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.de
\(\chi_{6019}(730,\cdot)\) \(\chi_{6019}(1138,\cdot)\) \(\chi_{6019}(1189,\cdot)\) \(\chi_{6019}(1207,\cdot)\) \(\chi_{6019}(1211,\cdot)\) \(\chi_{6019}(1220,\cdot)\) \(\chi_{6019}(1662,\cdot)\) \(\chi_{6019}(1865,\cdot)\) \(\chi_{6019}(1866,\cdot)\) \(\chi_{6019}(2152,\cdot)\) \(\chi_{6019}(2745,\cdot)\) \(\chi_{6019}(3386,\cdot)\) \(\chi_{6019}(3504,\cdot)\) \(\chi_{6019}(3508,\cdot)\) \(\chi_{6019}(3989,\cdot)\) \(\chi_{6019}(4180,\cdot)\) \(\chi_{6019}(4448,\cdot)\) \(\chi_{6019}(4461,\cdot)\) \(\chi_{6019}(4842,\cdot)\) \(\chi_{6019}(4903,\cdot)\) \(\chi_{6019}(5523,\cdot)\) \(\chi_{6019}(5570,\cdot)\) \(\chi_{6019}(5701,\cdot)\) \(\chi_{6019}(5856,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2316,1392)\) → \((e\left(\frac{1}{12}\right),e\left(\frac{13}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6019 }(730, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(i\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{25}{28}\right)\) |