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.ih
\(\chi_{4033}(14,\cdot)\) \(\chi_{4033}(51,\cdot)\) \(\chi_{4033}(162,\cdot)\) \(\chi_{4033}(208,\cdot)\) \(\chi_{4033}(288,\cdot)\) \(\chi_{4033}(430,\cdot)\) \(\chi_{4033}(473,\cdot)\) \(\chi_{4033}(532,\cdot)\) \(\chi_{4033}(822,\cdot)\) \(\chi_{4033}(1028,\cdot)\) \(\chi_{4033}(1050,\cdot)\) \(\chi_{4033}(1155,\cdot)\) \(\chi_{4033}(1266,\cdot)\) \(\chi_{4033}(1435,\cdot)\) \(\chi_{4033}(1842,\cdot)\) \(\chi_{4033}(1910,\cdot)\) \(\chi_{4033}(1932,\cdot)\) \(\chi_{4033}(1938,\cdot)\) \(\chi_{4033}(2095,\cdot)\) \(\chi_{4033}(2101,\cdot)\) \(\chi_{4033}(2123,\cdot)\) \(\chi_{4033}(2191,\cdot)\) \(\chi_{4033}(2598,\cdot)\) \(\chi_{4033}(2767,\cdot)\) \(\chi_{4033}(2878,\cdot)\) \(\chi_{4033}(2983,\cdot)\) \(\chi_{4033}(3005,\cdot)\) \(\chi_{4033}(3211,\cdot)\) \(\chi_{4033}(3501,\cdot)\) \(\chi_{4033}(3560,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{11}{12}\right),e\left(\frac{37}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{101}{108}\right)\) |