Basic properties
| Modulus: | \(4029\) | |
| Conductor: | \(1343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1343}(1126,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.cn
\(\chi_{4029}(4,\cdot)\) \(\chi_{4029}(13,\cdot)\) \(\chi_{4029}(115,\cdot)\) \(\chi_{4029}(208,\cdot)\) \(\chi_{4029}(268,\cdot)\) \(\chi_{4029}(310,\cdot)\) \(\chi_{4029}(361,\cdot)\) \(\chi_{4029}(421,\cdot)\) \(\chi_{4029}(514,\cdot)\) \(\chi_{4029}(523,\cdot)\) \(\chi_{4029}(625,\cdot)\) \(\chi_{4029}(676,\cdot)\) \(\chi_{4029}(727,\cdot)\) \(\chi_{4029}(871,\cdot)\) \(\chi_{4029}(880,\cdot)\) \(\chi_{4029}(973,\cdot)\) \(\chi_{4029}(1024,\cdot)\) \(\chi_{4029}(1126,\cdot)\) \(\chi_{4029}(1441,\cdot)\) \(\chi_{4029}(1543,\cdot)\) \(\chi_{4029}(1585,\cdot)\) \(\chi_{4029}(1747,\cdot)\) \(\chi_{4029}(1789,\cdot)\) \(\chi_{4029}(1849,\cdot)\) \(\chi_{4029}(1900,\cdot)\) \(\chi_{4029}(2104,\cdot)\) \(\chi_{4029}(2146,\cdot)\) \(\chi_{4029}(2206,\cdot)\) \(\chi_{4029}(2248,\cdot)\) \(\chi_{4029}(2257,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((1,-i,e\left(\frac{35}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4029 }(1126, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{43}{156}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{14}{39}\right)\) |