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.iu
\(\chi_{4033}(20,\cdot)\) \(\chi_{4033}(254,\cdot)\) \(\chi_{4033}(279,\cdot)\) \(\chi_{4033}(464,\cdot)\) \(\chi_{4033}(536,\cdot)\) \(\chi_{4033}(557,\cdot)\) \(\chi_{4033}(605,\cdot)\) \(\chi_{4033}(651,\cdot)\) \(\chi_{4033}(685,\cdot)\) \(\chi_{4033}(775,\cdot)\) \(\chi_{4033}(792,\cdot)\) \(\chi_{4033}(1382,\cdot)\) \(\chi_{4033}(1391,\cdot)\) \(\chi_{4033}(1519,\cdot)\) \(\chi_{4033}(1630,\cdot)\) \(\chi_{4033}(1737,\cdot)\) \(\chi_{4033}(1831,\cdot)\) \(\chi_{4033}(1848,\cdot)\) \(\chi_{4033}(1937,\cdot)\) \(\chi_{4033}(2022,\cdot)\) \(\chi_{4033}(2200,\cdot)\) \(\chi_{4033}(2427,\cdot)\) \(\chi_{4033}(2459,\cdot)\) \(\chi_{4033}(2498,\cdot)\) \(\chi_{4033}(2595,\cdot)\) \(\chi_{4033}(2644,\cdot)\) \(\chi_{4033}(2756,\cdot)\) \(\chi_{4033}(2799,\cdot)\) \(\chi_{4033}(2928,\cdot)\) \(\chi_{4033}(3049,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{23}{36}\right),e\left(\frac{19}{54}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(2595, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{47}{108}\right)\) | \(e\left(\frac{65}{108}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{10}{27}\right)\) |