Basic properties
Modulus: | \(6017\) | |
Conductor: | \(6017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(195\) | 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.bt
\(\chi_{6017}(47,\cdot)\) \(\chi_{6017}(136,\cdot)\) \(\chi_{6017}(181,\cdot)\) \(\chi_{6017}(302,\cdot)\) \(\chi_{6017}(445,\cdot)\) \(\chi_{6017}(488,\cdot)\) \(\chi_{6017}(521,\cdot)\) \(\chi_{6017}(643,\cdot)\) \(\chi_{6017}(676,\cdot)\) \(\chi_{6017}(746,\cdot)\) \(\chi_{6017}(764,\cdot)\) \(\chi_{6017}(786,\cdot)\) \(\chi_{6017}(872,\cdot)\) \(\chi_{6017}(949,\cdot)\) \(\chi_{6017}(966,\cdot)\) \(\chi_{6017}(988,\cdot)\) \(\chi_{6017}(1105,\cdot)\) \(\chi_{6017}(1115,\cdot)\) \(\chi_{6017}(1148,\cdot)\) \(\chi_{6017}(1215,\cdot)\) \(\chi_{6017}(1230,\cdot)\) \(\chi_{6017}(1325,\cdot)\) \(\chi_{6017}(1390,\cdot)\) \(\chi_{6017}(1582,\cdot)\) \(\chi_{6017}(1615,\cdot)\) \(\chi_{6017}(1688,\cdot)\) \(\chi_{6017}(1840,\cdot)\) \(\chi_{6017}(1874,\cdot)\) \(\chi_{6017}(2060,\cdot)\) \(\chi_{6017}(2082,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{195})$ |
Fixed field: | Number field defined by a degree 195 polynomial (not computed) |
Values on generators
\((3830,2190)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{2}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 6017 }(676, a) \) | \(1\) | \(1\) | \(e\left(\frac{88}{195}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{176}{195}\right)\) | \(e\left(\frac{152}{195}\right)\) | \(e\left(\frac{127}{195}\right)\) | \(e\left(\frac{16}{195}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) |