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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1007.bi
\(\chi_{1007}(2,\cdot)\) \(\chi_{1007}(3,\cdot)\) \(\chi_{1007}(14,\cdot)\) \(\chi_{1007}(21,\cdot)\) \(\chi_{1007}(22,\cdot)\) \(\chi_{1007}(32,\cdot)\) \(\chi_{1007}(33,\cdot)\) \(\chi_{1007}(34,\cdot)\) \(\chi_{1007}(41,\cdot)\) \(\chi_{1007}(48,\cdot)\) \(\chi_{1007}(51,\cdot)\) \(\chi_{1007}(67,\cdot)\) \(\chi_{1007}(71,\cdot)\) \(\chi_{1007}(72,\cdot)\) \(\chi_{1007}(79,\cdot)\) \(\chi_{1007}(86,\cdot)\) \(\chi_{1007}(98,\cdot)\) \(\chi_{1007}(108,\cdot)\) \(\chi_{1007}(109,\cdot)\) \(\chi_{1007}(124,\cdot)\) \(\chi_{1007}(127,\cdot)\) \(\chi_{1007}(128,\cdot)\) \(\chi_{1007}(147,\cdot)\) \(\chi_{1007}(154,\cdot)\) \(\chi_{1007}(162,\cdot)\) \(\chi_{1007}(167,\cdot)\) \(\chi_{1007}(173,\cdot)\) \(\chi_{1007}(181,\cdot)\) \(\chi_{1007}(185,\cdot)\) \(\chi_{1007}(186,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{468})$ |
Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{31}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1007 }(763, a) \) | \(1\) | \(1\) | \(e\left(\frac{149}{468}\right)\) | \(e\left(\frac{245}{468}\right)\) | \(e\left(\frac{149}{234}\right)\) | \(e\left(\frac{269}{468}\right)\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{149}{156}\right)\) | \(e\left(\frac{11}{234}\right)\) | \(e\left(\frac{209}{234}\right)\) | \(e\left(\frac{19}{78}\right)\) |