Hello!
And here are all the ruling authorities for this complicated dynasty. Most did not have wikidata items, but I included every one I could find. Lines 24 to 149:
https://docs.google.com/spreadsheets/d/17Cp1TyzOXknGDZu8_YCmwgd4gS56GvxvIATQW40rYmM/edit?usp=sharing
This is going to be a lot of work. x)
Wakhsh, Emirate of (included here in duplication on Zeno; one ruler missed previously)
Imad al-Din Tamghaj Khan, circa 1214 (https://www.zeno.ru/showphoto.php?photo=230147)
United Qarakhanid Khaganate
Harun ibn Sulayman, 991-992 (page 163 - V3300 AV dinar, struck only at Bukhara in 381)
Nasr ibn 'Ali, circa 993-1012 (N#120396)
(N#334317)
(N#346325)
(N#294373)
Ahmad ibn 'Ali, circa 994-1016 (N#327847)
(N#92540)
(N#294373)
(N#375253)
Al-Hasan ibn Malik, circa 996 (https://www.acsearch.info/search.html?id=8723675)
Ahmad ibn Nasr, 999-1014 (https://www.acsearch.info/search.html?id=1967135)
Nasr ibn al-Qasim, 1001-1004 (https://www.acsearch.info/search.html?id=4356434)
Alp Abu'l-Fawaris, circa 1003 (https://www.acsearch.info/search.html?id=7074078)
Bakr ibn al-Hasan, 1003-1009 (N#234917)
Muhammad ibn 'Ali, 1003-1024 (N#119087)
Muhammad ibn al-Husayn, circa 1004 (https://www.acsearch.info/search.html?id=7072380)
Siraj al-Dawla Yinal-Tegin, 1004-1005 (page 165 - 3332 AR dirham, at Hiftdih only)
Yusuf ibn 'Abd Allah, 1004-1106; 1012-1014 (N#92541)
Yusuf ibn Harun, circa 1005-1032 (N#92539)
'Imad al-Dawla Chaghri-Tegin, 1006-1016 (https://www.acsearch.info/search.html?id=6687584)
Abu'l-Fawaris Bektuz, circa 1009-1010 (https://www.acsearch.info/search.html?id=11432722)
Nizam al-Dawla Abu'l-Muzaffar Tungha-Tegin, 1009-1014 (https://www.acsearch.info/search.html?id=11532596)
Bakr ibn Muhammad, circa 1010 (https://www.acsearch.info/search.html?id=7324747)
Khaqan Simnani, 1013-1015 (page 164 - 3305S AE fals, Bukhara 404-406 only)
Khutlugh Oga, circa 1013-1016 (https://www.acsearch.info/search.html?id=10964828)
Mansur ibn 'Ali, 1013-1024 (https://www.acsearch.info/search.html?id=2329856)
Al-Husayn ibn al-Hasan, 1013-1027 (https://www.acsearch.info/search.html?id=10964829)
Ahmad ibn Muhammad ibn 'Ali, circa 1014-1020 (https://www.acsearch.info/search.html?id=1967144)
Ahmad Atam-Tegin, 1014-1033 (https://www.acsearch.info/search.html?id=9716593)
Bars Oga, circa 1015 (https://www.acsearch.info/search.html?id=1677283)
Al-Husayn ibn Mansur, 1015-1016 (N#321408)
Ibrahim ibn Nasr, governor, circa 1017-1040 (https://www.acsearch.info/search.html?id=1677284)
'Abd al-Rahman ibn Mahmud, 1018 (https://www.acsearch.info/search.html?id=6282103)
Ahmad ibn Mansur, 1018-1019 (https://www.acsearch.info/search.html?id=2854700)
'Ali ibn Nasr, circa 1020 (https://www.acsearch.info/search.html?id=1362109)
