Basic properties
| Modulus: | \(1007\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(468\) | 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.bj
\(\chi_{1007}(5,\cdot)\) \(\chi_{1007}(35,\cdot)\) \(\chi_{1007}(55,\cdot)\) \(\chi_{1007}(61,\cdot)\) \(\chi_{1007}(73,\cdot)\) \(\chi_{1007}(74,\cdot)\) \(\chi_{1007}(80,\cdot)\) \(\chi_{1007}(85,\cdot)\) \(\chi_{1007}(92,\cdot)\) \(\chi_{1007}(101,\cdot)\) \(\chi_{1007}(104,\cdot)\) \(\chi_{1007}(111,\cdot)\) \(\chi_{1007}(118,\cdot)\) \(\chi_{1007}(120,\cdot)\) \(\chi_{1007}(137,\cdot)\) \(\chi_{1007}(138,\cdot)\) \(\chi_{1007}(139,\cdot)\) \(\chi_{1007}(156,\cdot)\) \(\chi_{1007}(157,\cdot)\) \(\chi_{1007}(161,\cdot)\) \(\chi_{1007}(177,\cdot)\) \(\chi_{1007}(180,\cdot)\) \(\chi_{1007}(194,\cdot)\) \(\chi_{1007}(207,\cdot)\) \(\chi_{1007}(214,\cdot)\) \(\chi_{1007}(215,\cdot)\) \(\chi_{1007}(226,\cdot)\) \(\chi_{1007}(232,\cdot)\) \(\chi_{1007}(233,\cdot)\) \(\chi_{1007}(234,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{468})$ |
| Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{3}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1007 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{468}\right)\) | \(e\left(\frac{199}{468}\right)\) | \(e\left(\frac{79}{234}\right)\) | \(e\left(\frac{229}{468}\right)\) | \(e\left(\frac{139}{234}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{199}{234}\right)\) | \(e\left(\frac{77}{117}\right)\) | \(e\left(\frac{53}{78}\right)\) |