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.jo
\(\chi_{4033}(153,\cdot)\) \(\chi_{4033}(277,\cdot)\) \(\chi_{4033}(385,\cdot)\) \(\chi_{4033}(394,\cdot)\) \(\chi_{4033}(664,\cdot)\) \(\chi_{4033}(833,\cdot)\) \(\chi_{4033}(866,\cdot)\) \(\chi_{4033}(886,\cdot)\) \(\chi_{4033}(1060,\cdot)\) \(\chi_{4033}(1130,\cdot)\) \(\chi_{4033}(1223,\cdot)\) \(\chi_{4033}(1290,\cdot)\) \(\chi_{4033}(1345,\cdot)\) \(\chi_{4033}(1646,\cdot)\) \(\chi_{4033}(1648,\cdot)\) \(\chi_{4033}(1687,\cdot)\) \(\chi_{4033}(1697,\cdot)\) \(\chi_{4033}(2015,\cdot)\) \(\chi_{4033}(2018,\cdot)\) \(\chi_{4033}(2336,\cdot)\) \(\chi_{4033}(2346,\cdot)\) \(\chi_{4033}(2385,\cdot)\) \(\chi_{4033}(2387,\cdot)\) \(\chi_{4033}(2688,\cdot)\) \(\chi_{4033}(2743,\cdot)\) \(\chi_{4033}(2810,\cdot)\) \(\chi_{4033}(2903,\cdot)\) \(\chi_{4033}(2973,\cdot)\) \(\chi_{4033}(3147,\cdot)\) \(\chi_{4033}(3167,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{23}{36}\right),e\left(\frac{53}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(2743, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{107}{108}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{65}{108}\right)\) | \(e\left(\frac{97}{108}\right)\) |