Basic properties
| Modulus: | \(8033\) | |
| Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1932\) | 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 8033.cx
\(\chi_{8033}(20,\cdot)\) \(\chi_{8033}(24,\cdot)\) \(\chi_{8033}(45,\cdot)\) \(\chi_{8033}(53,\cdot)\) \(\chi_{8033}(65,\cdot)\) \(\chi_{8033}(78,\cdot)\) \(\chi_{8033}(94,\cdot)\) \(\chi_{8033}(103,\cdot)\) \(\chi_{8033}(107,\cdot)\) \(\chi_{8033}(110,\cdot)\) \(\chi_{8033}(111,\cdot)\) \(\chi_{8033}(140,\cdot)\) \(\chi_{8033}(170,\cdot)\) \(\chi_{8033}(181,\cdot)\) \(\chi_{8033}(197,\cdot)\) \(\chi_{8033}(199,\cdot)\) \(\chi_{8033}(219,\cdot)\) \(\chi_{8033}(227,\cdot)\) \(\chi_{8033}(257,\cdot)\) \(\chi_{8033}(297,\cdot)\) \(\chi_{8033}(335,\cdot)\) \(\chi_{8033}(342,\cdot)\) \(\chi_{8033}(355,\cdot)\) \(\chi_{8033}(371,\cdot)\) \(\chi_{8033}(373,\cdot)\) \(\chi_{8033}(384,\cdot)\) \(\chi_{8033}(401,\cdot)\) \(\chi_{8033}(430,\cdot)\) \(\chi_{8033}(451,\cdot)\) \(\chi_{8033}(455,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1932})$ |
| Fixed field: | Number field defined by a degree 1932 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{6}{7}\right),e\left(\frac{19}{276}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8033 }(20, a) \) | \(-1\) | \(1\) | \(e\left(\frac{629}{644}\right)\) | \(e\left(\frac{110}{483}\right)\) | \(e\left(\frac{307}{322}\right)\) | \(e\left(\frac{1789}{1932}\right)\) | \(e\left(\frac{395}{1932}\right)\) | \(e\left(\frac{773}{966}\right)\) | \(e\left(\frac{599}{644}\right)\) | \(e\left(\frac{220}{483}\right)\) | \(e\left(\frac{436}{483}\right)\) | \(e\left(\frac{1759}{1932}\right)\) |