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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4033.jg
\(\chi_{4033}(29,\cdot)\) \(\chi_{4033}(60,\cdot)\) \(\chi_{4033}(88,\cdot)\) \(\chi_{4033}(230,\cdot)\) \(\chi_{4033}(421,\cdot)\) \(\chi_{4033}(467,\cdot)\) \(\chi_{4033}(674,\cdot)\) \(\chi_{4033}(754,\cdot)\) \(\chi_{4033}(837,\cdot)\) \(\chi_{4033}(933,\cdot)\) \(\chi_{4033}(1102,\cdot)\) \(\chi_{4033}(1118,\cdot)\) \(\chi_{4033}(1192,\cdot)\) \(\chi_{4033}(1235,\cdot)\) \(\chi_{4033}(1303,\cdot)\) \(\chi_{4033}(1392,\cdot)\) \(\chi_{4033}(1414,\cdot)\) \(\chi_{4033}(1546,\cdot)\) \(\chi_{4033}(1614,\cdot)\) \(\chi_{4033}(1805,\cdot)\) \(\chi_{4033}(1947,\cdot)\) \(\chi_{4033}(1990,\cdot)\) \(\chi_{4033}(2049,\cdot)\) \(\chi_{4033}(2064,\cdot)\) \(\chi_{4033}(2154,\cdot)\) \(\chi_{4033}(2175,\cdot)\) \(\chi_{4033}(2280,\cdot)\) \(\chi_{4033}(2286,\cdot)\) \(\chi_{4033}(2567,\cdot)\) \(\chi_{4033}(2761,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{11}{12}\right),e\left(\frac{13}{54}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(2567, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{41}{108}\right)\) | \(e\left(\frac{107}{108}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{13}{27}\right)\) |