Basic properties
Modulus: | \(647\) | |
Conductor: | \(647\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(323\) | 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 647.g
\(\chi_{647}(2,\cdot)\) \(\chi_{647}(3,\cdot)\) \(\chi_{647}(4,\cdot)\) \(\chi_{647}(6,\cdot)\) \(\chi_{647}(7,\cdot)\) \(\chi_{647}(8,\cdot)\) \(\chi_{647}(9,\cdot)\) \(\chi_{647}(12,\cdot)\) \(\chi_{647}(13,\cdot)\) \(\chi_{647}(14,\cdot)\) \(\chi_{647}(16,\cdot)\) \(\chi_{647}(17,\cdot)\) \(\chi_{647}(18,\cdot)\) \(\chi_{647}(21,\cdot)\) \(\chi_{647}(24,\cdot)\) \(\chi_{647}(25,\cdot)\) \(\chi_{647}(26,\cdot)\) \(\chi_{647}(27,\cdot)\) \(\chi_{647}(28,\cdot)\) \(\chi_{647}(29,\cdot)\) \(\chi_{647}(31,\cdot)\) \(\chi_{647}(32,\cdot)\) \(\chi_{647}(34,\cdot)\) \(\chi_{647}(36,\cdot)\) \(\chi_{647}(39,\cdot)\) \(\chi_{647}(41,\cdot)\) \(\chi_{647}(42,\cdot)\) \(\chi_{647}(48,\cdot)\) \(\chi_{647}(49,\cdot)\) \(\chi_{647}(50,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{323})$ |
Fixed field: | Number field defined by a degree 323 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{79}{323}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 647 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{208}{323}\right)\) | \(e\left(\frac{167}{323}\right)\) | \(e\left(\frac{93}{323}\right)\) | \(e\left(\frac{79}{323}\right)\) | \(e\left(\frac{52}{323}\right)\) | \(e\left(\frac{243}{323}\right)\) | \(e\left(\frac{301}{323}\right)\) | \(e\left(\frac{11}{323}\right)\) | \(e\left(\frac{287}{323}\right)\) | \(e\left(\frac{108}{323}\right)\) |