'Ali ibn al-Hasan, 1020-1035 (https://www.acsearch.info/search.html?id=7074089)
Muhammad ibn Nasr, circa 1020-1055 (https://www.acsearch.info/search.html?id=11434252)
Nizam al-Dawla Yinal-Tegin, 1021 (https://www.acsearch.info/search.html?id=3676543)
Ahmad ibn al-Hasan, 1022-1023 (https://www.acsearch.info/search.html?id=9022271)
Yusuf ibn Mansur, 1022-1023 (https://www.acsearch.info/search.html?id=8723683)
Bektuzun, circa 1024 (https://www.acsearch.info/search.html?id=1677286)
Muhammad ibn al-Hasan, 1024-1027; 1037-1042 (https://www.acsearch.info/search.html?id=3957541)
Al-'Abbas ibn Muhammad ibn Nasr 1024-1042 (https://www.acsearch.info/search.html?id=3957539)
Kuj-Tegin, 1025-1034 (https://www.acsearch.info/search.html?id=11218376)
Sulayman ibn Harun, 1025-1035 (https://www.acsearch.info/search.html?id=8296832)
Yusuf ibn 'Ali, 1025-1042 (N#314024)
Rukn al-Dawla, 1030-1032 (https://www.acsearch.info/search.html?id=1677287)
Muhammad ibn Yusuf, 1030-1057 (https://www.acsearch.info/search.html?id=10461484) (into Eastern)
Sulayman ibn Yusuf, 1031-1056 (https://www.acsearch.info/search.html?id=9880461) (into Eastern)
Jibra'il ibn Yusuf, 1033-1042 (https://www.acsearch.info/search.html?id=9171483)
Shah Malik ibn Mubarak, circa 1038-1039 (https://www.acsearch.info/search.html?id=7324744)
Western Qarakhanid Khaganate
Ibrahim ibn Nasr, 1040-1068 (https://www.acsearch.info/search.html?id=3612113) (WESTERN)
Shu'ayth ibn Ibrahim, 1058-1062 (https://www.zeno.ru/showphoto.php?photo=94909)
Da'ud ibn Ibrahim, 1066-1068 (page 166 - 3364 BI dirham, as vassal of Ibrahim)
Toghan Khan 'Ali, 1068-1069 (page 167 - 3368 BI dirham, as vassal of Ibrahim; mint unknown but style of Samarqand)
Yusuf ibn Burhan al-Dawla, circa 1068-1069 (page 166 - 3365 BI dirham, at Quz-Urdu only, as vassal of Ibrahim)
Nasr ibn Ibrahim, 1068-1080 (https://www.acsearch.info/search.html?id=10461488)
Khidr Hakan Ahmad ibn Ibrahim, 1080-1081 (https://www.zeno.ru/showphoto.php?photo=276031)
Ahmad ibn Khidr, 1081-1095 (https://www.zeno.ru/showphoto.php?photo=251072)
Muhammad ibn Ibrahim, 1089 (https://www.zeno.ru/showphoto.php?photo=16196)
'Imad al-Dawla Mahmud, 1097 (page 167 - 3372 AE fals, Bukhara and Samarqand, AH 490 only)
Muhammad ibn Sulayman, 1102-1129 (https://www.zeno.ru/showphoto.php?photo=171742)
Ahmad ibn Muhammad, 1129-1130 (page 167 - 3375 AE fals, Samarqand )
Main Series (still Western Khaganate)
Mahmud III ibn Muhamad, 1136-1142 (page 168 - 3392 AE dirham, as local ruler at Samarqand before 536/1142, AE dirham)
Ibrahim Rukn al-Din ibn Muhammad, 1143-1153 (https://www.acsearch.info/search.html?id=10679324)
Mas'ud ibn al-Hasan, 1161-1171 (N#353219)
Mahmud ibn Husayn, circa 1157 (https://www.acsearch.info/search.html?id=9880462)
