Basic properties
Modulus: | \(4033\) | |
Conductor: | \(4033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.jl
\(\chi_{4033}(6,\cdot)\) \(\chi_{4033}(228,\cdot)\) \(\chi_{4033}(265,\cdot)\) \(\chi_{4033}(290,\cdot)\) \(\chi_{4033}(450,\cdot)\) \(\chi_{4033}(475,\cdot)\) \(\chi_{4033}(487,\cdot)\) \(\chi_{4033}(598,\cdot)\) \(\chi_{4033}(672,\cdot)\) \(\chi_{4033}(968,\cdot)\) \(\chi_{4033}(1079,\cdot)\) \(\chi_{4033}(1338,\cdot)\) \(\chi_{4033}(1474,\cdot)\) \(\chi_{4033}(1486,\cdot)\) \(\chi_{4033}(1585,\cdot)\) \(\chi_{4033}(1659,\cdot)\) \(\chi_{4033}(1918,\cdot)\) \(\chi_{4033}(2004,\cdot)\) \(\chi_{4033}(2029,\cdot)\) \(\chi_{4033}(2115,\cdot)\) \(\chi_{4033}(2374,\cdot)\) \(\chi_{4033}(2448,\cdot)\) \(\chi_{4033}(2547,\cdot)\) \(\chi_{4033}(2559,\cdot)\) \(\chi_{4033}(2695,\cdot)\) \(\chi_{4033}(2954,\cdot)\) \(\chi_{4033}(3065,\cdot)\) \(\chi_{4033}(3361,\cdot)\) \(\chi_{4033}(3435,\cdot)\) \(\chi_{4033}(3546,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((-i,e\left(\frac{37}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(487, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{31}{108}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{101}{108}\right)\) |