Basic properties
| Modulus: | \(8033\) | |
| Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(161\) | 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 8033.cc
\(\chi_{8033}(16,\cdot)\) \(\chi_{8033}(52,\cdot)\) \(\chi_{8033}(169,\cdot)\) \(\chi_{8033}(256,\cdot)\) \(\chi_{8033}(480,\cdot)\) \(\chi_{8033}(488,\cdot)\) \(\chi_{8033}(513,\cdot)\) \(\chi_{8033}(790,\cdot)\) \(\chi_{8033}(861,\cdot)\) \(\chi_{8033}(915,\cdot)\) \(\chi_{8033}(1006,\cdot)\) \(\chi_{8033}(1067,\cdot)\) \(\chi_{8033}(1127,\cdot)\) \(\chi_{8033}(1138,\cdot)\) \(\chi_{8033}(1263,\cdot)\) \(\chi_{8033}(1272,\cdot)\) \(\chi_{8033}(1283,\cdot)\) \(\chi_{8033}(1321,\cdot)\) \(\chi_{8033}(1412,\cdot)\) \(\chi_{8033}(1415,\cdot)\) \(\chi_{8033}(1437,\cdot)\) \(\chi_{8033}(1560,\cdot)\) \(\chi_{8033}(1586,\cdot)\) \(\chi_{8033}(1649,\cdot)\) \(\chi_{8033}(1678,\cdot)\) \(\chi_{8033}(1689,\cdot)\) \(\chi_{8033}(1731,\cdot)\) \(\chi_{8033}(1793,\cdot)\) \(\chi_{8033}(1863,\cdot)\) \(\chi_{8033}(1880,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{161})$ |
| Fixed field: | Number field defined by a degree 161 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{1}{7}\right),e\left(\frac{20}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8033 }(1437, a) \) | \(1\) | \(1\) | \(e\left(\frac{156}{161}\right)\) | \(e\left(\frac{31}{161}\right)\) | \(e\left(\frac{151}{161}\right)\) | \(e\left(\frac{2}{161}\right)\) | \(e\left(\frac{26}{161}\right)\) | \(e\left(\frac{136}{161}\right)\) | \(e\left(\frac{146}{161}\right)\) | \(e\left(\frac{62}{161}\right)\) | \(e\left(\frac{158}{161}\right)\) | \(e\left(\frac{106}{161}\right)\) |