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1.1: We first meet Antonio and Sebastian together with these lines, spoken to the man who is trying to save the ship on which they're sailing: "A pox o' your throat, you bawling, blasphemous, incharitable dog!" and from the brave Antonio, "Hang, cur! Hang, you whoreson, insolent noisemaker! We are less afraid to be drowned than thou art."
1.1: Later, when it's clear the ship will sink, Antonio suggests wryly that they all go to sink with the King (who is currently below deck saying his prayers, which these two neglect to do). Sebastian retorts, referring his own praying brother who is about to drown in a ship, "Let's take leave of him" and hurries off with Antonio.
2.1: For the first 95 lines of this scene, Antonio and Sebastian harass Gonzalo and all good sense—they make puns at his expense, and tease another lord, Adrian, waging bets on who will crow first, comparing the two good men to roosters. Keep in mind that the King is currently mourning his freshly dead son, Sebastian's nephew, while they go on and on. By line 54, when Gonzalo describes the beauty he sees in the island, these two can only see its ugliness—an example of Shakespeare reflecting how one is inside impacts what one sees outside. So put on a happy face.
2.1: As Alonso mourns, Sebastian is serious for the first time since the loss of Ferdinand. Rather than comfort his brother, he points out that Ferdinand's death is Alonso's fault. Had Alonso just married his daughter to a European, and not a distant African, Alonso could've avoided this mess. He goes on to basically say "I told you so," and ends saying that their trip has made more widows than they have men to handle.
2.1: Gonzalo takes this time to describe his vision of a utopian kingdom. Whether or not it is foolish, Antonio and Sebastian mock him mercilessly about nitpicky things and big ideas. They dismiss the pastoral ideal he conjures as a community full of "whores and knaves." They go on and on at him until Gonzalo gets genuinely irritated. Antonio relents, asking in a seemingly friendly way that Gonzalo take it easy: "good my lord, be not angry." Maybe he's not an awful guy after all? Wait for it…
2.1: Everyone else, including the King, has fallen asleep. As soon as Alonso's eyes are shut, Antonio whispers to Sebastian that his vital imagination sees a crown dropping on Sebastian's head. Sebastian says it must be the talk of sleep, otherwise such a thing wouldn't be uttered. Antonio insists Sebastian would be letting his fortunes sleep if he didn't do something. While Sebastian wiggles uncomfortably, Antonio points out he's more serious than usual. Sebastian waffles for a little bit, and lets Antonio skillfully lead him on to a conclusion that, if he hadn't secretly wanted it, would've been unthinkable to him. Finally, as Sebastian seems swayed to murder his own sleeping brother for the crown, he asks Antonio if his conscience doesn't prick him for taking his own brother's title of Duke of Milan. Still, Antonio's conscience doesn't bother him. Sebastian, weak-willed (kind of reminiscent of his brother this way), says he'll take Antonio's word for good, and Antonio's deed for precedent. Just as he's about to kill his brother, he is already bestowing favors on Antonio as if he were king.
2.1: Even as they are caught red-handed, Sebastian jumps immediately to a lie to cover their traitorous backsides, saying they heard a nasty noise and were only protecting the King with their drawn swords.
3.3.11: Even on the search for the lost Prince, Antonio and Sebastian still plot together. Antonio says he is glad the King thinks his son is dead, and reminds Sebastian not to lose focus on their goal. Sebastian promises to use the next opportunity. Now totally resolved to killing his brother, he says, "I say [we will do it] to-night. No more."
3.3: Antonio and Sebastian, even as they witness magic, have only silly things to say—Sebastian says he will believe now in unicorns and phoenixes, and Antonio promises to swear to anything that anyone needs sworn on, given what they've seen.
3.3: Sebastian is coarse—even after the wonder they've seen (spirits bringing them a banquet), all he can think on is that they've left the food behind. He's hungry, so he'll eat, magic or not.
3.3: Antonio, Sebastian, and Alonso have just been called out as traitors by the horrifying spectacle of the harpy. Though it has brought the King near to tears with remorse, Antonio and Sebastian feel nothing but stubbornness. Sebastian, referring to the spirits, doesn't worry about his own conscience or ill acts, and instead vows to fight every spirit, one "fiend" at a time. Antonio, his fiendish friend, agrees to be second behind him in the fight. No remorse at all. For shame, really.
5.1: After witnessing all the magic of the harpy, the banquet, and an angry Prospero, Sebastian still has cheek. Prospero makes an aside to Antonio and Sebastian, that though they have plotted evilly, he will not out them. Sebastian replies (instead of, "gee, thanks for saving my treacherous hide, I've really been a jerk"), "The devil speaks in him." He has nothing further to say on Prospero, but does declare it a high miracle when Ferdinand is discovered.
5.1: The last exchange of Sebastian and Antonio in the play is their commentary on Trinculo and Stefano. Rather than discuss their wicked attempt to kill Alonso, the pair makes fun of the other men's drunken state and silly outfits.