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Shreyasi Acharya, Dagmar Adamová, Alexander Adler, Jonatan Adolfsson, Gianluca Aglieri Rinella, Michelangelo Agnello, Neelima Agrawal, Zubayer Ahammed, Shakeel Ahmad, Sang Un Ahn, Ishaan Ahuja, Zaenal Akbar, Alexander Akindinov, Mohammad Al-Turany, Sk Noor Alam, Dmitry Aleksandrov, Bruno Alessandro, Haidar Mas’ud Alfanda, Jose Ruben Alfaro Molina, Bushra Ali, Yasir Ali, Andrea Alici, Negin Alizadehvandchali, Anton Alkin, Johan Alme, Torsten Alt, Igor Altsybeev, Mustafa Naji Anaam, Cristian Andrei, Dimitra Andreou, Anton Andronic, Massimo Angeletti, Venelin Anguelov, Federico Antinori, Pietro Antonioli, Anuj Chandra, Nicole Apadula, Laurent Bernard Aphecetche, Harald Appelshäuser, Silvia Arcelli, Roberta Arnaldi, Ionut Cristian Arsene, Mesut Arslandok, Andre Augustinus, Ralf Peter Averbeck, Sizar Aziz, Mohd Danish Azmi, Angela Badalà, Yong Wook Baek, Xiaozhi Bai, Raphaëlle Bailhache, Yoshini Bailung, Renu Bala, Alessandro Balbino, Alberto Baldisseri, Bartosz Balis, Debjani Banerjee, Roberto Barbera, Luca Barioglio, Maria Barlou, Gergely Gábor Barnaföldi, Lee Stuart Barnby, Valerie Ramillien Barret, Clara Bartels, Klaus Barth, Esther Bartsch, Filippo Baruffaldi, Nicole Bastid, Sumit Basu, Guillaume Batigne, Boris Batyunya, Dibakar Bauri, José Luis Bazo Alba, Ian Gardner Bearden, Caitlin Beattie, Pascal Becht, Iouri Belikov, Ailec de la Caridad Bell Hechavarria, Francesca Bellini, Rene Bellwied, Svetlana Belokurova, Vladimir Belyaev, Gyula Bencédi, Stefania Beolè, Alexandru Bercuci, Yaroslav Berdnikov, Anastasia Berdnikova, Luisa Bergmann, Mihaela Gabriela Besoiu, Latchezar Betev, Partha Pratim Bhaduri, Anju Bhasin, Inayat Rasool Bhat, Mohammad Asif Bhat, Buddhadeb Bhattacharjee, Purba Bhattacharya, Livio Bianchi, Nicola Bianchi, Jaroslav Bielčík, Jana Bielčíková, Jacek Biernat, Ante Bilandzic, Gabor Biro, Saikat Biswas, Justin Thomas Blair, Dmitry S. Blau, Mihail-Bogdan Blidaru, Christoph Blume, Gianluigi Boca, Friederike Bock, Alexey A. Bogdanov, Stefano Boi, Jeongsu Bok, Laszlo Boldizsar, Alexander I. Bolozdynya, Marek Bombara, Peter Matthew Bond, Germano Bonomi, Herve Borel, Alexander Borissov, Hannah Bossi, Elena Botta, Lars Bratrud, Peter Braun-Munzinger, Marco Bregant, Michal Broz, Giuseppe Eugenio Bruno, Matthew Daniel Buckland, Dmitry Budnikov, Henner Büsching, Stefania Bufalino, Ophélie Bugnon, Paul Bühler, Edith Zinhle Buthelezi, Jamila Bashir Butt, Alexander Bylinkin, Sebastian Adam Bysiak, Mengke Cai, Helen Louise Caines, Alberto Caliva, Ernesto Calvo Villar, Juan Manuel Mejia Camacho, Rabi Soto Camacho, Paolo Camerini, Fabio de Moraes Canedo, Francesca Carnesecchi, Robin Albert Andre Caron, Javier Ernesto Castillo Castellanos, Ester Anna Rita Casula, Fabio Catalano, Cesar Ceballos Sanchez, Pritam Chakraborty, Sinjini Chandra, Sylvain Chapeland, Marielle