Given a date as input in any convenient format, output a calendar with that date as the exact center of a five-week window. The header of the calendar must include the two-letter abbreviations for the days of the week (i.e., Su Mo Tu We Th Fr Sa).

For example, given April 2 2019 as input, the output should be

Sa Su Mo Tu We Th Fr
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31 1 2 3 4 5
 6 7 8 9 10 11 12
13 14 15 16 17 18 19

so that the given date is the exact middle of the calendar.

Given February 19 2020, output

Su Mo Tu We Th Fr Sa
 2 3 4 5 6 7 8
 9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
 1 2 3 4 5 6 7

For September 14 1752, show the following:

Mo Tu We Th Fr Sa Su
28 29 30 31 1 2 3
 4 5 6 7 8 9 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30 1

• Input and output can be given by any convenient method.


• The input is guaranteed non-empty and valid (i.e., you'll never receive "" or Feb 31 etc.).


• Assume Gregorian calendar for all dates.


• Leap years must be accounted for.


• Input dates will range from Jan 1 1600 to Dec 31 2500.


• You can print it to STDOUT or return it as a function result.


• Either a full program or a function are acceptable.


• Any amount of extraneous whitespace is acceptable, so long as the characters line up appropriately.


• 
  Standard loopholes are forbidden.


• This is code-golf so all usual golfing rules apply, and the shortest code (in bytes) wins.

Wolfram Language (Mathematica), 131 bytes

(s=#;Grid@Join[StringTake[#,2]&/@ToString/@(DayName[d[s,#]]&/@Range[-3,3]),Partition[Last@d[s,#]&/@Range[-17,17],7]])&
d=DatePlus

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I don't know why Grid doesn't work on TIO but this code outputs this

C# (Visual C# Interactive Compiler), 124 bytes

n=>for(int i=-24;i<18;)Write($"(i<-17?$"n.AddDays(i):ddd".Remove(2,1):n.AddDays(i).Day+""),3"+((46+i++)%7<1?"n":""));

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PHP, 197 191 bytes

$d=date_create($argn)->sub($i=new DateInterval(P17D));$i->d=1;while($x++<35)if($x<8)$h.=substr($d->format(D),0,2).' ';$o.=sprintf('% 2s ',$d->format(j));$d->add($i);echo wordwrap($h.$o,20);

Certainly longer than I'd like, but having the require date range outside of an epoch timestamp makes PHP longer.

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Input is STDIN, run with php -nF.

$ echo April 2 2019|php -nF cal.php

April 2 2019

Sa Su Mo Tu We Th Fr 
16 17 18 19 20 21 22 
23 24 25 26 27 28 29 
30 31 1 2 3 4 5 
 6 7 8 9 10 11 12 
13 14 15 16 17 18 19 

February 19 2020

Su Mo Tu We Th Fr Sa 
 2 3 4 5 6 7 8 
 9 10 11 12 13 14 15 
16 17 18 19 20 21 22 
23 24 25 26 27 28 29 
 1 2 3 4 5 6 7 

September 14 1752

Mo Tu We Th Fr Sa Su 
28 29 30 31 1 2 3 
 4 5 6 7 8 9 10 
11 12 13 14 15 16 17 
18 19 20 21 22 23 24 
25 26 27 28 29 30 1 

JavaScript (Node.js), 205 bytes

f=
d=>[...`012345`].map(r=>[...`0123456`].map(c=>`$new Date(d+864e5*(+c+r*7-24))[+r?`getUTCDate`:`toUTCString`]()`.slice(0,2).padStart(2)).join` `,d=new Date(d.slice(0,2)%4+20+d.slice(2)).getTime()).join`
`

<input type=date oninput=o.textContent=f(this.value)><pre id=o>

Try it online! Takes input as a string in YYYY-MM-DD format, but the input field in the snippet displays your local date format.

R, 66 bytes

function(d,g=format)write(c(g(d+-3:3,"%a"),g(d+-17:17,"%3d")),1,7)

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Pads date numbers with leading 0s; takes input as a Date, which can be created by using as.Date("YYYY/MM/DD").

Weirdly short for an R ascii-art answer...