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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 669.o
\(\chi_{669}(29,\cdot)\) \(\chi_{669}(38,\cdot)\) \(\chi_{669}(47,\cdot)\) \(\chi_{669}(50,\cdot)\) \(\chi_{669}(53,\cdot)\) \(\chi_{669}(62,\cdot)\) \(\chi_{669}(65,\cdot)\) \(\chi_{669}(74,\cdot)\) \(\chi_{669}(83,\cdot)\) \(\chi_{669}(86,\cdot)\) \(\chi_{669}(89,\cdot)\) \(\chi_{669}(101,\cdot)\) \(\chi_{669}(110,\cdot)\) \(\chi_{669}(116,\cdot)\) \(\chi_{669}(131,\cdot)\) \(\chi_{669}(143,\cdot)\) \(\chi_{669}(146,\cdot)\) \(\chi_{669}(152,\cdot)\) \(\chi_{669}(179,\cdot)\) \(\chi_{669}(188,\cdot)\) \(\chi_{669}(200,\cdot)\) \(\chi_{669}(203,\cdot)\) \(\chi_{669}(212,\cdot)\) \(\chi_{669}(218,\cdot)\) \(\chi_{669}(242,\cdot)\) \(\chi_{669}(248,\cdot)\) \(\chi_{669}(254,\cdot)\) \(\chi_{669}(260,\cdot)\) \(\chi_{669}(266,\cdot)\) \(\chi_{669}(278,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((224,226)\) → \((-1,e\left(\frac{65}{111}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 669 }(38, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{74}\right)\) | \(e\left(\frac{30}{37}\right)\) | \(e\left(\frac{137}{222}\right)\) | \(e\left(\frac{36}{37}\right)\) | \(e\left(\frac{53}{74}\right)\) | \(e\left(\frac{58}{111}\right)\) | \(e\left(\frac{35}{222}\right)\) | \(e\left(\frac{3}{37}\right)\) | \(e\left(\frac{65}{74}\right)\) | \(e\left(\frac{23}{37}\right)\) |