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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4033.jn
\(\chi_{4033}(42,\cdot)\) \(\chi_{4033}(50,\cdot)\) \(\chi_{4033}(96,\cdot)\) \(\chi_{4033}(242,\cdot)\) \(\chi_{4033}(274,\cdot)\) \(\chi_{4033}(442,\cdot)\) \(\chi_{4033}(610,\cdot)\) \(\chi_{4033}(614,\cdot)\) \(\chi_{4033}(624,\cdot)\) \(\chi_{4033}(923,\cdot)\) \(\chi_{4033}(1038,\cdot)\) \(\chi_{4033}(1160,\cdot)\) \(\chi_{4033}(1319,\cdot)\) \(\chi_{4033}(1573,\cdot)\) \(\chi_{4033}(1645,\cdot)\) \(\chi_{4033}(1781,\cdot)\) \(\chi_{4033}(1867,\cdot)\) \(\chi_{4033}(1980,\cdot)\) \(\chi_{4033}(2053,\cdot)\) \(\chi_{4033}(2166,\cdot)\) \(\chi_{4033}(2252,\cdot)\) \(\chi_{4033}(2388,\cdot)\) \(\chi_{4033}(2460,\cdot)\) \(\chi_{4033}(2714,\cdot)\) \(\chi_{4033}(2873,\cdot)\) \(\chi_{4033}(2995,\cdot)\) \(\chi_{4033}(3110,\cdot)\) \(\chi_{4033}(3409,\cdot)\) \(\chi_{4033}(3419,\cdot)\) \(\chi_{4033}(3423,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{5}{36}\right),e\left(\frac{23}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(624, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{41}{108}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{71}{108}\right)\) | \(e\left(\frac{91}{108}\right)\) |