Basic properties
| Modulus: | \(2011\) | |
| Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(201\) | 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 2011.k
\(\chi_{2011}(4,\cdot)\) \(\chi_{2011}(16,\cdot)\) \(\chi_{2011}(30,\cdot)\) \(\chi_{2011}(115,\cdot)\) \(\chi_{2011}(117,\cdot)\) \(\chi_{2011}(120,\cdot)\) \(\chi_{2011}(134,\cdot)\) \(\chi_{2011}(189,\cdot)\) \(\chi_{2011}(193,\cdot)\) \(\chi_{2011}(194,\cdot)\) \(\chi_{2011}(209,\cdot)\) \(\chi_{2011}(211,\cdot)\) \(\chi_{2011}(225,\cdot)\) \(\chi_{2011}(237,\cdot)\) \(\chi_{2011}(256,\cdot)\) \(\chi_{2011}(279,\cdot)\) \(\chi_{2011}(286,\cdot)\) \(\chi_{2011}(294,\cdot)\) \(\chi_{2011}(296,\cdot)\) \(\chi_{2011}(297,\cdot)\) \(\chi_{2011}(311,\cdot)\) \(\chi_{2011}(323,\cdot)\) \(\chi_{2011}(339,\cdot)\) \(\chi_{2011}(350,\cdot)\) \(\chi_{2011}(371,\cdot)\) \(\chi_{2011}(412,\cdot)\) \(\chi_{2011}(426,\cdot)\) \(\chi_{2011}(442,\cdot)\) \(\chi_{2011}(459,\cdot)\) \(\chi_{2011}(466,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{201})$ |
| Fixed field: | Number field defined by a degree 201 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{98}{201}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2011 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{201}\right)\) | \(e\left(\frac{98}{201}\right)\) | \(e\left(\frac{182}{201}\right)\) | \(e\left(\frac{53}{201}\right)\) | \(e\left(\frac{63}{67}\right)\) | \(e\left(\frac{5}{201}\right)\) | \(e\left(\frac{24}{67}\right)\) | \(e\left(\frac{196}{201}\right)\) | \(e\left(\frac{48}{67}\right)\) | \(e\left(\frac{121}{201}\right)\) |