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
\(5\) → \(e\left(\frac{525}{646}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 647 }(30, a) \) | \(-1\) | \(1\) | \(e\left(\frac{131}{323}\right)\) | \(e\left(\frac{144}{323}\right)\) | \(e\left(\frac{262}{323}\right)\) | \(e\left(\frac{525}{646}\right)\) | \(e\left(\frac{275}{323}\right)\) | \(e\left(\frac{49}{323}\right)\) | \(e\left(\frac{70}{323}\right)\) | \(e\left(\frac{288}{323}\right)\) | \(e\left(\frac{141}{646}\right)\) | \(e\left(\frac{223}{646}\right)\) |