Basic properties
Modulus: | \(669\) | |
Conductor: | \(669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(222\) | 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 669.p
\(\chi_{669}(5,\cdot)\) \(\chi_{669}(11,\cdot)\) \(\chi_{669}(20,\cdot)\) \(\chi_{669}(23,\cdot)\) \(\chi_{669}(35,\cdot)\) \(\chi_{669}(44,\cdot)\) \(\chi_{669}(71,\cdot)\) \(\chi_{669}(77,\cdot)\) \(\chi_{669}(80,\cdot)\) \(\chi_{669}(92,\cdot)\) \(\chi_{669}(107,\cdot)\) \(\chi_{669}(113,\cdot)\) \(\chi_{669}(122,\cdot)\) \(\chi_{669}(134,\cdot)\) \(\chi_{669}(137,\cdot)\) \(\chi_{669}(140,\cdot)\) \(\chi_{669}(149,\cdot)\) \(\chi_{669}(158,\cdot)\) \(\chi_{669}(161,\cdot)\) \(\chi_{669}(170,\cdot)\) \(\chi_{669}(173,\cdot)\) \(\chi_{669}(176,\cdot)\) \(\chi_{669}(185,\cdot)\) \(\chi_{669}(194,\cdot)\) \(\chi_{669}(233,\cdot)\) \(\chi_{669}(245,\cdot)\) \(\chi_{669}(269,\cdot)\) \(\chi_{669}(284,\cdot)\) \(\chi_{669}(290,\cdot)\) \(\chi_{669}(293,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{111})$ |
Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((224,226)\) → \((-1,e\left(\frac{73}{222}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 669 }(284, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{74}\right)\) | \(e\left(\frac{14}{37}\right)\) | \(e\left(\frac{85}{111}\right)\) | \(e\left(\frac{2}{37}\right)\) | \(e\left(\frac{5}{74}\right)\) | \(e\left(\frac{101}{222}\right)\) | \(e\left(\frac{76}{111}\right)\) | \(e\left(\frac{25}{74}\right)\) | \(e\left(\frac{55}{74}\right)\) | \(e\left(\frac{28}{37}\right)\) |