Basic properties
| Modulus: | \(4028\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1007}(45,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4028.ci
\(\chi_{4028}(45,\cdot)\) \(\chi_{4028}(125,\cdot)\) \(\chi_{4028}(273,\cdot)\) \(\chi_{4028}(277,\cdot)\) \(\chi_{4028}(349,\cdot)\) \(\chi_{4028}(353,\cdot)\) \(\chi_{4028}(429,\cdot)\) \(\chi_{4028}(581,\cdot)\) \(\chi_{4028}(657,\cdot)\) \(\chi_{4028}(809,\cdot)\) \(\chi_{4028}(881,\cdot)\) \(\chi_{4028}(957,\cdot)\) \(\chi_{4028}(1033,\cdot)\) \(\chi_{4028}(1185,\cdot)\) \(\chi_{4028}(1337,\cdot)\) \(\chi_{4028}(1413,\cdot)\) \(\chi_{4028}(1417,\cdot)\) \(\chi_{4028}(1489,\cdot)\) \(\chi_{4028}(1569,\cdot)\) \(\chi_{4028}(1641,\cdot)\) \(\chi_{4028}(1645,\cdot)\) \(\chi_{4028}(1717,\cdot)\) \(\chi_{4028}(1797,\cdot)\) \(\chi_{4028}(1869,\cdot)\) \(\chi_{4028}(1873,\cdot)\) \(\chi_{4028}(1949,\cdot)\) \(\chi_{4028}(2101,\cdot)\) \(\chi_{4028}(2253,\cdot)\) \(\chi_{4028}(2329,\cdot)\) \(\chi_{4028}(2405,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2015,2757,2281)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{29}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4028 }(45, a) \) | \(-1\) | \(1\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{5}{12}\right)\) |