Basic properties
| Modulus: | \(871\) | |
| Conductor: | \(871\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | 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 871.cg
\(\chi_{871}(6,\cdot)\) \(\chi_{871}(19,\cdot)\) \(\chi_{871}(84,\cdot)\) \(\chi_{871}(93,\cdot)\) \(\chi_{871}(102,\cdot)\) \(\chi_{871}(150,\cdot)\) \(\chi_{871}(167,\cdot)\) \(\chi_{871}(188,\cdot)\) \(\chi_{871}(236,\cdot)\) \(\chi_{871}(240,\cdot)\) \(\chi_{871}(266,\cdot)\) \(\chi_{871}(301,\cdot)\) \(\chi_{871}(323,\cdot)\) \(\chi_{871}(345,\cdot)\) \(\chi_{871}(358,\cdot)\) \(\chi_{871}(384,\cdot)\) \(\chi_{871}(457,\cdot)\) \(\chi_{871}(475,\cdot)\) \(\chi_{871}(488,\cdot)\) \(\chi_{871}(505,\cdot)\) \(\chi_{871}(552,\cdot)\) \(\chi_{871}(553,\cdot)\) \(\chi_{871}(557,\cdot)\) \(\chi_{871}(583,\cdot)\) \(\chi_{871}(596,\cdot)\) \(\chi_{871}(639,\cdot)\) \(\chi_{871}(657,\cdot)\) \(\chi_{871}(674,\cdot)\) \(\chi_{871}(691,\cdot)\) \(\chi_{871}(709,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((470,404)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{20}{33}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 871 }(6, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{89}{132}\right)\) |