Basic properties
| Modulus: | \(1007\) | |
| Conductor: | \(1007\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1007.be
\(\chi_{1007}(26,\cdot)\) \(\chi_{1007}(45,\cdot)\) \(\chi_{1007}(87,\cdot)\) \(\chi_{1007}(125,\cdot)\) \(\chi_{1007}(140,\cdot)\) \(\chi_{1007}(178,\cdot)\) \(\chi_{1007}(220,\cdot)\) \(\chi_{1007}(239,\cdot)\) \(\chi_{1007}(273,\cdot)\) \(\chi_{1007}(277,\cdot)\) \(\chi_{1007}(292,\cdot)\) \(\chi_{1007}(296,\cdot)\) \(\chi_{1007}(315,\cdot)\) \(\chi_{1007}(330,\cdot)\) \(\chi_{1007}(349,\cdot)\) \(\chi_{1007}(353,\cdot)\) \(\chi_{1007}(368,\cdot)\) \(\chi_{1007}(391,\cdot)\) \(\chi_{1007}(406,\cdot)\) \(\chi_{1007}(410,\cdot)\) \(\chi_{1007}(429,\cdot)\) \(\chi_{1007}(444,\cdot)\) \(\chi_{1007}(463,\cdot)\) \(\chi_{1007}(482,\cdot)\) \(\chi_{1007}(562,\cdot)\) \(\chi_{1007}(581,\cdot)\) \(\chi_{1007}(615,\cdot)\) \(\chi_{1007}(634,\cdot)\) \(\chi_{1007}(638,\cdot)\) \(\chi_{1007}(657,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{29}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1007 }(999, a) \) | \(-1\) | \(1\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) |