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.de
\(\chi_{6001}(84,\cdot)\) \(\chi_{6001}(645,\cdot)\) \(\chi_{6001}(662,\cdot)\) \(\chi_{6001}(815,\cdot)\) \(\chi_{6001}(883,\cdot)\) \(\chi_{6001}(900,\cdot)\) \(\chi_{6001}(968,\cdot)\) \(\chi_{6001}(1070,\cdot)\) \(\chi_{6001}(1410,\cdot)\) \(\chi_{6001}(1444,\cdot)\) \(\chi_{6001}(1495,\cdot)\) \(\chi_{6001}(1682,\cdot)\) \(\chi_{6001}(1733,\cdot)\) \(\chi_{6001}(1767,\cdot)\) \(\chi_{6001}(2107,\cdot)\) \(\chi_{6001}(2209,\cdot)\) \(\chi_{6001}(2277,\cdot)\) \(\chi_{6001}(2294,\cdot)\) \(\chi_{6001}(2362,\cdot)\) \(\chi_{6001}(2515,\cdot)\) \(\chi_{6001}(2532,\cdot)\) \(\chi_{6001}(3093,\cdot)\) \(\chi_{6001}(3501,\cdot)\) \(\chi_{6001}(3603,\cdot)\) \(\chi_{6001}(3875,\cdot)\) \(\chi_{6001}(3994,\cdot)\) \(\chi_{6001}(4011,\cdot)\) \(\chi_{6001}(4215,\cdot)\) \(\chi_{6001}(4317,\cdot)\) \(\chi_{6001}(4521,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((2825,3180)\) → \((-1,e\left(\frac{43}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(2532, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{87}{88}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{43}{88}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{9}{11}\right)\) |