Basic properties
Modulus: | \(4029\) | |
Conductor: | \(4029\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | 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 4029.cp
\(\chi_{4029}(47,\cdot)\) \(\chi_{4029}(149,\cdot)\) \(\chi_{4029}(344,\cdot)\) \(\chi_{4029}(353,\cdot)\) \(\chi_{4029}(455,\cdot)\) \(\chi_{4029}(548,\cdot)\) \(\chi_{4029}(1007,\cdot)\) \(\chi_{4029}(1016,\cdot)\) \(\chi_{4029}(1109,\cdot)\) \(\chi_{4029}(1160,\cdot)\) \(\chi_{4029}(1169,\cdot)\) \(\chi_{4029}(1220,\cdot)\) \(\chi_{4029}(1262,\cdot)\) \(\chi_{4029}(1271,\cdot)\) \(\chi_{4029}(1373,\cdot)\) \(\chi_{4029}(1475,\cdot)\) \(\chi_{4029}(1619,\cdot)\) \(\chi_{4029}(1628,\cdot)\) \(\chi_{4029}(1772,\cdot)\) \(\chi_{4029}(1781,\cdot)\) \(\chi_{4029}(1823,\cdot)\) \(\chi_{4029}(1883,\cdot)\) \(\chi_{4029}(1925,\cdot)\) \(\chi_{4029}(2129,\cdot)\) \(\chi_{4029}(2180,\cdot)\) \(\chi_{4029}(2240,\cdot)\) \(\chi_{4029}(2282,\cdot)\) \(\chi_{4029}(2444,\cdot)\) \(\chi_{4029}(2486,\cdot)\) \(\chi_{4029}(2588,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((-1,-i,e\left(\frac{1}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(1109, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{8}{39}\right)\) |