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.cv
\(\chi_{6001}(21,\cdot)\) \(\chi_{6001}(285,\cdot)\) \(\chi_{6001}(421,\cdot)\) \(\chi_{6001}(633,\cdot)\) \(\chi_{6001}(931,\cdot)\) \(\chi_{6001}(948,\cdot)\) \(\chi_{6001}(1067,\cdot)\) \(\chi_{6001}(1441,\cdot)\) \(\chi_{6001}(1721,\cdot)\) \(\chi_{6001}(1849,\cdot)\) \(\chi_{6001}(1874,\cdot)\) \(\chi_{6001}(1959,\cdot)\) \(\chi_{6001}(2027,\cdot)\) \(\chi_{6001}(2410,\cdot)\) \(\chi_{6001}(2469,\cdot)\) \(\chi_{6001}(2503,\cdot)\) \(\chi_{6001}(2648,\cdot)\) \(\chi_{6001}(2792,\cdot)\) \(\chi_{6001}(2826,\cdot)\) \(\chi_{6001}(2835,\cdot)\) \(\chi_{6001}(3260,\cdot)\) \(\chi_{6001}(3268,\cdot)\) \(\chi_{6001}(3336,\cdot)\) \(\chi_{6001}(3421,\cdot)\) \(\chi_{6001}(3447,\cdot)\) \(\chi_{6001}(3574,\cdot)\) \(\chi_{6001}(3872,\cdot)\) \(\chi_{6001}(4059,\cdot)\) \(\chi_{6001}(4297,\cdot)\) \(\chi_{6001}(4662,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((2825,3180)\) → \((-i,e\left(\frac{17}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(3336, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{83}{88}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{39}{88}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{37}{44}\right)\) |