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.jx
\(\chi_{4033}(39,\cdot)\) \(\chi_{4033}(200,\cdot)\) \(\chi_{4033}(351,\cdot)\) \(\chi_{4033}(597,\cdot)\) \(\chi_{4033}(607,\cdot)\) \(\chi_{4033}(612,\cdot)\) \(\chi_{4033}(912,\cdot)\) \(\chi_{4033}(1127,\cdot)\) \(\chi_{4033}(1149,\cdot)\) \(\chi_{4033}(1243,\cdot)\) \(\chi_{4033}(1278,\cdot)\) \(\chi_{4033}(1430,\cdot)\) \(\chi_{4033}(1475,\cdot)\) \(\chi_{4033}(1515,\cdot)\) \(\chi_{4033}(1536,\cdot)\) \(\chi_{4033}(1758,\cdot)\) \(\chi_{4033}(1800,\cdot)\) \(\chi_{4033}(1956,\cdot)\) \(\chi_{4033}(2077,\cdot)\) \(\chi_{4033}(2233,\cdot)\) \(\chi_{4033}(2275,\cdot)\) \(\chi_{4033}(2497,\cdot)\) \(\chi_{4033}(2518,\cdot)\) \(\chi_{4033}(2558,\cdot)\) \(\chi_{4033}(2603,\cdot)\) \(\chi_{4033}(2755,\cdot)\) \(\chi_{4033}(2790,\cdot)\) \(\chi_{4033}(2884,\cdot)\) \(\chi_{4033}(2906,\cdot)\) \(\chi_{4033}(3121,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{35}{36}\right),e\left(\frac{97}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(1758, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{67}{108}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(-1\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{85}{108}\right)\) | \(e\left(\frac{77}{108}\right)\) |