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important 
1 far-reaching, grave, large, material, meaningful, momentous, of substance, primary, salient, serious, signal, significant, substantial, urgent, weighty 
2 big-time  (informal) eminent, foremost, high-level, high-ranking, influential, leading, major league  (informal) notable, noteworthy, of note, outstanding, powerful, pre-eminent, prominent, seminal 
3  (usually with)  basic, essential, of concern  or  interest, relevant, valuable, valued, inconsequential, insignificant, minor, needless, negligible, secondary, trivial, undistinctive, unimportant, unnecessary 
all-important  
central, consequential, critical, crucial, essential, key, momentous, necessary, pivotal, significant, urgent, vital 
self-important  
arrogant, big-headed, bumptious, cocky, conceited, full of oneself, overbearing, pompous, presumptuous, pushy  (informal) strutting, swaggering, swollen-headed