Genoa don't have a UEFA license, so they've been replaced by Sampdoria. Same city, just a different team.
Qualified for the group stage (48 teams in total):
Schalke 04 111.883 (GER)
Napoli >84.102 (ITA)
Tottenham Hotspur 84.078 (ENG)
Villarreal >58.942 (ESP)
Olympique Marseille 55.483 (FRA)
Dnipro Dnipropetrovsk 52.033 (UKR)
Sporting Braga 51.776 (POR)
Fiorentina >49.102 (ITA)
Anderlecht 47.440 (BEL)
Liverpool 47.078 (ENG)
Besiktas 36.520 (TUR)
Lokomotiv Moscow 23.099 (RUS)
FC Augsburg 15.883 (GER)
FC Groningen 8.695 (NED)
+ 1 Greek side
+ 1 Swiss side
+ 22 winners from the playoff
+ 10 losers from the CL playoff
Playoff round (44 teams in total):
Winners from the 3rd round and 15 losers from the CL 3rd qualifying round.
3rd qualifying round (58 teams in total):
Borussia Dortmund 99.883 (GER)
Athletic Bilbao >56.942 (ESP)
AZ Alkmaar 46.695 (NED)
Dinamo Moscow 27.599 (RUS)
Standard Liège 25.440 (BEL)
Girondins Bordeaux 24.483 (FRA)
Sampdoria >18.102 (ITA)
Vitória Guimarães 17.776 (POR)
AS Saint-Étienne 16.983 (FRA)
Slovan Liberec 16.325 (CZE)
Southampton FC 16.078 (ENG)
FK Krasnodar 15.099 (RUS)
CF Os Belenenses 12.276 (POR)
Vorskla Poltava 11.033 (UKR)
Zorya Luhansk 10.533 (UKR)
Vitesse Arnhem 10.195 (NED)
FK Jablonec 9.325 (CZE)
AEK Larnaca 8.460 (CYP)
Hapoel Kiryat Shmona 7.200 (ISR)
Istanbul Basaksehir 6.520 (TUR)
ASA Tirgu Mures 5.259 (ROM)
SCR Altach 5.135 (AUT)
2nd qualifying round (66 teams in total):
FC København 40.960 (DEN)
Trabzonspor 36.520 (TUR)
NK Rijeka 13.700 (CRO)
Astra Giurgiu 9.759 (ROM)
Dinamo Minsk 9.650 (BEL)
Mladá Boleslav 8.825 (CZE)
Charleroi 7.440 (BEL)
IFK Göteborg 6.045 (SWE)
Hapoel Beer-Sheva 4.700 (ISR)
Inverness CT 3.580 (SCO)
Cherno More Varna 3.350 (BUL)
and quite a few more.
1st qualifying round (102 teams in total):
West Ham United 16.078 (ENG)
Sheriff Tiraspol 14.500 (MOL)
Rosenborg BK 11.875 (NOR)
IF Elfsborg 11.545 (SWE)
Hajduk Split 11.200 (CRO)
Apollon Limassol 10.460 (CYP)
Omonia Nicosia 10.460 (CYP)
Slovan Bratislava 9.250 (SVK)
AIK Stockholm 9.045 (SWE)
Neftchi Baku 9.000 (AZE)
MSK Zilina 8.750 (SVK)
FK Aktobe 8.575 (KAZ)
Go Ahead Eagles 8.195 (NED)
Red Star Belgrade 7.775 (SER)
DVSC Debrecen 7.700 (HUN)
Brøndby IF 7.460 (DEN)
Shakhtior Saligorsk 7.150 (BEL)
Litex Lovech 6.850 (BUL)
Vojvodina Novi Sad 6.275 (SER)
Spartak Trnava 6.250 (SVK)
St. Johnstone 6.080 (SCO)
Randers FC 5.960 (DEN)
Strømsgodset IF 5.875 (NOR)
FC Botosani 5.259 (ROM)
Lokomotiva Zagreb 5.200 (CRO)
FC Beroe Stara Zagora 4.850 (BUL)
Torpedo Zhodino 4.650 (BEL)
Aberdeen 4.580 (SCO)
NK Koper 4.475 (SLO)
Beitar Jerusalem 4.200 (ISR)
NK Domzale 3.475 (SLO)
Cukaricki Belgrade 3.275 (SER)
NK Celje 3.225 (SLO)
Ferencváros 3.200 (HUN)
Odd Grenland 2.875 (NOR)
MTK Budapest 2.450 (HUN)
and lots and lots more of
@scaramanga's favorite teams from across Europe. Anyone with a coefficient of 3.450 or more will be seeded in the first round, so West Ham's opponents will most likely come from Wales, Ireland, Northern Ireland, Faroe Islands, Iceland, Finland or some former member of Yugoslavia or the Soviet Republic.
These three will have a playoff to decide who goes into group stage, 2nd and 3rd qualifying rounds respectively.
Asteras Tripolis 13.380 (GRE)
PAOK Thessaloniki 40.880 (GRE)
Atromitos FC 10.380 (GRE)
FC Zürich (16.875 ) will go into the group stage and FC Thun (10.375) in the 3rd qualifying round unless Sion (8.375) win the Swiss cup final. If they win, the two others will be shifted down a notch. If they don't, someone else (Wolfsberger based on league positions) will go into the 2nd round. The cup winner here only gets a group stage spot because Sevilla have qualified for the CL.
Same goes for Sturm Graz (9.135). If Austria Wien (20.635) win the Austrian cup final, they go into the 3rd round and Sturm Graz the 2nd. Otherwise someone else (Luzern based on league position) will go into the 2nd. Ninth placed Vaduz have already qualified by winning the cup in Liechtenstein.
In Poland nothing has been determined yet.
