As a Spectrum Lantern, you harness the power of all attributes of each Lantern Corps, even the Life and Death Lanterns, making you a formidable fighter, and very well known in the universe. Even more so by a certain Thanagarian hero
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This is what you look like (full credit for this artwork goes to NickLD on deviantart)
As a Spectrum Lantern, you have the power of all the Corps, especially those that are the most difficult to control. You have control over:
White/Life
Red/Rage
Orange/Avarice
Yellow/Fear
Green/Willpower
Cyan/Friendship (Made this one up myself)
Blue/Hope
Indigo/Compassion
Magenta/Peace (This one I made up)
Violet/Love
Black/Death
When you decide to tap into a specific Lantern colour, you will summon the symbols of each Lantern Corps and speak the emotion you will need, but you do not gain their attribute. Example: speaking the word "Rage" will give you the powers of a Red Lantern, but will not force you to expel corrosive blood from your mouth. (Not kidding that actually happens) It looks like this
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Based off what I've read on the wiki, some colours can drain or empower others, e.g. blue draining yellow, suppressing orange and red and empowering green. As a Spectrum Lantern, the draining or suppressing will not happen with yours. But some colours will empower others if used at the same time. You can even summon the Emotional Embodiments themselves at times to converse with them. If you need to speak with a certain Emotional Embodiment all you need to do is recite their oath. Example, reciting the Yellow Lantern Oath will bring the Embodiment of Fear, Parallax. If you need to summon them all at once, you recite your Spectrum Oath:
In waking days
In vengeful nights
No lanterns will escape our might
We fight with honor
With every light
Fear us now
Our Spectrum Light
Backstory: You are the last of a long lost race of people. After the loss of your people, and home, you have come into contact with each Emotional Embodiment. They have seen the power you hold within you, and what you have gone through, and make you the first ever Spectrum Lantern, allowing you control over each emotion, and even some unknown to others. You now work as a peacekeeper, bringing order to the universe with help from the Embodiments themselves