Antibody or Fab fragment, wherein at least one amino group of the N-terminal amino acid of the light chain and/or of the N-terminal amino acid of the heavy chain is bound by an amidic bond to a molecule comprising a fluorophore group A, wherein said bond constitutes at least 70% of the total binding of said molecule to said antibody or Fab, preferably at least 80%, 85%, 90%, or 98% of the total bond of said molecule to said antibody or Fab; wherein said amino group of the N-terminal amino acid of the light chain and/or of the N-terminal amino acid of the heavy chain is bound by an amidic bond to a Z group with formula -CO-A; wherein said group A is selected from: - fluorophore CF568; - 2-[(1E,3E)-5-[(2Z,3S)-3-(5-methoxy-5-oxopentyl)-3-methyl-5-sulfo-1-(3-sulfopropyl)-2,3-dihydro-1H-indol-2-ylidene]penta-1,3-dien-1-yl]-3,3-dimethyl-5-sulfo-1-(3-sulfopropyl)-3H-indol-2-yl, having structure - 2-(2,2,10,10-tetramethyl-4,8-bis(sulfonatomethyl)-2,10-dihydro-1H-pyrano[3,2-g:5,6-g']diquinolin-11-ium-6-yl)terephthalate (AF568, both regioisomers), having structure - (7S,17R)-12-[4-(methoxycarbonyl)phenyl]-7,8,8,16,16,17-hexamethyl-2-oxa-6,18-diazapentacyclo[11.7.0. 03,11.0 5,9.0 15,19]icosa-1,3,5,9,11,14,19-heptaen-6-ium-4,20-disulfonate, having structure - [10,10,22,22-tetramethyl-20-(sulfomethyl)-16-{2,3,4,5-tetrafluoro-6-[(4-methoxy-4-oxobutyl)(methyl)carbamoyl]phenyl}-3-oxa-9lambda4,23-diazaheptacyclo[17.7.1.1 5,9.0 2,17.0 4,15.0 23,27.0 13,28]octacosa-1,4,9,1 1,13,15,17,19,20-nonaen-12-yl]methanesulfonic acid (ASred), having structure - 2-({3-[12,20-bis(hydroxymethyl)-10,10,22,22-tetramethyl-3-oxa-9lambda4, 23-diazaheptacyclo[17.7.1.1 5,9.0 2,17.0 4,15.0 23,27.0 13,28]octacosa-1,4,9,11,13,15,17,19,20-onaen-16-yl]-2,5,6-trifluoro-4-[(4-methoxy-4-oxobutyl)(m ethyl)carbamoyl]phenyl}sulfanyl)ethane-1-sulfonic acid, having structure - ({10,10,22,22-tetramethyl-20-[(phosphonooxy)methyl]-16-{2,3,4,5-tetrafluo ro-6-[(4-methoxy-4-oxobutyl)(methyl)carbamoyl]phenyl}-3-oxa-9lambda4,2 3-diazaheptacyclo[17.7.1.1 1,9.0 2,17.0 4,15.0 23,27.0 13,28]octacosa-1,4,9,11,13, 15,17,19,20-nonaen-12-yl}methoxy)phosphonic acid (ABBERIOR star 635P), having structure - fluorophore CF568; - 2-[(1E,3E)-5-[(2Z,3S)-3-(5-methoxy-5-oxopentyl)-3-methyl-5-sulfo-1-(3-sulfopropyl)-2,3-dihydro-1H-indol-2-ylidene]penta-1,3-dien-1-yl]-3,3-dimethyl-5-sulfo-1-(3-sulfopropyl)-3H-indol-2-yl, having structure - 2-(2,2,10,10-tetramethyl-4,8-bis(sulfonatomethyl)-2,10-dihydro-1H-pyrano[3,2-g:5,6-g']diquinolin-11-ium-6-yl)terephthalate (AF568, both regioisomers), having structure - (7S,17R)-12-[4-(methoxycarbonyl)phenyl]-7,8,8,16,16,17-hexamethyl-2-oxa-6,18-diazapentacyclo[11.7.0. 03,11.0 5,9.0 15,19]icosa-1,3,5,9,11,14,19-heptaen-6-ium-4,20-disulfonate, having structure - [10,10,22,22-tetramethyl-20-(sulfomethyl)-16-{2,3,4,5-tetrafluoro-6-[(4-methoxy-4-oxobutyl)(methyl)carbamoyl]phenyl}-3-oxa-9lambda4,23-diazaheptacyclo[17.7.1.1 5,9.0 2,17.0 4,15.0 23,27.0 13,28]octacosa-1,4,9,1 1,13,15,17,19,20-nonaen-12-yl]methanesulfonic acid (ASred), having structure - 2-({3-[12,20-bis(hydroxymethyl)-10,10,22,22-tetramethyl-3-oxa-9lambda4, 23-diazaheptacyclo[17.7.1.1 5,9.0 2,17.0 4,15.0 23,27.0 13,28]octacosa-1,4,9,11,13,15,17,19,20-onaen-16-yl]-2,5,6-trifluoro-4-[(4-methoxy-4-oxobutyl)(m ethyl)carbamoyl]phenyl}sulfanyl)ethane-1-sulfonic acid, having structure - ({10,10,22,22-tetramethyl-20-[(phosphonooxy)methyl]-16-{2,3,4,5-tetrafluo ro-6-[(4-methoxy-4-oxobutyl)(methyl)carbamoyl]phenyl}-3-oxa-9lambda4,2 3-diazaheptacyclo[17.7.1.1 1,9.0 2,17.0 4,15.0 23,27.0 13,28]octacosa-1,4,9,11,13, 15,17,19,20-nonaen-12-yl}methoxy)phosphonic acid (ABBERIOR star 635P), having structure