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.jh
\(\chi_{4033}(140,\cdot)\) \(\chi_{4033}(193,\cdot)\) \(\chi_{4033}(347,\cdot)\) \(\chi_{4033}(356,\cdot)\) \(\chi_{4033}(415,\cdot)\) \(\chi_{4033}(510,\cdot)\) \(\chi_{4033}(606,\cdot)\) \(\chi_{4033}(748,\cdot)\) \(\chi_{4033}(791,\cdot)\) \(\chi_{4033}(865,\cdot)\) \(\chi_{4033}(976,\cdot)\) \(\chi_{4033}(1065,\cdot)\) \(\chi_{4033}(1081,\cdot)\) \(\chi_{4033}(1087,\cdot)\) \(\chi_{4033}(1287,\cdot)\) \(\chi_{4033}(1429,\cdot)\) \(\chi_{4033}(1562,\cdot)\) \(\chi_{4033}(1620,\cdot)\) \(\chi_{4033}(1827,\cdot)\) \(\chi_{4033}(1873,\cdot)\) \(\chi_{4033}(1953,\cdot)\) \(\chi_{4033}(2132,\cdot)\) \(\chi_{4033}(2317,\cdot)\) \(\chi_{4033}(2376,\cdot)\) \(\chi_{4033}(2391,\cdot)\) \(\chi_{4033}(2434,\cdot)\) \(\chi_{4033}(2502,\cdot)\) \(\chi_{4033}(2613,\cdot)\) \(\chi_{4033}(2863,\cdot)\) \(\chi_{4033}(2894,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{11}{12}\right),e\left(\frac{53}{54}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4033 }(1087, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{73}{108}\right)\) | \(e\left(\frac{79}{108}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{26}{27}\right)\) |