ArgumentOutOfRangeException: Argument is out of range. Parameter name: index What am I doing wrong?

When I move in the game, I get "ArgumentOutOfRangeException: Argument is out of range. Parameter name: index" pointing towards the "Playerpos[0] = fx;" Line! I understand an easy fix would be to make Playerpos a vector2, but because I am serializing Playerpos, it can't be a Vector2, so I believe this is the only way. What I am wanting is Playerpos to look like a vector2 (x,y) without it looking like a record of the player moves.

Basically, I am asking how to replace an element (Playerpos[0]) with an x/y coordinate?

 using UnityEngine;
 using System.Collections;
 using System.Collections.Generic;
 public class PlayerMovement : MonoBehaviour {
     [HideInInspector]
     public List<float> Playerpos;
     private float x;
     private float y;
     private float fx;
     private float fy;
     private float speed;
     private GameObject c;
     private float cz;
     [HideInInspector]
     public Vector2 playerpos;
     void Start(){
         c = GameObject.Find("Main Camera");
         cz = c.transform.position.z;
         x = this.transform.position.x;
         y = this.transform.position.y;}       
 
     void Update () {
         if (Input.GetButtonDown("Horizontal") && Input.GetAxisRaw("Horizontal") > 0 && Physics.CheckSphere(new Vector2((x+1),y), 0)){
             print("right");
             fx += 1;
             transform.position = new Vector3(fx, y, -2);
             c.transform.position = new Vector3(fx, y,cz);
             Playerpos[0]+= fx;
             x = fx;}
         else if (Input.GetButtonDown("Horizontal") && Input.GetAxisRaw("Horizontal") < 0 && Physics.CheckSphere(new Vector2((x-1), y), 0)){
             print("left");
             fx -= 1;
             transform.position = new Vector3(fx, y, -2);
             c.transform.position = new Vector3(fx, y, cz);
             Playerpos[0] = fx;
             print(Playerpos[1]);
             x = fx;}
         else if (Input.GetButtonDown("Vertical") && Input.GetAxisRaw("Vertical") > 0 && Physics.CheckSphere(new Vector2(x, (y+1)), 0)){
             print("up");
             fy += 1;
             transform.position = new Vector3(x, fy, -2);
             c.transform.position = new Vector3(x, fy, cz);
             Playerpos.Insert(1, fy);
             print(Playerpos);
             y = fy;}
         else if (Input.GetButtonDown("Vertical") && Input.GetAxisRaw("Vertical") < 0 && Physics.CheckSphere(new Vector2(x, (y-1)), 0)){
             print("down");
             fy -= 1;
             transform.position = new Vector3(x, fy, -2);
             c.transform.position = new Vector3(x, fy, cz);
             Playerpos.Insert(1, fy);
             y = fy;
             print(Playerpos);
         }
         playerpos = new Vector2(x, y);
     }
 }
 

This is my first time using Unity Answers, so apologies if I am being dumb, and Thank you for the future help!