Chartier, Subhasis Chattopadhyay, Sukalyan Chattopadhyay, Alex Henri Jean Chauvin, Tonatiuh García Chávez, Tiantian Cheng, Cvetan Valeriev Cheshkov, Brigitte Cheynis, Vasco Miguel Chibante Barroso, David Dobrigkeit Chinellato, Soyeon Cho, Peter Chochula, Panagiotis Christakoglou, Christian Holm Christensen, Peter L. Christiansen, Tatsuya Chujo, Corrado Cicalò, Luisa Cifarelli, Federico Cindolo, Michael Rudolf Ciupek, Giulia Clai, Jean Willy Andre Cleymans, Fabio Filippo Colamaria, Jonathan Samuel Colburn, Domenico Colella, Alberto Collu, Manuel Colocci, Matteo Concas, Gustavo Conesa Balbastre, Zaida Conesa del Valle, Giacomo Contin, Jesus Guillermo Contreras Nuno, Maurice Louis Coquet, Thomas Michael Cormier, Pietro Cortese, Mauro Rogerio Cosentino, Filippo Costa, Susanna Costanza, Philippe Crochet, Reynier Cruz Torres, Eleazar Cuautle Flores, Pengyao Cui, Leticia Cunqueiro Mendez, Andrea Dainese, Florian Paul André Damas, Meike Charlotte Danisch, Andrea Danu, Indranil Das, Prottay Das, Prottoy Das, Supriya Das, Sadhana Dash, Annalisa De Caro, Giacinto De Cataldo, Lorenzo De Cilladi, Jan de Cuveland, Alessandro De Falco, Daniele De Gruttola, Nora De Marco, Chiara De Martin, Salvatore De Pasquale, Suman Deb, Hermann Franz Degenhardt, Kamil Rafal Deja, Luigi Dello Stritto, Wenjing Deng, Preeti Dhankher, Domenico Di Bari, Antonio Di Mauro, Raúl Arteche Díaz, Thomas Dietel, Yanchun Ding, Roberto Divià, Dhruv Utpalkumar Dixit, Øystein Djuvsland, Uliana Dmitrieva, Jaehyeon Do, Alexandru Florin Dobrin, Benjamin Donigus, Anand Kumar Dubey, Andrea Dubla, Sandeep Dudi, Dukhishyam Mallick, Pascal Dupieux, Natalia Dzalaiova, Tabea Maria Eder, Raymond James Ehlers, Viljar Nilsen Eikeland, Florian Eisenhut, Domenico Elia, Barbara Ewa Erazmus, Francesca Ercolessi, Filip Erhardt, Andrey Erokhin, Magnus Rentsch Ersdal, Bruno Espagnon, Giulio Eulisse, David Evans, Sergey Evdokimov, Laura Fabbietti, Mattia Faggin, Julien Faivre, Feng Fan, Alessandra Fantoni, Markus Fasel, Pietro Fecchio, Alessandro Feliciello, Grigori A. Feofilov, Arturo Fernández Téllez, Andrea Ferrero, Alessandro Ferretti, Victor Jose Gaston Feuillard, Jan Figiel, Sergey Filchagin, Dmitry Finogeev, Fiorella Maria Celeste Fionda, Gabriele Fiorenza, Fernando Antonio Flor, Amanda Nicole Flores, Siegfried Förtsch, Sergey Fokin, Enrico Fragiacomo, Eszter Frajna, Ulrich Fuchs, Nicola Funicello, Christophe Furget, Artur Furs, Jens Jørgen Gaardhøje, Martino Gagliardi, Alberto Martín Gago Medina, Arthur Willem Jean Gal, Carlos Duarte Galvan, Paraskevi Ganoti, Jose Maria Garabatos Cuadrado, Jesús Ricardo Alvarado Garcia, Edmundo Javier Garcia-Solis, Kunal Garg, Corrado Gargiulo, Aydan Garibli, Katharina Garner, Katharina Demmich, Piotr Gasik, Erin Frances Gauger, Amrit Gautam, Maria Beatriz de Leone Gay Ducati, Maria Beatriz de Leone Gay Ducati, Marie Germain, Jhuma Ghosh, Premomoy