Basic properties
Modulus: | \(6027\) | |
Conductor: | \(6027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(140\) | 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 6027.dz
\(\chi_{6027}(20,\cdot)\) \(\chi_{6027}(62,\cdot)\) \(\chi_{6027}(125,\cdot)\) \(\chi_{6027}(251,\cdot)\) \(\chi_{6027}(377,\cdot)\) \(\chi_{6027}(566,\cdot)\) \(\chi_{6027}(692,\cdot)\) \(\chi_{6027}(818,\cdot)\) \(\chi_{6027}(923,\cdot)\) \(\chi_{6027}(986,\cdot)\) \(\chi_{6027}(1112,\cdot)\) \(\chi_{6027}(1238,\cdot)\) \(\chi_{6027}(1427,\cdot)\) \(\chi_{6027}(1553,\cdot)\) \(\chi_{6027}(1679,\cdot)\) \(\chi_{6027}(1742,\cdot)\) \(\chi_{6027}(1784,\cdot)\) \(\chi_{6027}(1847,\cdot)\) \(\chi_{6027}(1973,\cdot)\) \(\chi_{6027}(2099,\cdot)\) \(\chi_{6027}(2288,\cdot)\) \(\chi_{6027}(2414,\cdot)\) \(\chi_{6027}(2540,\cdot)\) \(\chi_{6027}(2603,\cdot)\) \(\chi_{6027}(2708,\cdot)\) \(\chi_{6027}(2834,\cdot)\) \(\chi_{6027}(2960,\cdot)\) \(\chi_{6027}(3149,\cdot)\) \(\chi_{6027}(3275,\cdot)\) \(\chi_{6027}(3401,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{140})$ |
Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{9}{14}\right),e\left(\frac{1}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(692, a) \) | \(1\) | \(1\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{31}{140}\right)\) | \(e\left(\frac{19}{20}\right)\) |