Which class gives most new magical powers for 1 level dip

Background: I have a bard, who is a bit lacking in low level spell selection, so I’ve been looking into multiclassing to get some more.

Stats (you can give +2 ASI for the benefit of multiclassing):

STR 11, DEX 17, CON 14, INT 9, WIS 14, CHA 20

So, Wizard is out.

For classes that pick subclass at level 1, subclass features count of course.

From what I have gathered from unofficial internet snippets, Tasha’s Cauldron of Everything seems give some nice options (like 4 cantrips and 5 1st level spells?!). But I don’t have that book myself to verify, and I may have missed other options, so the question:

What is the most different spells or spell-like powers a 1-level multiclass dip can give?

To clarify: I mean spells the character can actually have available, not the number they can choose from. I also realize now, that divine casters who pick spells every morning are their own category, not directly comparable. Still, for purposes of this Q, count the daily prepared spells.

Bard isn’t option for me, so I’ll include it as an example: 4 cantrips, 2 spells, 1 magical ability (Bardic Inspiration).

UA is ok, though I’d prefer official classes.

Scientific notations with negative powers for plotting

Plot[x^2, {x, 0, 100},Ticks -> {{#, ScientificForm@#} & /@ Range[0., 100., 30.], {#, ScientificForm@#} & /@ Range[0., 100^2, 1000.]}, PlotRange -> All];  PowerTicks[label_][min_, max_] :=Block[{min10, max10}, min10 = Floor[Log10[min]];  max10 = Ceiling[Log10[max]]; Join[Table[{10^i,If[label, Superscript[10, i], Spacer[{0, 0}]]}, {i, min10, max10}], Flatten[Table[{k 10^i,Spacer[{0, 0}], {0.005, 0.`},{Thickness[0.001`]}}, {i, min10,max10}, {k, 9}], 1]]] ListLogLogPlot[Range[20]^3, Frame -> True, FrameTicks -> {{PowerTicks[True],PowerTicks[False]}, {PowerTicks[True], PowerTicks[False]}}] 

The above code very well for the positive powers. Could some one please check it how does it change for the negative powers. More specific, on both axes the scales should be rangeing {10^-5, 10^-4....10^0, 10^1, 10^2,...10^5}. Thanks!

Best spells or powers for punishing anyone too close to me

I have a character with a reach of 20-25 feet depending on the buffs I have operational, with a specialty in grappling. The goal is to grab enemies and drag them to my space—and have my space, or better spaces near me, be very unpleasant places to be. For example, I have a blackguard’s aura of despair, and I’m considering Focalor’s aura of sadness and the enlightened spirit’s aura of menace.

But beyond those save-nuking auras, I’m kind of coming up short on how to most make “near me” be the worst possible place for an enemy to be. I’m looking for passive effects so I can focus my actions on just dragging in as many foes as possible. I figure spells or powers are probably my bet on this front, but I’m not coming up with much:

D&D 3.5e:

  • Acid sheath—2 acid damage per round to creatures in a grapple with me
  • Aura of the sun—1d6 positive energy damage to undead around me each round
  • Aura of cold—comes in lesser and greater varieties, which do 1d6 or 2d6 cold damage, respectively, per round to creatures within 10 feet.
  • Babau slime—1d8 acid damage per round to grappled creatures.
  • Balor nimbus—6d6 (as a 2nd-level spell) fire damage per round to grappled creatures.
  • Body of the sun—1d4/2 levels fire damage per round to creatures within 5 feet.
  • Corona of cold—1d12 cold damage per round, and applies a −2 penalty to Strength and Dexterity and halves speed, to creatures within 10 feet.
  • Negative energy aura—1 damage per 3 levels, or 2 healing for undead creatures, each round, in 10-ft radius.
  • Positive energy aura—1 healing per 3 levels, or 2 damage for undead creatures, each round, in 10-ft radius.
  • Pulse of hate–2d6 “unholy” damage per round in 10-ft radius.

