Basic properties
Modulus: | \(6001\) | |
Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6001.cy
\(\chi_{6001}(168,\cdot)\) \(\chi_{6001}(213,\cdot)\) \(\chi_{6001}(331,\cdot)\) \(\chi_{6001}(450,\cdot)\) \(\chi_{6001}(519,\cdot)\) \(\chi_{6001}(648,\cdot)\) \(\chi_{6001}(722,\cdot)\) \(\chi_{6001}(842,\cdot)\) \(\chi_{6001}(1001,\cdot)\) \(\chi_{6001}(1181,\cdot)\) \(\chi_{6001}(1634,\cdot)\) \(\chi_{6001}(1743,\cdot)\) \(\chi_{6001}(1862,\cdot)\) \(\chi_{6001}(1987,\cdot)\) \(\chi_{6001}(2134,\cdot)\) \(\chi_{6001}(2286,\cdot)\) \(\chi_{6001}(2331,\cdot)\) \(\chi_{6001}(2593,\cdot)\) \(\chi_{6001}(2637,\cdot)\) \(\chi_{6001}(2684,\cdot)\) \(\chi_{6001}(2960,\cdot)\) \(\chi_{6001}(2990,\cdot)\) \(\chi_{6001}(3119,\cdot)\) \(\chi_{6001}(3313,\cdot)\) \(\chi_{6001}(3698,\cdot)\) \(\chi_{6001}(3861,\cdot)\) \(\chi_{6001}(3980,\cdot)\) \(\chi_{6001}(4105,\cdot)\) \(\chi_{6001}(4214,\cdot)\) \(\chi_{6001}(4252,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((2825,3180)\) → \((e\left(\frac{3}{8}\right),e\left(\frac{17}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(1987, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{57}{88}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{87}{88}\right)\) |