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.dd
\(\chi_{6001}(83,\cdot)\) \(\chi_{6001}(434,\cdot)\) \(\chi_{6001}(695,\cdot)\) \(\chi_{6001}(723,\cdot)\) \(\chi_{6001}(882,\cdot)\) \(\chi_{6001}(1080,\cdot)\) \(\chi_{6001}(1120,\cdot)\) \(\chi_{6001}(1328,\cdot)\) \(\chi_{6001}(1368,\cdot)\) \(\chi_{6001}(1606,\cdot)\) \(\chi_{6001}(1692,\cdot)\) \(\chi_{6001}(2089,\cdot)\) \(\chi_{6001}(2110,\cdot)\) \(\chi_{6001}(2116,\cdot)\) \(\chi_{6001}(2150,\cdot)\) \(\chi_{6001}(2246,\cdot)\) \(\chi_{6001}(2582,\cdot)\) \(\chi_{6001}(2756,\cdot)\) \(\chi_{6001}(2915,\cdot)\) \(\chi_{6001}(2933,\cdot)\) \(\chi_{6001}(3068,\cdot)\) \(\chi_{6001}(3086,\cdot)\) \(\chi_{6001}(3245,\cdot)\) \(\chi_{6001}(3419,\cdot)\) \(\chi_{6001}(3755,\cdot)\) \(\chi_{6001}(3851,\cdot)\) \(\chi_{6001}(3885,\cdot)\) \(\chi_{6001}(3891,\cdot)\) \(\chi_{6001}(3912,\cdot)\) \(\chi_{6001}(4309,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((2825,3180)\) → \((e\left(\frac{1}{8}\right),e\left(\frac{41}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(3885, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(-i\) | \(e\left(\frac{73}{88}\right)\) |