Basic properties
Modulus: | \(647\) | |
Conductor: | \(647\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(646\) | 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 647.h
\(\chi_{647}(5,\cdot)\) \(\chi_{647}(10,\cdot)\) \(\chi_{647}(11,\cdot)\) \(\chi_{647}(15,\cdot)\) \(\chi_{647}(19,\cdot)\) \(\chi_{647}(20,\cdot)\) \(\chi_{647}(22,\cdot)\) \(\chi_{647}(23,\cdot)\) \(\chi_{647}(30,\cdot)\) \(\chi_{647}(33,\cdot)\) \(\chi_{647}(35,\cdot)\) \(\chi_{647}(37,\cdot)\) \(\chi_{647}(38,\cdot)\) \(\chi_{647}(44,\cdot)\) \(\chi_{647}(45,\cdot)\) \(\chi_{647}(46,\cdot)\) \(\chi_{647}(47,\cdot)\) \(\chi_{647}(57,\cdot)\) \(\chi_{647}(59,\cdot)\) \(\chi_{647}(60,\cdot)\) \(\chi_{647}(61,\cdot)\) \(\chi_{647}(65,\cdot)\) \(\chi_{647}(66,\cdot)\) \(\chi_{647}(69,\cdot)\) \(\chi_{647}(70,\cdot)\) \(\chi_{647}(71,\cdot)\) \(\chi_{647}(73,\cdot)\) \(\chi_{647}(76,\cdot)\) \(\chi_{647}(77,\cdot)\) \(\chi_{647}(80,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{323})$ |
Fixed field: | Number field defined by a degree 646 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{317}{646}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 647 }(20, a) \) | \(-1\) | \(1\) | \(e\left(\frac{172}{323}\right)\) | \(e\left(\frac{194}{323}\right)\) | \(e\left(\frac{21}{323}\right)\) | \(e\left(\frac{317}{646}\right)\) | \(e\left(\frac{43}{323}\right)\) | \(e\left(\frac{232}{323}\right)\) | \(e\left(\frac{193}{323}\right)\) | \(e\left(\frac{65}{323}\right)\) | \(e\left(\frac{15}{646}\right)\) | \(e\left(\frac{601}{646}\right)\) |