Basic properties
| Modulus: | \(8033\) | |
| Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(644\) | 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.co
\(\chi_{8033}(33,\cdot)\) \(\chi_{8033}(38,\cdot)\) \(\chi_{8033}(42,\cdot)\) \(\chi_{8033}(51,\cdot)\) \(\chi_{8033}(109,\cdot)\) \(\chi_{8033}(125,\cdot)\) \(\chi_{8033}(129,\cdot)\) \(\chi_{8033}(138,\cdot)\) \(\chi_{8033}(149,\cdot)\) \(\chi_{8033}(216,\cdot)\) \(\chi_{8033}(245,\cdot)\) \(\chi_{8033}(303,\cdot)\) \(\chi_{8033}(328,\cdot)\) \(\chi_{8033}(381,\cdot)\) \(\chi_{8033}(386,\cdot)\) \(\chi_{8033}(415,\cdot)\) \(\chi_{8033}(528,\cdot)\) \(\chi_{8033}(556,\cdot)\) \(\chi_{8033}(586,\cdot)\) \(\chi_{8033}(615,\cdot)\) \(\chi_{8033}(672,\cdot)\) \(\chi_{8033}(702,\cdot)\) \(\chi_{8033}(758,\cdot)\) \(\chi_{8033}(789,\cdot)\) \(\chi_{8033}(805,\cdot)\) \(\chi_{8033}(816,\cdot)\) \(\chi_{8033}(846,\cdot)\) \(\chi_{8033}(863,\cdot)\) \(\chi_{8033}(892,\cdot)\) \(\chi_{8033}(904,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{644})$ |
| Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{1}{14}\right),e\left(\frac{65}{92}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8033 }(33, a) \) | \(-1\) | \(1\) | \(e\left(\frac{599}{644}\right)\) | \(e\left(\frac{59}{322}\right)\) | \(e\left(\frac{277}{322}\right)\) | \(e\left(\frac{179}{644}\right)\) | \(e\left(\frac{73}{644}\right)\) | \(e\left(\frac{129}{322}\right)\) | \(e\left(\frac{509}{644}\right)\) | \(e\left(\frac{59}{161}\right)\) | \(e\left(\frac{67}{322}\right)\) | \(e\left(\frac{471}{644}\right)\) |