Basic properties
Modulus: | \(847\) | |
Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(165\) | 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 847.bc
\(\chi_{847}(4,\cdot)\) \(\chi_{847}(16,\cdot)\) \(\chi_{847}(25,\cdot)\) \(\chi_{847}(37,\cdot)\) \(\chi_{847}(53,\cdot)\) \(\chi_{847}(58,\cdot)\) \(\chi_{847}(60,\cdot)\) \(\chi_{847}(86,\cdot)\) \(\chi_{847}(93,\cdot)\) \(\chi_{847}(102,\cdot)\) \(\chi_{847}(114,\cdot)\) \(\chi_{847}(135,\cdot)\) \(\chi_{847}(137,\cdot)\) \(\chi_{847}(158,\cdot)\) \(\chi_{847}(163,\cdot)\) \(\chi_{847}(170,\cdot)\) \(\chi_{847}(179,\cdot)\) \(\chi_{847}(191,\cdot)\) \(\chi_{847}(207,\cdot)\) \(\chi_{847}(212,\cdot)\) \(\chi_{847}(214,\cdot)\) \(\chi_{847}(235,\cdot)\) \(\chi_{847}(240,\cdot)\) \(\chi_{847}(247,\cdot)\) \(\chi_{847}(256,\cdot)\) \(\chi_{847}(268,\cdot)\) \(\chi_{847}(284,\cdot)\) \(\chi_{847}(289,\cdot)\) \(\chi_{847}(291,\cdot)\) \(\chi_{847}(312,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((122,365)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{31}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
\( \chi_{ 847 }(235, a) \) | \(1\) | \(1\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{131}{165}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{51}{55}\right)\) |