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.hy
\(\chi_{4033}(24,\cdot)\) \(\chi_{4033}(166,\cdot)\) \(\chi_{4033}(168,\cdot)\) \(\chi_{4033}(466,\cdot)\) \(\chi_{4033}(476,\cdot)\) \(\chi_{4033}(701,\cdot)\) \(\chi_{4033}(942,\cdot)\) \(\chi_{4033}(994,\cdot)\) \(\chi_{4033}(1108,\cdot)\) \(\chi_{4033}(1132,\cdot)\) \(\chi_{4033}(1162,\cdot)\) \(\chi_{4033}(1314,\cdot)\) \(\chi_{4033}(1364,\cdot)\) \(\chi_{4033}(1482,\cdot)\) \(\chi_{4033}(1537,\cdot)\) \(\chi_{4033}(1795,\cdot)\) \(\chi_{4033}(1863,\cdot)\) \(\chi_{4033}(1948,\cdot)\) \(\chi_{4033}(2085,\cdot)\) \(\chi_{4033}(2170,\cdot)\) \(\chi_{4033}(2238,\cdot)\) \(\chi_{4033}(2496,\cdot)\) \(\chi_{4033}(2551,\cdot)\) \(\chi_{4033}(2669,\cdot)\) \(\chi_{4033}(2719,\cdot)\) \(\chi_{4033}(2871,\cdot)\) \(\chi_{4033}(2901,\cdot)\) \(\chi_{4033}(2925,\cdot)\) \(\chi_{4033}(3039,\cdot)\) \(\chi_{4033}(3091,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{31}{36}\right),e\left(\frac{41}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1132, a) \) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{7}{54}\right)\) | \(1\) | \(e\left(\frac{71}{108}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(-1\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{17}{108}\right)\) | \(e\left(\frac{37}{108}\right)\) |