Ghosh, Sanjay Kumar Ghosh, Marco Giacalone, Paola Gianotti, Paolo Giubellino, Piero Giubilato, Aude Marie Camille Glaenzer, Peter Glässel, Daniel Jia Qin Goh, Victor Gonzalez, Laura Helena González Trueba, Sergey Gorbunov, Marek Boguslaw Gorgon, Lidia Maria Görlich, Sven Gotovac, Varlen Grabski, Łukasz Kamil Graczykowski, Leo Clifford Greiner, Alessandro Grelli, Costin Grigoraș, Vladislav Grigoryev, Smbat Grigoryan, Fabrizio Grosa, Jan Fiete Große-Oetringhaus, Raffaele Grosso, Gabriel Garcia Guardiano, Rachid Guernane, Maxime Rene Joseph Guilbaud, Kristjan Herlache Gulbrandsen, Taku Gunji, Wenda Guo, Anik Gupta, Ramni Gupta, Sergio Paisano Guzman, László Gyulai, Michael Karim Habib, Cynthia Marie Hadjidakis, Hideki Hamagaki, Mohammed Hamid, Ryan Hannigan, Md Rihan Haque, Alena Harlenderova, Alena Gromada, John William Harris, Austin Vincent Harton, Jan Anton Hasenbichler, Hadi Hassan, Despina Hatzifotiadou, Philip Hauer, Laura Brittany Havener, Stefan Thomas Heckel, Ernst Hellbär, Håvard Helstrup, Tomáš Herman, Emma Gonzalez Hernandez, Gerardo Antonio Herrera Corral, Florian Herrmann, Kristin Fanebust Hetland, Hartmut Hillemanns, Christopher Hills, Boris Hippolyte, Bas Hofman, Bernhard Hohlweger, Jan Honermann, Geunhee Hong, David Horak, Sebastian Hornung, Adrian Horzyk, Ritsuya Hosokawa, Yongzhen Hou, Peter Hristov, Chun-Lu Huang, Charles Hughes, Patrick Huhn, Laura Maria Huhta, Charlotte Van Hulse, Thomas J. Humanic, Hushnud Hushnud, Lucia Anna Tarasovičová, Lucia Anna Tarasovičová, Alek Hutson, James Philip Iddon, Radiy Ilkaev, Hira Ilyas, Motoi Inaba, Gian Michele Innocenti, Mikhail Ippolitov, Artem Isakov, Tommaso Isidori, Md Samsul Islam, Marian Ivanov, Vladimir Ivanov, Vladimir Izucheev, Miroslaw Jablonski, Barbara Jacak, Nicolò Jacazio, Peter Martin Jacobs, Slavka Jadlovska, Jan Jadlovsky, Syaefudin Jaelani, Cristiane Jahnke, Monika Joanna Jakubowska, Ashish Jalotra, Malgorzata Anna Janik, Thomas Janson, Marko Jercic, Oliver Thomas Jevons, Alom Antonio Paz Jimenez, Florian Jonas, Peter Graham Jones, John M. Jowett, Jerome Jung, Michael Jung, Antoine Jean-Simon Junique, Anton Jusko, Jetnipit Kaewjai, Peter Kalinak, Annalena Sophie Kalteyer, Alexander Philipp Kalweit, Vladimir Kaplin, Ayben Karasu Uysal, David Karatović, Oleg V. Karavichev, Tatiana L. Karavicheva, Przemyslaw Karczmarczyk, Evgeny Karpechev, Varchaswi Kashyap, Andrey Kazantsev, Udo Kebschull, Ralf Keidel, D.L. D. Keijdener, Markus Keil, Bernhard Ketzer, Zhanna Khabanova, Ahsan Mehmood Khan, Shaista Khan, Alexei Khanzadeev, Yury Kharlov, Anisa Khatun, Arvind Khuntia, Bjarte Kileng, Beomkyu Kim, Chong Kim, Dong Jo Kim, Eun Joo Kim, Jaehyun Kim, Jinsook Kim, Jiyoung Kim, Junlee Kim, Minjung Kim, Se Yong Kim, Taejun Kim, Stefan Kirsch, Ivan Kisel, Sergej N. Kiselev, Adam Ryszard Kisiel, Jacek Pawel Kitowski, Jennifer Lynn Klay, Jochen Klein, Spencer