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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4033.jk
\(\chi_{4033}(156,\cdot)\) \(\chi_{4033}(384,\cdot)\) \(\chi_{4033}(399,\cdot)\) \(\chi_{4033}(563,\cdot)\) \(\chi_{4033}(569,\cdot)\) \(\chi_{4033}(584,\cdot)\) \(\chi_{4033}(970,\cdot)\) \(\chi_{4033}(1096,\cdot)\) \(\chi_{4033}(1229,\cdot)\) \(\chi_{4033}(1318,\cdot)\) \(\chi_{4033}(1457,\cdot)\) \(\chi_{4033}(1540,\cdot)\) \(\chi_{4033}(1577,\cdot)\) \(\chi_{4033}(1688,\cdot)\) \(\chi_{4033}(1694,\cdot)\) \(\chi_{4033}(1895,\cdot)\) \(\chi_{4033}(1975,\cdot)\) \(\chi_{4033}(2006,\cdot)\) \(\chi_{4033}(2027,\cdot)\) \(\chi_{4033}(2058,\cdot)\) \(\chi_{4033}(2138,\cdot)\) \(\chi_{4033}(2339,\cdot)\) \(\chi_{4033}(2345,\cdot)\) \(\chi_{4033}(2456,\cdot)\) \(\chi_{4033}(2493,\cdot)\) \(\chi_{4033}(2576,\cdot)\) \(\chi_{4033}(2715,\cdot)\) \(\chi_{4033}(2804,\cdot)\) \(\chi_{4033}(2937,\cdot)\) \(\chi_{4033}(3063,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{97}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1540, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{91}{108}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{49}{108}\right)\) | \(e\left(\frac{5}{108}\right)\) |