Basic properties
Modulus: | \(4033\) | |
Conductor: | \(4033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(108\) | 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 4033.ja
\(\chi_{4033}(11,\cdot)\) \(\chi_{4033}(159,\cdot)\) \(\chi_{4033}(212,\cdot)\) \(\chi_{4033}(418,\cdot)\) \(\chi_{4033}(825,\cdot)\) \(\chi_{4033}(878,\cdot)\) \(\chi_{4033}(1100,\cdot)\) \(\chi_{4033}(1269,\cdot)\) \(\chi_{4033}(1322,\cdot)\) \(\chi_{4033}(1359,\cdot)\) \(\chi_{4033}(1380,\cdot)\) \(\chi_{4033}(1454,\cdot)\) \(\chi_{4033}(1470,\cdot)\) \(\chi_{4033}(1565,\cdot)\) \(\chi_{4033}(1692,\cdot)\) \(\chi_{4033}(1840,\cdot)\) \(\chi_{4033}(1877,\cdot)\) \(\chi_{4033}(2009,\cdot)\) \(\chi_{4033}(2358,\cdot)\) \(\chi_{4033}(2416,\cdot)\) \(\chi_{4033}(2675,\cdot)\) \(\chi_{4033}(2765,\cdot)\) \(\chi_{4033}(2823,\cdot)\) \(\chi_{4033}(3008,\cdot)\) \(\chi_{4033}(3082,\cdot)\) \(\chi_{4033}(3119,\cdot)\) \(\chi_{4033}(3246,\cdot)\) \(\chi_{4033}(3283,\cdot)\) \(\chi_{4033}(3431,\cdot)\) \(\chi_{4033}(3653,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{13}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1840, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{67}{108}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{107}{108}\right)\) |