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.ic
\(\chi_{4033}(5,\cdot)\) \(\chi_{4033}(22,\cdot)\) \(\chi_{4033}(35,\cdot)\) \(\chi_{4033}(116,\cdot)\) \(\chi_{4033}(135,\cdot)\) \(\chi_{4033}(239,\cdot)\) \(\chi_{4033}(550,\cdot)\) \(\chi_{4033}(594,\cdot)\) \(\chi_{4033}(661,\cdot)\) \(\chi_{4033}(812,\cdot)\) \(\chi_{4033}(875,\cdot)\) \(\chi_{4033}(945,\cdot)\) \(\chi_{4033}(1078,\cdot)\) \(\chi_{4033}(1317,\cdot)\) \(\chi_{4033}(1495,\cdot)\) \(\chi_{4033}(1498,\cdot)\) \(\chi_{4033}(1623,\cdot)\) \(\chi_{4033}(1683,\cdot)\) \(\chi_{4033}(1715,\cdot)\) \(\chi_{4033}(1759,\cdot)\) \(\chi_{4033}(1942,\cdot)\) \(\chi_{4033}(2092,\cdot)\) \(\chi_{4033}(2420,\cdot)\) \(\chi_{4033}(2751,\cdot)\) \(\chi_{4033}(3125,\cdot)\) \(\chi_{4033}(3130,\cdot)\) \(\chi_{4033}(3132,\cdot)\) \(\chi_{4033}(3295,\cdot)\) \(\chi_{4033}(3460,\cdot)\) \(\chi_{4033}(3491,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1963,2295)\) → \((e\left(\frac{5}{36}\right),e\left(\frac{1}{27}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4033 }(1623, a) \) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{29}{54}\right)\) | \(-1\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{85}{108}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(-i\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{13}{54}\right)\) |