If you need to test your system at 3500 requests per second you need to use slightly different approach, to wit add Constant Throughput Timer to your Test Plan and configure it to limit JMeter requests rate
However from what I can see from your Summary Report the majority of samplers are executed at rate of 3 requests per second and it have to be at least 58 requests per second in order to achieve 3500 requests per minute. So most probably your application simply cannot handle the load.
I would recommend first of all checking out whether your application has enough headroom to operate in terms of CPU, RAM, Network, Disk, Swap, etc. You can use i.e. JMeter PerfMon Plugin.
Also make sure that JMeter itself can produce the required load, default JMeter configuration might be not suitable for conducting the load of 1000 concurrent users so make sure you follow JMeter Best Practices, especially:
- Run your test in non-GUI mode
- Disable all the Listeners
- Increase JMeter HEAP size as by defaults it's only 1 GB which might be not enough.