Database schema:

CREATE TABLE "Community_Area" (
	community_area_no INTEGER -- example: ['2', '1'],
	community_area_name TEXT -- example: ['Rogers Park', 'West Ridge'],
	side TEXT -- example: ['North ', 'Far North '],
	population TEXT -- example: ['71,942', '54,991'],
	PRIMARY KEY (community_area_no)
)


CREATE TABLE "Crime" (
	report_no INTEGER -- example: ['23758', '23757'],
	case_number TEXT -- example: ['JB100159', 'JB100522'],
	date TEXT -- example: ['1/1/2018 2:46', '1/1/2018 11:33'],
	block TEXT -- example: ['039XX W CORNELIA AVE', '026XX N HAMPDEN CT'],
	iucr_no TEXT -- example: ['143B', '110'],
	location_description TEXT -- example: ['APARTMENT', 'AUTO'],
	arrest TEXT -- example: ['FALSE', 'TRUE'],
	domestic TEXT -- example: ['FALSE', 'TRUE'],
	beat INTEGER -- example: ['1935', '1732'],
	district_no INTEGER -- example: ['17', '19'],
	ward_no INTEGER -- example: ['30', '43'],
	community_area_no INTEGER -- example: ['7', '21'],
	fbi_code_no TEXT -- example: ['15', '01A'],
	latitude TEXT -- example: ['41.94456125', '41.92972657'],
	longitude TEXT -- example: ['-87.72668181', '-87.64092074'],
	PRIMARY KEY (report_no), 
	CONSTRAINT fk_crime_ward FOREIGN KEY(ward_no) REFERENCES "Ward" (ward_no),
	CONSTRAINT fk_crime_iucr FOREIGN KEY(iucr_no) REFERENCES "IUCR" (iucr_no),
	CONSTRAINT fk_crime_district FOREIGN KEY(district_no) REFERENCES "District" (district_no),
	CONSTRAINT fk_crime_community_area FOREIGN KEY(community_area_no) REFERENCES "Community_Area" (community_area_no),
	CONSTRAINT fk_crime_fbi_code FOREIGN KEY(fbi_code_no) REFERENCES "FBI_Code" (fbi_code_no)
)


CREATE TABLE "District" (
	district_no INTEGER -- example: ['2', '1'],
	district_name TEXT -- example: ['Central', 'Wentworth'],
	address TEXT -- example: ['1718 South State Street', '5101 South Wentworh Avenue'],
	zip_code INTEGER -- example: ['60616', '60609'],
	commander TEXT -- example: ['Jake M. Alderden', 'Joshua Wallace'],
	email TEXT -- example: ['\xa0CAPS002District@chicagopolice.org', '\xa0CAPS001District@chicagopolice.org'],
	phone TEXT -- example: ['312-747-8366', '312-745-4290'],
	fax TEXT -- example: ['312-747-5396', '312-745-3694'],
	tty TEXT -- example: ['312-747-6656', '312-745-3693'],
	twitter TEXT -- example: ['\xa0ChicagoCAPS01', '\xa0ChicagoCAPS02'],
	PRIMARY KEY (district_no)
)


CREATE TABLE "FBI_Code" (
	fbi_code_no TEXT -- example: ['01B', '01A'],
	title TEXT -- example: ['Involuntary Manslaughter', 'Homicide 1st & 2nd Degree'],
	description TEXT -- example: ['The killing of one human being by another.', 'The killing of another person through negligence.'],
	crime_against TEXT -- example: ['Persons', 'Property'],
	PRIMARY KEY (fbi_code_no)
)


CREATE TABLE "IUCR" (
	iucr_no TEXT -- example: ['031B', '031A'],
	primary_description TEXT -- example: ['HOMICIDE', 'CRIM SEXUAL ASSAULT'],
	secondary_description TEXT -- example: ['FIRST DEGREE MURDER', 'SECOND DEGREE MURDER'],
	index_code TEXT -- example: ['I', 'N'],
	PRIMARY KEY (iucr_no)
)


CREATE TABLE "Neighborhood" (
	neighborhood_name TEXT -- example: ['Albany Park', 'Altgeld Gardens'],
	community_area_no INTEGER -- example: ['54', '14'],
	PRIMARY KEY (neighborhood_name), 
	CONSTRAINT fk_neighborhood_community_area FOREIGN KEY(community_area_no) REFERENCES "Community_Area" (community_area_no)
)


CREATE TABLE "Ward" (
	ward_no INTEGER -- example: ['2', '1'],
	alderman_first_name TEXT -- example: ['Daniel', 'Brian'],
	alderman_last_name TEXT -- example: ['Hopkins', 'La Spata'],
	alderman_name_suffix TEXT -- example: ['Jr.'],
	ward_office_address TEXT -- example: ['1400 N. Ashland', '1958 N. Milwaukee Ave.'],
	ward_office_zip TEXT -- example: ['60647', '60622'],
	ward_email TEXT -- example: ['ward02@cityofchicago.org', 'info@the1stward.com'],
	ward_office_phone TEXT -- example: ['312.643.2299', '872.206.2685'],
	ward_office_fax TEXT -- example: ['312.448.8829', '773.536.7296'],
	city_hall_office_room INTEGER -- example: ['305', '200'],
	city_hall_office_phone TEXT -- example: ['312.744.8734', '312.744.6836'],
	city_hall_office_fax TEXT -- example: ['312.744.6712', '312.744.7738'],
	"Population" INTEGER -- example: ['56149', '55805'],
	PRIMARY KEY (ward_no)
)

Question: List the case number of the crimes in wards with population below 52000 that have beat greater than the 90% of the average beat of all crimes.
Evidence: population below 52000 refers to population < 52000; beat greater than the 90% of the average beat refers to beat > multiply(avg(beat), 0.9) where population < 52000

SQL:
SELECT COUNT(T1.report_no) FROM Crime AS T1 INNER JOIN Ward AS T2 ON T1.ward_no = T2.ward_no WHERE T2.Population < 52000 AND T1.beat > ( SELECT AVG(T1.beat) * 0.9 FROM Crime AS T1 INNER JOIN Ward AS T2 ON T1.ward_no = T2.ward_no WHERE T2.Population < 52000 )