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.da
\(\chi_{6001}(349,\cdot)\) \(\chi_{6001}(417,\cdot)\) \(\chi_{6001}(535,\cdot)\) \(\chi_{6001}(672,\cdot)\) \(\chi_{6001}(841,\cdot)\) \(\chi_{6001}(1250,\cdot)\) \(\chi_{6001}(1277,\cdot)\) \(\chi_{6001}(1583,\cdot)\) \(\chi_{6001}(1630,\cdot)\) \(\chi_{6001}(1936,\cdot)\) \(\chi_{6001}(1947,\cdot)\) \(\chi_{6001}(2253,\cdot)\) \(\chi_{6001}(2280,\cdot)\) \(\chi_{6001}(2592,\cdot)\) \(\chi_{6001}(2633,\cdot)\) \(\chi_{6001}(2858,\cdot)\) \(\chi_{6001}(3113,\cdot)\) \(\chi_{6001}(3181,\cdot)\) \(\chi_{6001}(3211,\cdot)\) \(\chi_{6001}(3323,\cdot)\) \(\chi_{6001}(3442,\cdot)\) \(\chi_{6001}(3466,\cdot)\) \(\chi_{6001}(3534,\cdot)\) \(\chi_{6001}(3918,\cdot)\) \(\chi_{6001}(4004,\cdot)\) \(\chi_{6001}(4201,\cdot)\) \(\chi_{6001}(4554,\cdot)\) \(\chi_{6001}(4677,\cdot)\) \(\chi_{6001}(4735,\cdot)\) \(\chi_{6001}(4796,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((2825,3180)\) → \((e\left(\frac{1}{8}\right),e\left(\frac{35}{44}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(417, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{81}{88}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{53}{88}\right)\) |