Basic properties
| Modulus: | \(1007\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | 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.bf
\(\chi_{1007}(10,\cdot)\) \(\chi_{1007}(13,\cdot)\) \(\chi_{1007}(15,\cdot)\) \(\chi_{1007}(89,\cdot)\) \(\chi_{1007}(97,\cdot)\) \(\chi_{1007}(116,\cdot)\) \(\chi_{1007}(148,\cdot)\) \(\chi_{1007}(155,\cdot)\) \(\chi_{1007}(174,\cdot)\) \(\chi_{1007}(203,\cdot)\) \(\chi_{1007}(205,\cdot)\) \(\chi_{1007}(222,\cdot)\) \(\chi_{1007}(261,\cdot)\) \(\chi_{1007}(280,\cdot)\) \(\chi_{1007}(281,\cdot)\) \(\chi_{1007}(307,\cdot)\) \(\chi_{1007}(314,\cdot)\) \(\chi_{1007}(333,\cdot)\) \(\chi_{1007}(364,\cdot)\) \(\chi_{1007}(395,\cdot)\) \(\chi_{1007}(413,\cdot)\) \(\chi_{1007}(420,\cdot)\) \(\chi_{1007}(439,\cdot)\) \(\chi_{1007}(440,\cdot)\) \(\chi_{1007}(452,\cdot)\) \(\chi_{1007}(466,\cdot)\) \(\chi_{1007}(470,\cdot)\) \(\chi_{1007}(471,\cdot)\) \(\chi_{1007}(490,\cdot)\) \(\chi_{1007}(523,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{7}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1007 }(1003, a) \) | \(-1\) | \(1\) | \(e\left(\frac{35}{234}\right)\) | \(e\left(\frac{23}{234}\right)\) | \(e\left(\frac{35}{117}\right)\) | \(e\left(\frac{10}{117}\right)\) | \(e\left(\frac{29}{117}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{23}{117}\right)\) | \(e\left(\frac{55}{234}\right)\) | \(e\left(\frac{22}{39}\right)\) |