Pathfinder

  • Cape of wasps—described as a wasp swarm sharing your space, which means other creatures sharing your space (e.g. creatures you’ve grappled under 3.5e rules, which we are using) arguably take the 2d6+poison swarm damage of the wasp swarm each round. The spell doesn’t come out and say that, though, and sharing a space with someone is a lot harder in Pathfinder than it is in 3.5e, so it’s unclear if this was intended functionality.

So what I’m looking for are official spells or powers from D&D 3.5e (all WotC-published sources as well as Dragon and Dungeon magazine issues, including 3.5e-legal 3e material) or Pathfinder (all Paizo-or-Dreamscarred-Press-published sources) that introduce some kind of emanation or aura that extends from my space, out to 20 feet or less (if it’s larger, I have no need to drag them into it). The emanation must last for some period of time, the longer the better. I would restrict this more (class, level, effects), except that I’ve already done a bunch of research and come up with nearly nothing. My character is a psion egoist, but adaptation or multiclassing might be possible. However, Epic and Mythic material are both banned.

For this question, I’ll hear out answers that include polymorph, but know that I view polymorph pretty dimly and also that it would conflict with some of the things that my character is already doing (i.e. various character features would be lost), so polymorph options rate pretty poorly in my estimation—I’d appreciate it if we’d restrict mentions of it to truly stand-out effects you couldn’t get elsewhere.

Can a user benefit from personal powers stored in an empowered object?

I realized while writing this question that I have another issue with empowered objects. Specifically, it is the object using the stored powers, rather than the wearer/wielder/user. Can such an object "target" the user with personal or "self-only" powers? I intend to have a more powerful psionic NPC loan a PC a Psychometabolic item, but most of the powers it’ll have access to are self-targeting and I realized I wasn’t sure if the PC could even use them.

Is it worth buying the “Super Powers Companion 2nd Edition” if I have 1st Ed. and the free changes supplements?

I own the original SW: Super Powers pdf that came out some years ago, however my group and I have been playing with the PDF that Pinnacle released with the rules for power creation.

I’d like to know if the changes in the second edition are significant enough to consider buying it, since I haven’t been able to find a list of the chapters of the book to know if there’s anything special beyond the rules changes on powers, such campaign creation advice, how to make heroic NPCs and villains, etc.

How can we find the powers of a complex number?

this is the complex number im dealing with zb=(1/7)* (Cos[pi/3]+iSin[pi/3])

I need to represent for the first 10 powers in the plane. I also need to label the points with "z to the power n(n is the power for which i elevate zb)

I need to label the axes, i need to do all this in mathematica

My questions 1.How can I represent a complex number in mathematica 2.How can I represent for the first 10 powers the plane. 3.How can I label each point on the graph to the corresponding power?

my professor gave me a hint to use the callout[] command in mathematica. thank you!

What bonus would be balanced against a restriction on a changeling powers?

I am playing as a changeling in a new campaign where every officially published races are accepted. We told the DM the races and classes we wanted to play in advance and he was OK with it. However, during the first session, he said that my changeling will only be able to change their appearance once per day, during a long rest.

I am going to try to negotiate a bonus in exchange for this restriction.
There are two options I’d like to propose, but don’t know which one would be fair :

  1. The actor feat – So even if my character can’t change very often, they are very good at it.

  2. Unsettling visage, from the UA version of the changeling – It’s in theme and could be fun to describe.

I like "Actor" more, but would it be balanced to get it at first level?

(Please tell me if there are any mistake, English isn’t my first language)

Psionic powers for Aegis

When a 4 level Aegis (Elan race) meet prerequisite, he choose "Unlocked Talent" and "Access psionic Talent" so He can access n°5 0-level and a 1-level psionic power. But there are more psionic power lists: Cryptic, Dread, Psion, etc…Nothing for Aegis. From which list the Aegis can pick powers?