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.jj
\(\chi_{4033}(57,\cdot)\) \(\chi_{4033}(283,\cdot)\) \(\chi_{4033}(422,\cdot)\) \(\chi_{4033}(486,\cdot)\) \(\chi_{4033}(644,\cdot)\) \(\chi_{4033}(721,\cdot)\) \(\chi_{4033}(883,\cdot)\) \(\chi_{4033}(1018,\cdot)\) \(\chi_{4033}(1034,\cdot)\) \(\chi_{4033}(1387,\cdot)\) \(\chi_{4033}(1404,\cdot)\) \(\chi_{4033}(1423,\cdot)\) \(\chi_{4033}(1502,\cdot)\) \(\chi_{4033}(1596,\cdot)\) \(\chi_{4033}(1726,\cdot)\) \(\chi_{4033}(1900,\cdot)\) \(\chi_{4033}(1904,\cdot)\) \(\chi_{4033}(1922,\cdot)\) \(\chi_{4033}(2111,\cdot)\) \(\chi_{4033}(2129,\cdot)\) \(\chi_{4033}(2133,\cdot)\) \(\chi_{4033}(2307,\cdot)\) \(\chi_{4033}(2437,\cdot)\) \(\chi_{4033}(2531,\cdot)\) \(\chi_{4033}(2610,\cdot)\) \(\chi_{4033}(2629,\cdot)\) \(\chi_{4033}(2646,\cdot)\) \(\chi_{4033}(2999,\cdot)\) \(\chi_{4033}(3015,\cdot)\) \(\chi_{4033}(3150,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{19}{36}\right),e\left(\frac{13}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1404, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{31}{108}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{73}{108}\right)\) | \(e\left(\frac{89}{108}\right)\) |