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.jy
\(\chi_{4033}(146,\cdot)\) \(\chi_{4033}(161,\cdot)\) \(\chi_{4033}(207,\cdot)\) \(\chi_{4033}(412,\cdot)\) \(\chi_{4033}(501,\cdot)\) \(\chi_{4033}(1239,\cdot)\) \(\chi_{4033}(1347,\cdot)\) \(\chi_{4033}(1512,\cdot)\) \(\chi_{4033}(1576,\cdot)\) \(\chi_{4033}(1593,\cdot)\) \(\chi_{4033}(1641,\cdot)\) \(\chi_{4033}(1682,\cdot)\) \(\chi_{4033}(1734,\cdot)\) \(\chi_{4033}(1757,\cdot)\) \(\chi_{4033}(1774,\cdot)\) \(\chi_{4033}(1906,\cdot)\) \(\chi_{4033}(1911,\cdot)\) \(\chi_{4033}(1944,\cdot)\) \(\chi_{4033}(2089,\cdot)\) \(\chi_{4033}(2122,\cdot)\) \(\chi_{4033}(2127,\cdot)\) \(\chi_{4033}(2259,\cdot)\) \(\chi_{4033}(2276,\cdot)\) \(\chi_{4033}(2299,\cdot)\) \(\chi_{4033}(2351,\cdot)\) \(\chi_{4033}(2392,\cdot)\) \(\chi_{4033}(2440,\cdot)\) \(\chi_{4033}(2457,\cdot)\) \(\chi_{4033}(2521,\cdot)\) \(\chi_{4033}(2686,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{35}{36}\right),e\left(\frac{13}{108}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4033 }(2276, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{55}{108}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(-1\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{37}{108}\right)\) | \(e\left(\frac{17}{108}\right)\) |