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.dc
\(\chi_{6001}(2,\cdot)\) \(\chi_{6001}(8,\cdot)\) \(\chi_{6001}(32,\cdot)\) \(\chi_{6001}(128,\cdot)\) \(\chi_{6001}(512,\cdot)\) \(\chi_{6001}(638,\cdot)\) \(\chi_{6001}(750,\cdot)\) \(\chi_{6001}(790,\cdot)\) \(\chi_{6001}(797,\cdot)\) \(\chi_{6001}(950,\cdot)\) \(\chi_{6001}(1301,\cdot)\) \(\chi_{6001}(1794,\cdot)\) \(\chi_{6001}(2191,\cdot)\) \(\chi_{6001}(2201,\cdot)\) \(\chi_{6001}(2552,\cdot)\) \(\chi_{6001}(2763,\cdot)\) \(\chi_{6001}(2803,\cdot)\) \(\chi_{6001}(2813,\cdot)\) \(\chi_{6001}(2841,\cdot)\) \(\chi_{6001}(3000,\cdot)\) \(\chi_{6001}(3001,\cdot)\) \(\chi_{6001}(3160,\cdot)\) \(\chi_{6001}(3188,\cdot)\) \(\chi_{6001}(3198,\cdot)\) \(\chi_{6001}(3238,\cdot)\) \(\chi_{6001}(3449,\cdot)\) \(\chi_{6001}(3800,\cdot)\) \(\chi_{6001}(3810,\cdot)\) \(\chi_{6001}(4207,\cdot)\) \(\chi_{6001}(4700,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((2825,3180)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{1}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(2552, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(1\) | \(e\left(\frac{71}{88}\right)\) |