Basic properties
Modulus: | \(6017\) | |
Conductor: | \(6017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(65\) | 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 6017.be
\(\chi_{6017}(350,\cdot)\) \(\chi_{6017}(509,\cdot)\) \(\chi_{6017}(784,\cdot)\) \(\chi_{6017}(808,\cdot)\) \(\chi_{6017}(840,\cdot)\) \(\chi_{6017}(900,\cdot)\) \(\chi_{6017}(922,\cdot)\) \(\chi_{6017}(1444,\cdot)\) \(\chi_{6017}(1534,\cdot)\) \(\chi_{6017}(1611,\cdot)\) \(\chi_{6017}(1687,\cdot)\) \(\chi_{6017}(1934,\cdot)\) \(\chi_{6017}(1994,\cdot)\) \(\chi_{6017}(2016,\cdot)\) \(\chi_{6017}(2116,\cdot)\) \(\chi_{6017}(2150,\cdot)\) \(\chi_{6017}(2160,\cdot)\) \(\chi_{6017}(2425,\cdot)\) \(\chi_{6017}(2781,\cdot)\) \(\chi_{6017}(2996,\cdot)\) \(\chi_{6017}(3028,\cdot)\) \(\chi_{6017}(3085,\cdot)\) \(\chi_{6017}(3210,\cdot)\) \(\chi_{6017}(3254,\cdot)\) \(\chi_{6017}(3635,\cdot)\) \(\chi_{6017}(3657,\cdot)\) \(\chi_{6017}(3722,\cdot)\) \(\chi_{6017}(3799,\cdot)\) \(\chi_{6017}(3875,\cdot)\) \(\chi_{6017}(4090,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\((3830,2190)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{10}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 6017 }(2016, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) |