Basic properties
Modulus: | \(6019\) | |
Conductor: | \(6019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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.cy
\(\chi_{6019}(281,\cdot)\) \(\chi_{6019}(294,\cdot)\) \(\chi_{6019}(476,\cdot)\) \(\chi_{6019}(736,\cdot)\) \(\chi_{6019}(1071,\cdot)\) \(\chi_{6019}(1656,\cdot)\) \(\chi_{6019}(1997,\cdot)\) \(\chi_{6019}(2137,\cdot)\) \(\chi_{6019}(2527,\cdot)\) \(\chi_{6019}(2582,\cdot)\) \(\chi_{6019}(3063,\cdot)\) \(\chi_{6019}(3255,\cdot)\) \(\chi_{6019}(3453,\cdot)\) \(\chi_{6019}(3541,\cdot)\) \(\chi_{6019}(3671,\cdot)\) \(\chi_{6019}(4181,\cdot)\) \(\chi_{6019}(4467,\cdot)\) \(\chi_{6019}(4597,\cdot)\) \(\chi_{6019}(4893,\cdot)\) \(\chi_{6019}(5374,\cdot)\) \(\chi_{6019}(5387,\cdot)\) \(\chi_{6019}(5569,\cdot)\) \(\chi_{6019}(5819,\cdot)\) \(\chi_{6019}(5829,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2316,1392)\) → \((i,e\left(\frac{1}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6019 }(281, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{65}{84}\right)\) |