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.iv
\(\chi_{4033}(124,\cdot)\) \(\chi_{4033}(227,\cdot)\) \(\chi_{4033}(352,\cdot)\) \(\chi_{4033}(353,\cdot)\) \(\chi_{4033}(457,\cdot)\) \(\chi_{4033}(533,\cdot)\) \(\chi_{4033}(727,\cdot)\) \(\chi_{4033}(772,\cdot)\) \(\chi_{4033}(907,\cdot)\) \(\chi_{4033}(1093,\cdot)\) \(\chi_{4033}(1095,\cdot)\) \(\chi_{4033}(1206,\cdot)\) \(\chi_{4033}(1497,\cdot)\) \(\chi_{4033}(1541,\cdot)\) \(\chi_{4033}(1684,\cdot)\) \(\chi_{4033}(1874,\cdot)\) \(\chi_{4033}(2040,\cdot)\) \(\chi_{4033}(2168,\cdot)\) \(\chi_{4033}(2370,\cdot)\) \(\chi_{4033}(2423,\cdot)\) \(\chi_{4033}(2533,\cdot)\) \(\chi_{4033}(2555,\cdot)\) \(\chi_{4033}(2585,\cdot)\) \(\chi_{4033}(2588,\cdot)\) \(\chi_{4033}(2773,\cdot)\) \(\chi_{4033}(2814,\cdot)\) \(\chi_{4033}(2965,\cdot)\) \(\chi_{4033}(2978,\cdot)\) \(\chi_{4033}(3032,\cdot)\) \(\chi_{4033}(3273,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{31}{36}\right),e\left(\frac{19}{27}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1095, a) \) | \(-1\) | \(1\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{31}{108}\right)\) | \(e\left(\frac{103}{108}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{13}{54}\right)\) |