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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1007.bd
\(\chi_{1007}(8,\cdot)\) \(\chi_{1007}(12,\cdot)\) \(\chi_{1007}(27,\cdot)\) \(\chi_{1007}(31,\cdot)\) \(\chi_{1007}(50,\cdot)\) \(\chi_{1007}(65,\cdot)\) \(\chi_{1007}(84,\cdot)\) \(\chi_{1007}(88,\cdot)\) \(\chi_{1007}(103,\cdot)\) \(\chi_{1007}(126,\cdot)\) \(\chi_{1007}(141,\cdot)\) \(\chi_{1007}(145,\cdot)\) \(\chi_{1007}(164,\cdot)\) \(\chi_{1007}(179,\cdot)\) \(\chi_{1007}(198,\cdot)\) \(\chi_{1007}(217,\cdot)\) \(\chi_{1007}(297,\cdot)\) \(\chi_{1007}(316,\cdot)\) \(\chi_{1007}(350,\cdot)\) \(\chi_{1007}(369,\cdot)\) \(\chi_{1007}(373,\cdot)\) \(\chi_{1007}(392,\cdot)\) \(\chi_{1007}(426,\cdot)\) \(\chi_{1007}(445,\cdot)\) \(\chi_{1007}(525,\cdot)\) \(\chi_{1007}(544,\cdot)\) \(\chi_{1007}(563,\cdot)\) \(\chi_{1007}(578,\cdot)\) \(\chi_{1007}(597,\cdot)\) \(\chi_{1007}(601,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{3}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1007 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{9}{26}\right)\) |