Basic properties
Modulus: | \(8016\) | |
Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(83\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{167}(84,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.y
\(\chi_{8016}(49,\cdot)\) \(\chi_{8016}(97,\cdot)\) \(\chi_{8016}(289,\cdot)\) \(\chi_{8016}(337,\cdot)\) \(\chi_{8016}(433,\cdot)\) \(\chi_{8016}(481,\cdot)\) \(\chi_{8016}(529,\cdot)\) \(\chi_{8016}(577,\cdot)\) \(\chi_{8016}(625,\cdot)\) \(\chi_{8016}(961,\cdot)\) \(\chi_{8016}(1009,\cdot)\) \(\chi_{8016}(1201,\cdot)\) \(\chi_{8016}(1297,\cdot)\) \(\chi_{8016}(1345,\cdot)\) \(\chi_{8016}(1393,\cdot)\) \(\chi_{8016}(1633,\cdot)\) \(\chi_{8016}(1681,\cdot)\) \(\chi_{8016}(1777,\cdot)\) \(\chi_{8016}(1873,\cdot)\) \(\chi_{8016}(1921,\cdot)\) \(\chi_{8016}(1969,\cdot)\) \(\chi_{8016}(2065,\cdot)\) \(\chi_{8016}(2161,\cdot)\) \(\chi_{8016}(2209,\cdot)\) \(\chi_{8016}(2401,\cdot)\) \(\chi_{8016}(2593,\cdot)\) \(\chi_{8016}(2737,\cdot)\) \(\chi_{8016}(2881,\cdot)\) \(\chi_{8016}(3025,\cdot)\) \(\chi_{8016}(3121,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 83 polynomial |
Values on generators
\((3007,2005,5345,673)\) → \((1,1,1,e\left(\frac{63}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 8016 }(1921, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{83}\right)\) | \(e\left(\frac{47}{83}\right)\) | \(e\left(\frac{21}{83}\right)\) | \(e\left(\frac{15}{83}\right)\) | \(e\left(\frac{19}{83}\right)\) | \(e\left(\frac{2}{83}\right)\) | \(e\left(\frac{12}{83}\right)\) | \(e\left(\frac{43}{83}\right)\) | \(e\left(\frac{71}{83}\right)\) | \(e\left(\frac{26}{83}\right)\) |