Basic properties
| Modulus: | \(6019\) | |
| Conductor: | \(6019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(308\) | 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 6019.du
\(\chi_{6019}(44,\cdot)\) \(\chi_{6019}(83,\cdot)\) \(\chi_{6019}(96,\cdot)\) \(\chi_{6019}(99,\cdot)\) \(\chi_{6019}(125,\cdot)\) \(\chi_{6019}(187,\cdot)\) \(\chi_{6019}(304,\cdot)\) \(\chi_{6019}(317,\cdot)\) \(\chi_{6019}(343,\cdot)\) \(\chi_{6019}(385,\cdot)\) \(\chi_{6019}(398,\cdot)\) \(\chi_{6019}(473,\cdot)\) \(\chi_{6019}(486,\cdot)\) \(\chi_{6019}(515,\cdot)\) \(\chi_{6019}(580,\cdot)\) \(\chi_{6019}(684,\cdot)\) \(\chi_{6019}(840,\cdot)\) \(\chi_{6019}(879,\cdot)\) \(\chi_{6019}(918,\cdot)\) \(\chi_{6019}(970,\cdot)\) \(\chi_{6019}(1006,\cdot)\) \(\chi_{6019}(1009,\cdot)\) \(\chi_{6019}(1022,\cdot)\) \(\chi_{6019}(1032,\cdot)\) \(\chi_{6019}(1110,\cdot)\) \(\chi_{6019}(1113,\cdot)\) \(\chi_{6019}(1123,\cdot)\) \(\chi_{6019}(1230,\cdot)\) \(\chi_{6019}(1240,\cdot)\) \(\chi_{6019}(1243,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{308})$ |
| Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((2316,1392)\) → \((-i,e\left(\frac{37}{154}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6019 }(44, a) \) | \(1\) | \(1\) | \(e\left(\frac{283}{308}\right)\) | \(e\left(\frac{37}{154}\right)\) | \(e\left(\frac{129}{154}\right)\) | \(e\left(\frac{241}{308}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{3}{308}\right)\) | \(e\left(\frac{233}{308}\right)\) | \(e\left(\frac{37}{77}\right)\) | \(e\left(\frac{54}{77}\right)\) | \(e\left(\frac{179}{308}\right)\) |