Robert Klein, Christian Klein-Bösing, Matthias Kleiner, Thomas Klemenz, Alexander Kluge, Anders Garritt Knospe, Chinorat Kobdaj, Markus Konrad Köhler, Thorsten Kollegger, Andrey Kondratyev, Natalia Kondratyeva, Evgeny Kondratyuk, Joshua Leon König, Stephan Alexander Königstorfer, Piotr Jan Konopka, Georgy Kornakov, Sebastian Dominik Koryciak, Artem Kotliarov, Oleksandr Kovalenko, Vladimir Kovalenko, Marek Kowalski, Ivan Králik, Adela Kravčáková, Lukas Kreis, Marian Krivda, Filip Krizek, Katarina Krizkova Gajdosova, Martin Kroesen, Mario Krüger, Evgeny Kryshen, Mikolaj Krzewicki, Vit Kucera, Christian Claude Kuhn, Paulus Gerardus Kuijer, Takuya Kumaoka, Deekshit Kumar, Lokesh Kumar, Navneet Kumar, Sourav Kundu, Podist Kurashvili, Alexander Kurepin, Alexey B. Kurepin, Alexey Kuryakin, Svetlana Kushpil, Jakub Kvapil, Min Jung Kweon, Jiyeon Kwon, Youngil Kwon, Sarah Louise La Pointe, Paola La Rocca, Yue Shi Lai, Anantachai Lakrathok, Massimo Lamanna, Rune Langoy, Kirill Lapidus, Pavel Larionov, Elisa Laudi, Lukas Lautner, Roman Lavicka, Tatiana V. Lazareva, Ramona Lea, Johannes Lehrbach, Roy Crawford Lemmon, Ildefonso Leon Monzon, Ezra Douglas Lesser, Michael Lettrich, Peter Lévai, Xiaomei Li, Xing Long Li, Jørgen André Lien, Roman Lietava, Bong-Hwi Lim, Sanghoon Lim, Volker Lindenstruth, Amelia Lindner, Christian Lippmann, Alwina Ruixin Liu, Dong Hai Liu, Jian Liu, Ingrid Mckibben Lofnes, Vitaly Loginov, Constantinos Loizides, Petra Lončar, Jorge Andres López, Xavier Bernard Lopez, Ernesto López Torres, Jens Robert Lühder, Marcello Lunardon, Grazia Luparello, Yu-Gang Ma, Alla Maevskaya, Magnus Mager, Tariq Mahmoud, Antonin Maire, Mikhail Malaev, Nasir Mehdi Malik, Qasim Waheed Malik, Salman Khurshid Malik, Liudmila Malinina, Dmitry Mal Kevich, Dmitry Mal’Kevich, Neelkamal Mallick, Giuseppe Mandaglio, Vladislav Manko, Franck Manso, Vito Manzari, Yaxian Mao, Giacomo Vito Margagliotti, Anselmo Margotti, Ana Maria Marin, Christina Markert, Marco Marquard, Nicole Alice Martin, Paolo Martinengo, Jacobb Lee Martinez, Mario Iván Martínez Hernández, Ginés Martínez Garcia, Silvia Masciocchi, Massimo Masera, Alberto Masoni, Laure Marie Massacrier, Annalisa Mastroserio, Andreas Michael Mathis, Oliver Matonoha, Paula Fernanda Toledo Matuoka, Adam Tomasz Matyja, Christoph Mayer, Antonio Lafuente Mazuecos, Francesco Mazzaschi, Marianna Mazzilli, Alessandra Maria Mazzoni, Joyful Elma Mdhluli, Adrian Florin Mechler, Yury Melikyan, Arturo Alejandro Menchaca-rocha, Elisa Meninno, Anjaly Sasikumar Menon, Michal Meres, Sibaliso Mhlanga, Yasuo Miake, Luca Micheletti, Lucrezia Camilla Migliorin, Dimitar Lubomirov Mihaylov, Konstantin Mikhaylov, Aditya Nath Mishra, Dariusz Czeslaw Miskowiec, Abhi Modak, Auro Prasad Mohanty, Bedangadas Mohanty, Mohammed Mohisin Khan, Mikael Andreas Molander, Zuzana Moravcova, Cindy Mordasini, Denise Aparecida