Basic properties
| Modulus: | \(4033\) | |
| Conductor: | \(109\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{109}(6,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4033.is
\(\chi_{4033}(149,\cdot)\) \(\chi_{4033}(260,\cdot)\) \(\chi_{4033}(297,\cdot)\) \(\chi_{4033}(371,\cdot)\) \(\chi_{4033}(556,\cdot)\) \(\chi_{4033}(630,\cdot)\) \(\chi_{4033}(667,\cdot)\) \(\chi_{4033}(704,\cdot)\) \(\chi_{4033}(815,\cdot)\) \(\chi_{4033}(963,\cdot)\) \(\chi_{4033}(1037,\cdot)\) \(\chi_{4033}(1148,\cdot)\) \(\chi_{4033}(1185,\cdot)\) \(\chi_{4033}(1370,\cdot)\) \(\chi_{4033}(1407,\cdot)\) \(\chi_{4033}(1629,\cdot)\) \(\chi_{4033}(1814,\cdot)\) \(\chi_{4033}(1925,\cdot)\) \(\chi_{4033}(1999,\cdot)\) \(\chi_{4033}(2110,\cdot)\) \(\chi_{4033}(2295,\cdot)\) \(\chi_{4033}(2517,\cdot)\) \(\chi_{4033}(2554,\cdot)\) \(\chi_{4033}(2739,\cdot)\) \(\chi_{4033}(2776,\cdot)\) \(\chi_{4033}(2887,\cdot)\) \(\chi_{4033}(2961,\cdot)\) \(\chi_{4033}(3109,\cdot)\) \(\chi_{4033}(3220,\cdot)\) \(\chi_{4033}(3257,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((1,e\left(\frac{1}{108}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4033 }(2295, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{25}{108}\right)\) | \(e\left(\frac{83}{108}\right)\) |