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.ik
\(\chi_{4033}(133,\cdot)\) \(\chi_{4033}(276,\cdot)\) \(\chi_{4033}(309,\cdot)\) \(\chi_{4033}(338,\cdot)\) \(\chi_{4033}(684,\cdot)\) \(\chi_{4033}(716,\cdot)\) \(\chi_{4033}(757,\cdot)\) \(\chi_{4033}(816,\cdot)\) \(\chi_{4033}(944,\cdot)\) \(\chi_{4033}(1031,\cdot)\) \(\chi_{4033}(1134,\cdot)\) \(\chi_{4033}(1186,\cdot)\) \(\chi_{4033}(1350,\cdot)\) \(\chi_{4033}(1704,\cdot)\) \(\chi_{4033}(1754,\cdot)\) \(\chi_{4033}(1796,\cdot)\) \(\chi_{4033}(1892,\cdot)\) \(\chi_{4033}(1976,\cdot)\) \(\chi_{4033}(2057,\cdot)\) \(\chi_{4033}(2141,\cdot)\) \(\chi_{4033}(2237,\cdot)\) \(\chi_{4033}(2279,\cdot)\) \(\chi_{4033}(2329,\cdot)\) \(\chi_{4033}(2683,\cdot)\) \(\chi_{4033}(2847,\cdot)\) \(\chi_{4033}(2899,\cdot)\) \(\chi_{4033}(3002,\cdot)\) \(\chi_{4033}(3089,\cdot)\) \(\chi_{4033}(3217,\cdot)\) \(\chi_{4033}(3276,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{29}{36}\right),e\left(\frac{89}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1134, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{17}{108}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{101}{108}\right)\) | \(e\left(\frac{61}{108}\right)\) |