Muhammad ibn Mas'ud, 1171-1179 (https://www.acsearch.info/search.html?id=1362110)
Rukn al-Din Muhammad ibn Ghiyath, circa 1177-1179 (https://www.acsearch.info/search.html?id=1832889)
'Abd al-Khalid, circa 1178-1179 (https://www.acsearch.info/search.html?id=3262959)
Ibrahim ibn al-Husayn, 1178-1203 (https://www.acsearch.info/search.html?id=1967150)
'Uthman ibn Ibrahim, 1203-1210 (https://www.acsearch.info/search.html?id=9171492)
Eastern Qarakhanid Khaganate
Ahmad ibn Muhammad, 1045-1052 (https://www.acsearch.info/search.html?id=6687586)
Bahram, 1048-1053 (https://www.acsearch.info/search.html?id=11218378)
Jalal al-Dawla Tungha-Tegin, 1048-1057 (https://www.zeno.ru/showphoto.php?photo=16015; vassal of Muhammad)
Shams al-Dawla Arslan Ilek, 1052-1057 (https://www.zeno.ru/showphoto.php?photo=298966)
Nasir al-Dawla Ghazi, 1053-1054 (page 167 - 3381 BI dirham RRR - Struck at Barskhan 445-446)
Ibrahim ibn Muhammad ibn Yusuf, 1057-1062 (https://www.acsearch.info/search.html?id=6687588)
Burhan al-Dawla Ayyub, 1062 (https://www.acsearch.info/search.html?id=7322887)
Yusuf ibn Sulayman, 1068-1080 (https://www.zeno.ru/showphoto.php?photo=18333)
Nizam al-Dawla Mahmud, 1069-1070 (page 167 - 3385 BI dirham minted at Ghanaj / AH 462)
Sharaf al-Dawla Mu'izz, 1067-1070 (page 167 - 3386 BI dirham, as vassal of Ibrahim b. Nasr of the western khanate (459 only))
Hasan ibn Sulayman, 1088-1089 (https://www.zeno.ru/showphoto.php?photo=303200)
Jibra'il ibn 'Umar, 1100-1101 (https://www.acsearch.info/search.html?id=7072397)
Tafghaj Khan Ibrahim, circa 1106 (https://www.zeno.ru/showphoto.php?photo=306378)
Taliqan, Qarakhanids of
Rukn al-Din Muhammad ibn Mas'ud, 1165 (page 168 - 3412 AV dinar, Taliqan mint only; AH 560)
Kashgar, Qarakhanids of
Muhammad Arslan Khan, 1158-? (page 169 - 3426 AE fals (former #1518); 553)
Sulayman Tafghaj Khan, ?-1179 (page 169 - 3427 AE broad dirham (former #1515); no mint/date)
Yusuf Arslan Khan ibn Muhammad, 1205 (https://www.zeno.ru/showphoto.php?photo=114029)
Ilaq, Qarakhanids of
Irtash, 1013-1014 (https://www.acsearch.info/search.html?id=9737306)
Mansur ibn Ahmad, 992-999 (https://www.acsearch.info/search.html?id=1677264)
Muhammad ibn Mansur, 1001-1006 (N#226580)
Salar ibn Muhammad, 1009 (https://www.acsearch.info/search.html?id=1832881)
Ishtikhan, Qarakhanids of
Chaghri Subashi, 1024-1033 (https://www.acsearch.info/search.html?id=11690899)
Kharashkath, Qarakhanids of
Il-Kulug, 1013 (https://www.acsearch.info/search.html?id=1967140)
Ilyas al-Hajjaj, circa 1014-1020 (https://www.acsearch.info/search.html?id=10964830)
"Yinal Yusuf", circa 1015 (https://www.acsearch.info/search.html?id=7991264)
Karmina, Qarakhanids of
Mu'izz al-Dawla Yabghu, 1024-1029 (https://www.acsearch.info/search.html?id=8117912)
