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.il
\(\chi_{4033}(31,\cdot)\) \(\chi_{4033}(302,\cdot)\) \(\chi_{4033}(339,\cdot)\) \(\chi_{4033}(401,\cdot)\) \(\chi_{4033}(524,\cdot)\) \(\chi_{4033}(783,\cdot)\) \(\chi_{4033}(857,\cdot)\) \(\chi_{4033}(956,\cdot)\) \(\chi_{4033}(993,\cdot)\) \(\chi_{4033}(1042,\cdot)\) \(\chi_{4033}(1178,\cdot)\) \(\chi_{4033}(1190,\cdot)\) \(\chi_{4033}(1227,\cdot)\) \(\chi_{4033}(1301,\cdot)\) \(\chi_{4033}(1412,\cdot)\) \(\chi_{4033}(1437,\cdot)\) \(\chi_{4033}(1511,\cdot)\) \(\chi_{4033}(1523,\cdot)\) \(\chi_{4033}(1671,\cdot)\) \(\chi_{4033}(1696,\cdot)\) \(\chi_{4033}(1844,\cdot)\) \(\chi_{4033}(1881,\cdot)\) \(\chi_{4033}(1955,\cdot)\) \(\chi_{4033}(2066,\cdot)\) \(\chi_{4033}(2177,\cdot)\) \(\chi_{4033}(2263,\cdot)\) \(\chi_{4033}(2325,\cdot)\) \(\chi_{4033}(2485,\cdot)\) \(\chi_{4033}(2917,\cdot)\) \(\chi_{4033}(3003,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((-i,e\left(\frac{23}{54}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1227, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{67}{108}\right)\) | \(e\left(\frac{73}{108}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{23}{27}\right)\) |