I want to light 1000 NEO PIXEL LEDs on Arduino UNO

I'm thinking of lighting 1000 NEO PIXEL LEDs on ArduinoUNO.
(https://www.switch-science.com/catalog/1399/)

There is no problem around the power supply, but
I will not be able to send a signal for about 600 units.

As a program,

#include<Adafruit_NeoPixel.h>
#define PIN6
Adafruit_NeoPixel strip = Adafruit_NeoPixel (1000, PIN, NEO_GRB+NEO_KHZ800);

void setup() {
     strip.begin();
     strip.show(); // Initialize all pixels to 'off'
}

void loop() {
      for(inti=0;i<strip.numPixels();i++){
           strip.setPixelColor(i, 150, 150, 150);
      }
      strip.show();
}

I don't mess with it from the default like this, but

Adafruit_NeoPixel strip=Adafruit_NeoPixel (1000, PIN, NEO_GRB+NEO_KHZ800);

If the number is 1000, it doesn't shine, and if it's about 600, it will glow.
If you divide Arduino into two and each LED is 500, it will glow, so it doesn't seem to be a problem with LEDs or power supplies.

If anyone understands, I would appreciate it if you could give me a reference opinion.
Thank you for your cooperation.