Zygote of Spirogyra produces four haploid nuclei in which one is functional. This process is known as zygotic meiosis or zygotic division. Let's understand the process in detail:

1. Zygote Formation:
Spirogyra is a filamentous green algae that reproduces sexually through conjugation. During conjugation, two filaments of Spirogyra come in close contact and form conjugation tubes. The cytoplasm of one filament (donor) passes through the conjugation tube and fuses with the cytoplasm of the other filament (recipient), resulting in the formation of a zygote.

2. Zygotic Meiosis:
Once the zygote is formed, it undergoes meiosis to produce haploid nuclei. Meiosis is a type of cell division that involves two rounds of nuclear division, resulting in the formation of four haploid daughter cells.

3. First Division:
In the first division of zygotic meiosis, the zygote nucleus undergoes karyokinesis (nuclear division) without cytokinesis (cytoplasmic division). As a result, it forms two nuclei within a single cell. These two nuclei are known as primary nuclei.

4. Second Division:
In the second division of zygotic meiosis, each primary nucleus undergoes karyokinesis to form two daughter nuclei. This results in the formation of four haploid nuclei within the zygote cell.

5. Functional Nuclei:
Out of the four haploid nuclei produced, only one nucleus is functional. This functional nucleus undergoes further development and gives rise to a new filamentous Spirogyra plant. The remaining three nuclei degenerate and are discarded.

6. Importance of Functional Nucleus:
The functional nucleus contains the genetic material necessary for the growth and development of the new Spirogyra filament. It undergoes mitotic divisions to form new cells and eventually results in the formation of a mature filamentous plant.

In conclusion, the zygote of Spirogyra produces four haploid nuclei through zygotic meiosis. Out of these four nuclei, only one is functional and plays a crucial role in the development of a new Spirogyra plant. The other three nuclei degenerate and are not involved in further growth and development.