### Algebra 83

#### Quiver

```[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
```

#### Relations

```[ 5, 3, 4, 2 ]
[ 4, 2, 5, 3 ]
[ 2, 5, 3, 4 ]
[ 3, 4, 2, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
```

#### Cartan matrix

```(1 1 1 0 1 0 1)
(0 1 1 0 1 0 1)
(0 1 1 1 0 0 0)
(0 1 0 1 1 0 1)
(0 0 1 1 1 0 1)
(0 0 1 1 1 1 0)
(0 0 0 0 0 1 1)
```

#### Good mutations

```vertex  1 -> Algebra  130    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  218    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
```

### Algebra 130

#### Quiver

```[ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
```

#### Relations

```[ 5, 3, 4, 2 ]
[ 4, 2, 5, 3 ]
[ 2, 5, 3, 4 ]
[ 3, 4, 2, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
```

#### Cartan matrix

```(1 0 0 0 0 0 0)
(1 1 1 0 1 0 1)
(1 1 1 1 0 0 0)
(1 1 0 1 1 0 1)
(0 0 1 1 1 0 1)
(0 0 1 1 1 1 0)
(0 0 0 0 0 1 1)
```

#### Good mutations

```vertex  1 -> Algebra   83    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  277    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
```

### Algebra 176

#### Quiver

```[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
```

#### Relations

```[ 5, 3, 4, 1 ]
[ 4, 1, 5, 3 ]
[ 1, 5, 3, 4 ]
[ 3, 4, 1, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
```

#### Cartan matrix

```(1 0 1 0 1 0 1)
(1 1 1 1 0 0 0)
(1 0 1 1 0 0 0)
(1 0 0 1 1 0 1)
(0 0 1 1 1 0 1)
(0 0 1 1 1 1 0)
(0 0 0 0 0 1 1)
```

#### Good mutations

```vertex  2 -> Algebra  208    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra  186    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
```

### Algebra 186

#### Quiver

```[ 1, 5 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
```

#### Relations

```[ 5, 3, 1 ]
[ 3, 4, 2 ]
[ 1, 5, 3 ]
[ 2, 3, 4 ]
[ 5, 3, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 4, 2, 3 ] - [ 4, 5, 3 ]
[ 3, 1, 5 ] - [ 3, 4, 5 ]
```

#### Cartan matrix

```(1 0 0 0 1 0 1)
(1 1 1 0 0 0 0)
(1 0 1 1 1 0 1)
(0 1 1 1 1 0 1)
(0 0 1 0 1 0 1)
(0 0 1 0 1 1 0)
(0 0 0 0 0 1 1)
```

#### Good mutations

```vertex  1 -> Algebra  336    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  239    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  176    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
```

### Algebra 208

#### Quiver

```[ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 5, 2 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
```

#### Relations

```[ 5, 2, 4, 1 ]
[ 4, 1, 5, 2 ]
[ 1, 5, 2, 4 ]
[ 2, 4, 1, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
```

#### Cartan matrix

```(1 1 1 0 1 0 1)
(1 1 1 1 0 0 0)
(0 0 1 0 0 0 0)
(1 0 0 1 1 0 1)
(0 1 1 1 1 0 1)
(0 1 1 1 1 1 0)
(0 0 0 0 0 1 1)
```

#### Good mutations

```vertex  2 -> Algebra  218    permutation [ 1, 4, 3, 2, 5, 6, 7 ]
vertex  3 -> Algebra  176    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
```

### Algebra 218

#### Quiver

```[ 1, 5 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
```

#### Relations

```[ 5, 2, 1 ]
[ 1, 5, 2 ]
[ 4, 5, 2 ]
[ 4, 5, 3 ]
[ 3, 4, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 5, 2, 4 ] - [ 5, 3, 4 ]
[ 2, 1, 5 ] - [ 2, 4, 5 ]
```

#### Cartan matrix

```(1 0 1 0 1 0 1)
(1 1 0 1 1 0 1)
(0 0 1 1 0 0 0)
(0 0 0 1 1 0 1)
(0 1 1 1 1 0 1)
(0 1 1 1 1 1 0)
(0 0 0 0 0 1 1)
```