Moreira de Godoy, Igor Morozov, Andreas Morsch, Teo Mrnjavac, Valeria Muccifora, Eugen Mudnic, Daniel Mühlheim, Sanjib Muhuri, James Declan Mulligan, Alice Mulliri, Marcelo Gameiro Munhoz, Robert Helmut Munzer, Hikari Murakami, Sean Murray, Luciano Musa, Jan Musinsky, Julian Wojciech Myrcha, Bharati Naik, Rahul Ramachandran Nair, Basanta Kumar Nandi, Rosario Nania, Eugenio Nappi, Adrian Fereydon Nassirpour, Abhishek Nath, Christine Nattrass, Alexandra Neagu, Lukas Nellen, Simon Voigt Nesbo, Gvozden Nešković, Dmitrii Nesterov, Borge Svane Nielsen, Sergey Nikolaev, Sergey Nikulin, Vladimir Nikulin, Francesco Noferini, Seoyoung Noh, Petr V. Nomokonov, Jaime Norman, Norbert Novitzky, Piotr Nowakowski, Alexander Nyanin, Joakim Ingemar Nystrand, Masanori Ogino, Alice Ohlson, Vitaly A. Okorokov, Janusz Oleniacz, Antonio Carlos Oliveira da Silva, Michael Henry Oliver, Anna Önnerstad, Chiara Oppedisano, Antonio Ortiz Velasquez, Takumi Osako, Anders Nils Erik Oskarsson, Jacek Tomasz Otwinowski, Motomi Oya, Ken Oyama, Yvonne C. Pachmayer, Sonali Padhan, Davide Pagano, Guy Paic, Antonio Palasciano, Jinjin Pan, Stefano Matthias Panebianco, Jonghan Park, Jasper Elias Parkkila, Surya Prakash Pathak, Rajendra Nath Patra, Biswarup Paul, Hua Pei, Thomas Peitzmann, Xinye Peng, Luis Gustavo Pereira, Hugo Denis Antonio Pereira da Costa, Dmitry Yurevich Peresunko, Guillermo Mesa Perez, Sébastien Perrin, Yury N. Pestov, Vojtech Petráček, Mihai A. 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• This article reports on the inclusive production cross section of several quarkonium states, J/ψ, ψ(2S), Υ(1S), Υ(2S), and Υ(3S), measured with the ALICE detector at the LHC, in pp collisions at s√=5.02 TeV. The analysis is performed in the dimuon decay channel at forward rapidity (2.5<y<4). The integrated cross sections and transverse-momentum (pT) and rapidity (y) differential cross sections for J/ψ, ψ(2S), Υ(1S), and the ψ(2S)-to-J/ψ cross section ratios are presented. The integrated cross sections, assuming unpolarized quarkonia, are: σJ/ψ(pT<20 GeV/c) = 5.88 ± 0.03 ± 0.34 μb, σψ(2S)(pT<12 GeV/c) = 0.87 ± 0.06 ± 0.10 μb, σΥ(1S)(pT<15 GeV/c) = 45.5 ± 3.9 ± 3.5 nb, σΥ(2S)(pT<15 GeV/c) = 22.4 ± 3.2 ± 2.7 nb, and σΥ(3S)(pT<15 GeV/c) = 4.9 ± 2.2 ± 1.0 nb, where the first (second) uncertainty is the statistical (systematic) one. For the first time, the cross sections of the three Υ states, as well as the ψ(2S) one as a function of pT and y, are measured at s√=5.02 TeV at forward rapidity. These measurements also significantly extend the J/ψ pT reach and supersede previously published results. A comparison with ALICE measurements in pp collisions at s√=2.76, 7, 8, and 13 TeV is presented and the energy dependence of quarkonium production cross sections is discussed. Finally, the results are compared with the predictions from several production models.