Inanj Kuktuz, 1026 (https://www.acsearch.info/search.html?id=8723685)
Yabghu Sayf al-Dawla, 1028 (page 170 - 3440 AE fals, Karmina 419)
Baha' al-Dawla Jibra'il ibn Muhammad, 1029 (page 170 - 3441 AE fals, Karmina 420)
Al-Sughd, Qarakhanids of
"Ba Salih", circa 1014 (https://www.acsearch.info/search.html?id=11690898)
Chaghri Subashi, circa 1028 (page 169 - 3435 AE fals, Ishtikhan 417-426 & al-Sughd 421)
Balkh, Qarakhanids of
'Ala al-Din Arslan Khan, circa 1160-1179 (https://www.zeno.ru/showphoto.php?photo=124558)
Sanjar Qadir Taghaj Khan, 1177-1186 (https://www.acsearch.info/search.html?id=3344945)
*Khusrawshah ibn Sanjar ibn Hasan, 1179-1186 (page 170 - D1523 AE dirham, struck at Balkh, known dated 574)
'Uddat al-Dunya wa'l-Din 'Ali ibn Ja'far, until 1198 (https://www.zeno.ru/showphoto.php?photo=295071)
Banakath, Qarakhanids of
Mu'izz al-Din Qilij Khaqan, 1178-1182 (https://www.zeno.ru/showphoto.php?photo=70114)
'Imad al-Din Ulugh Igdish Chaghri Khan, 1200-1206 (N#346327)
Chaghaniyan, Qarakhanids of
Muzaffar Kiya, 1005-1015 (https://www.acsearch.info/search.html?id=2854699)
Abu'l-Fath Togryl Khan, circa 1178 (https://www.zeno.ru/showphoto.php?photo=68874)
Rukn al-Dunya wa'l-Din Khusraw Shah, 1179-1236 (https://www.zeno.ru/showphoto.php?photo=62551)
Kasan, Qarakhanids of
Nasr ibn al-Husayn, 1169-1173 (https://www.acsearch.info/search.html?id=1278117)
Jalal al-Din Muhammad ibn Nasr, 1178-1202 (N#197185)
Mu'izz al-Din Ulugh Tughril Khan, 1208-1209 (https://www.acsearch.info/search.html?id=10461489)
Marghinan, Qarakhanids of
Husam al-Din Ulugh Toghan, 1205-1206 (https://www.acsearch.info/search.html?id=9881887)
Parab, Qarakhanids of
Shams al-Din Qutlugh Bilga Khaqan, circa 1200-1205 (https://www.acsearch.info/search.html?id=2854702)
Tirmidh, Qarakhanids of
Ahmad ibn Toghan-Tegin, 1164-1166 (https://www.acsearch.info/search.html?id=10964837)
Qurlugh Tabgach Khan, 1171-1179 (https://www.zeno.ru/showphoto.php?photo=27633)
Malik Yaghan Khan, 1177-1178 (https://www.zeno.ru/showphoto.php?photo=76647)
Tughril Khaqan, 1190-1195 (https://www.zeno.ru/showphoto.php?photo=322549)
Ghiyath al-Dunya wa'l-Din Mahmud, 1212 (https://www.acsearch.info/search.html?id=9880467)
Uzkand, Qarakhanids of
Al-Husayn ibn al-Hasan, circa 1145-1180 (page 168 - 3414 AE dirham, Uzjand dates AH 560s-570s)
Ibrahim ibn al-Husayn, 1156-1178 (N#197536)
Ahmad ibn Ibrahim, 1178-1210 (https://www.acsearch.info/search.html?id=8723687)
Mahmud ibn Ahmad, 1210-1212 (https://www.acsearch.info/search.html?id=11234932)
Tafghaj Khan, circa 1210-1219 (https://www.acsearch.info/search.html?id=573690)
Uncertain Qarakhanids apanage
Nasir al-Din, circa 1164-1212 (https://www.acsearch.info/search.html?id=10679325)
[And that is it! I hope…]
