# E107: Conductor: primitive vs. induced characters

```{figure} ../_static/experiments/e107_hero.png
:alt: E107 hero
:class: experiment-hero

E107: Conductor: primitive vs. induced characters
```

**Tags:** `number-theory`, `dirichlet-characters`, `quantitative-exploration`, `visualization`, `l-functions`

## Highlights

- Focused numeric experiment with a small set of figures.
- Parameters saved to `params.json` for reproducibility.
- Defaults are chosen, so the experiment remains feasible for the CI “slow” suite.

## What is computed

- Compute conductors and separate primitive from imprimitive characters.

## Notes

- This page summarizes the intent; see the generated `report.md` in `out/` for concrete outputs.

## Published run snapshot

If this experiment is included in the docs gallery, include the published snapshot (report + params).

```{include} ../reports/e107.md
:start-after: "<!-- REPORT:BEGIN -->"
:end-before: "<!-- REPORT:END -->"
```

::: {dropdown} params.json (snapshot)
:open:

```{literalinclude} ../params/e107.json
:language: json
```

:::

## References

- See `docs/background/dirichlet-characters.md`.
- See `docs/background/dirichlet-l-functions.md` and `docs/background/dirichlet-convolution.md`.

## Related experiments

- {doc}`e079` (Primitive vs. imprimitive characters: conductors.)
- {doc}`e068` (Dirichlet L(s,χ): series vs. Euler product (partial approximations).)
- {doc}`e069` (L(1,χ): slow convergence and smoothing.)
- {doc}`e122` (E122: Character averages over primes)
- {doc}`e065` (Orthogonality matrix for Dirichlet characters.)