Basic properties
| Modulus: | \(2014\) | |
| 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 2014.be
\(\chi_{2014}(45,\cdot)\) \(\chi_{2014}(87,\cdot)\) \(\chi_{2014}(125,\cdot)\) \(\chi_{2014}(239,\cdot)\) \(\chi_{2014}(273,\cdot)\) \(\chi_{2014}(277,\cdot)\) \(\chi_{2014}(315,\cdot)\) \(\chi_{2014}(349,\cdot)\) \(\chi_{2014}(353,\cdot)\) \(\chi_{2014}(391,\cdot)\) \(\chi_{2014}(429,\cdot)\) \(\chi_{2014}(463,\cdot)\) \(\chi_{2014}(581,\cdot)\) \(\chi_{2014}(615,\cdot)\) \(\chi_{2014}(657,\cdot)\) \(\chi_{2014}(691,\cdot)\) \(\chi_{2014}(809,\cdot)\) \(\chi_{2014}(843,\cdot)\) \(\chi_{2014}(881,\cdot)\) \(\chi_{2014}(919,\cdot)\) \(\chi_{2014}(923,\cdot)\) \(\chi_{2014}(957,\cdot)\) \(\chi_{2014}(995,\cdot)\) \(\chi_{2014}(999,\cdot)\) \(\chi_{2014}(1033,\cdot)\) \(\chi_{2014}(1147,\cdot)\) \(\chi_{2014}(1185,\cdot)\) \(\chi_{2014}(1227,\cdot)\) \(\chi_{2014}(1299,\cdot)\) \(\chi_{2014}(1303,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{29}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2014 }(45, a) \) | \(-1\) | \(1\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{5}{12}\right)\) |