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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4033.io
\(\chi_{4033}(30,\cdot)\) \(\chi_{4033}(67,\cdot)\) \(\chi_{4033}(262,\cdot)\) \(\chi_{4033}(321,\cdot)\) \(\chi_{4033}(696,\cdot)\) \(\chi_{4033}(733,\cdot)\) \(\chi_{4033}(854,\cdot)\) \(\chi_{4033}(987,\cdot)\) \(\chi_{4033}(1040,\cdot)\) \(\chi_{4033}(1175,\cdot)\) \(\chi_{4033}(1188,\cdot)\) \(\chi_{4033}(1261,\cdot)\) \(\chi_{4033}(1468,\cdot)\) \(\chi_{4033}(1730,\cdot)\) \(\chi_{4033}(1797,\cdot)\) \(\chi_{4033}(1801,\cdot)\) \(\chi_{4033}(1952,\cdot)\) \(\chi_{4033}(2167,\cdot)\) \(\chi_{4033}(2361,\cdot)\) \(\chi_{4033}(2409,\cdot)\) \(\chi_{4033}(2435,\cdot)\) \(\chi_{4033}(2445,\cdot)\) \(\chi_{4033}(2557,\cdot)\) \(\chi_{4033}(2685,\cdot)\) \(\chi_{4033}(2852,\cdot)\) \(\chi_{4033}(3062,\cdot)\) \(\chi_{4033}(3092,\cdot)\) \(\chi_{4033}(3284,\cdot)\) \(\chi_{4033}(3444,\cdot)\) \(\chi_{4033}(3540,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{89}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(262, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{35}{108}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{101}{108}\right)\) | \(e\left(\frac{7}{108}\right)\) |