2417,\cdot)\) \(\chi_{8016}(2609,\cdot)\) \(\chi_{8016}(2801,\cdot)\) \(\chi_{8016}(2849,\cdot)\) \(\chi_{8016}(2945,\cdot)\) \(\chi_{8016}(3041,\cdot)\) ...
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
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 8016 }(1409, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{83}\right)\) | \(e\left(\frac{22}{83}\right)\) | \(e\left(\frac{85}{166}\right)\) | \(e\left(\frac{37}{166}\right)\) | \(e\left(\frac{76}{83}\right)\) | \(e\left(\frac{8}{83}\right)\) | \(e\left(\frac{48}{83}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{153}{166}\right)\) | \(e\left(\frac{21}{83}\right)\) |