#### Good mutations

```vertex  1 -> Algebra  365    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra   83    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  239    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex  4 -> Algebra  208    permutation [ 1, 4, 3, 2, 5, 6, 7 ]
```

### Algebra 239

#### Quiver

```[ 1, 5 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
```

#### Relations

```[ 5, 2, 1 ]
[ 1, 5, 2 ]
[ 3, 4, 5, 2 ]
[ 4, 5, 2, 3 ]
[ 5, 2, 3, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 2, 1, 5 ] - [ 2, 3, 4, 5 ]
```

#### Cartan matrix

```(1 0 0 0 1 0 1)
(1 1 1 1 1 0 1)
(0 0 1 1 1 0 1)
(0 1 0 1 1 0 1)
(0 1 1 0 1 0 1)
(0 1 1 0 1 1 0)
(0 0 0 0 0 1 1)
```

#### Good mutations

```vertex  3 -> Algebra  186    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  218    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
```

### Algebra 277

#### Quiver

```[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
```

#### Relations

```[ 2, 4, 1 ]
[ 4, 5, 3 ]
[ 1, 2, 4 ]
[ 2, 4, 5 ]
[ 3, 4, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 4, 1, 2 ] - [ 4, 5, 2 ]
[ 5, 2, 4 ] - [ 5, 3, 4 ]
```

#### Cartan matrix

```(1 1 0 0 0 0 0)
(0 1 0 1 0 0 0)
(1 0 1 1 0 0 0)
(1 1 0 1 1 0 1)
(0 1 1 1 1 0 1)
(0 1 1 1 1 1 0)
(0 0 0 0 0 1 1)
```

#### Good mutations

```vertex  1 -> Algebra  365    permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  130    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  294    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
```

### Algebra 294

#### Quiver

```[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
```

#### Relations

```[ 2, 3, 1 ]
[ 1, 2, 3 ]
[ 4, 5, 2, 3 ]
[ 5, 2, 3, 4 ]
[ 2, 3, 4, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 3, 1, 2 ] - [ 3, 4, 5, 2 ]
```

#### Cartan matrix

```(1 1 0 0 0 0 0)
(0 1 1 1 0 0 0)
(1 1 1 1 1 0 1)
(0 1 0 1 1 0 1)
(0 1 1 0 1 0 1)
(0 1 1 0 1 1 0)
(0 0 0 0 0 1 1)
```

#### Good mutations

```vertex  4 -> Algebra  277    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
```

### Algebra 336

#### Quiver

```[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 1 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
```

#### Relations

```[ 3, 4, 5, 1 ]
[ 3, 4, 2 ]
[ 2, 3, 4 ]
[ 5, 1, 3, 4 ]
[ 1, 3, 4, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 4, 2, 3 ] - [ 4, 5, 1, 3 ]
```

#### Cartan matrix

```(1 0 1 1 0 0 0)
(0 1 1 0 0 0 0)
(0 0 1 1 1 0 1)
(1 1 1 1 1 0 1)
(1 0 1 0 1 0 1)
(1 0 1 0 1 1 0)
(0 0 0 0 0 1 1)
```

#### Good mutations

```vertex  1 -> Algebra  186    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
```

### Algebra 365

#### Quiver

```[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
```

#### Relations

```[ 2, 4, 5, 1 ]
[ 4, 5, 1, 2 ]
[ 4, 5, 3 ]
[ 1, 2, 4, 5 ]
[ 3, 4, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 5, 1, 2, 4 ] - [ 5, 3, 4 ]
```

#### Cartan matrix

```(1 1 0 1 0 0 0)
(0 1 0 1 1 0 1)
(0 0 1 1 0 0 0)
(1 0 0 1 1 0 1)
(1 1 1 1 1 0 1)
(1 1 1 1 1 1 0)
(0 0 0 0 0 1 1)
```

#### Good mutations

```vertex  1 -> Algebra  218    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  277    permutation [ 2, 1, 3, 4, 5, 6, 7 ]
```