for $m \ge \max_i n_i$. Similarly, the restrictions are given by:

$$ (\text{SDP}_n^{m1, \le}) \quad \left\{ \begin{array}{ll} \sup_{\substack{Q \in \text{Sym}_{(m+1)M} \\ \mathbf{F} \in \mathbb{R}^{(m+1)M}}} & F_n \\ \text{subject to} & \sum_{\mathbf{k} \le m\mathbf{1}} F_{\mathbf{k}} = 1 \\ \text{and} & \forall \mathbf{k} \le m\mathbf{1}, \quad F_{\mathbf{k}} \ge 0 \\ \text{and} & \forall l \le m\mathbf{1}, \quad \sum_{i+j=2l} Q_{ij} = \sum_{\mathbf{k} \ge l} \frac{(-1)^{|\mathbf{k}|+|l|}}{l!} \binom{\mathbf{k}}{l} F_{\mathbf{k}} \\ \text{and} & \forall \mathbf{r} \le 2m\mathbf{1}, \mathbf{r} \ne 2l, \forall l \le m\mathbf{1}, \quad \sum_{i+j=\mathbf{r}} Q_{ij} = 0 \\ \text{and} & Q \ge 0, \end{array} \right. $$

for $m \ge \max_i n_i$. We denote its optimal value by $\omega_n^{m1, \le}$. The corresponding dual programs are given by:

$$ (\text{D-SDP}_n^{m1, \le}) \quad \left\{ \begin{array}{ll} \inf_{\substack{A \in \text{Sym}_{(m+1)M} \\ y, \mu \in \mathbb{R} \times \mathbb{R}^{(m+1)M}}} & y \\ \text{subject to} & y \ge 1 + \mu_n \\ \text{and} & \forall \mathbf{k} \le m\mathbf{1}, \mathbf{k} \ne \mathbf{n}, \quad y \ge \mu_k \\ \text{and} & \forall l \le m\mathbf{1}, \forall i + j = 2l, \quad A_{ij} = \sum_{\mathbf{k} \le l} \mu_k \binom{l}{\mathbf{k}} l! \\ \text{and} & A \ge 0, \end{array} \right. $$

for $m \ge \max_i n_i$.

The programs $(\text{SDP}_n^{m1, \ge})$ and $(\text{SDP}_n^{m1, \le})$ are the relaxations and restrictions of $(\text{LP}_n)$ obtained by considering polynomials of individual degree in each variable less or equal to $m$. These programs respectively provide hierarchies of relaxations and restrictions of $(\text{LP}_n)$, since the set of $M$-variate polynomials with monomials lower than $m\mathbf{1}$ is included in the set of $M$-variate polynomials with monomials lower than $(m+1)\mathbf{1}$.

Note that these hierarchies of programs obtained by setting $m$ of the form $m\mathbf{1}$ capture the behaviour of all bounds that can be obtained from the more general family of programs indexed by $m = (m_1, \dots, m_M)$, since $m \le (\max_i m_i)\mathbf{1}$, i.e., the bound obtained by considering the program indexed by $(\max_i m_i)\mathbf{1}$ supersedes the bound obtained by considering the program indexed by $m$. Formally, for all $m = (m_1, \dots, m_M) \in \mathbb{N}^M$,

$$ \omega_n^{m, \ge} \ge \omega_n^{(\max_i m_i)\mathbf{1}, \ge} \quad \text{and} \quad \omega_n^{m, \le} \le \omega_n^{(\max_i m_i)\mathbf{1}, \le}. \qquad (173) $$

Finally, we show that both ways of defining the hierarchies are equivalent:

**Lemma 17.** For all $m \in \mathbb{N}$,

$$ \omega_n^{m, \ge} \ge \omega_n^{m\mathbf{1}, \ge} \ge \omega_n^{Mm, \ge}, \qquad (174) $$

and

$$ \omega_n^{m, \le} \le \omega_n^{m\mathbf{1}, \le} \le \omega_n^{Mm, \le}. \qquad (175) $$

*Proof.* For all $\mathbf{k} \in \mathbb{N}^M$ and all $m \in \mathbb{N}$ we have

$$ |\mathbf{k}| \le m \Rightarrow \mathbf{k} \le m\mathbf{1} = (m, \dots, m) \Rightarrow |\mathbf{k}| \le Mm. \qquad (176) $$
We thus obtain the corresponding inclusions between sets of M-variate polynomials: (i) M-variate polynomials of degree less or equal to m have all their monomials lower than m1, and (ii) all M-variate polynomials with monomials lower than m1 have degree less or equal to Mm. Hence,

$$ \mathcal{R}_{m,+}(\mathbb{R}_+^M) \stackrel{(i)}{\subset} \mathcal{R}_{m1,+}(\mathbb{R}_+^M) \stackrel{(ii)}{\subset} \mathcal{R}_{Mm,+}(\mathbb{R}_+^M). \qquad (177) $$

In particular, $(SDP_n^{m,\ge})$ is a relaxation of $(SDP_n^{m,\le})$ which is itself a relaxation of $(SDP_n^{Mm,\ge})$, and $(SDP_n^{m,\le})$ is a restriction of $(SDP_n^{m,\ge})$ which is itself a restriction of $(SDP_n^{Mm,\le})$. □

This result implies that the two versions of the hierarchies of relaxations are interleaved (Eq. (174)), and that the two versions of the hierarchies of restrictions are also interleaved (Eq. (175)). As such, for any bound obtained with one version of the hierarchy at some fixed level, a better bound can be obtained with the other version at some other level. While this means that the hierarchies are equivalent, note that in practice it may be simpler to solve numerically the version where the parameter space is smaller.

## H.3 Convergence of the multimode hierarchies

For $n = (n_1, \dots, n_M) \in \mathbb{N}^M$, the sequences $(\omega_n^{m,\ge})_{m\ge|n|}$ and $(\omega_n^{m1,\ge})_{m\ge\max_i n_i}$ (resp. $(\omega_n^{m,\le})_{m\ge|n|}$ and $(\omega_n^{m1,\le})_{m\ge\max_i n_i}$) are decreasing (resp. increasing) sequences, lower bounded (resp. upper bounded) by $\omega_n$. Hence, these sequences are converging.

We show in what follows that $(\omega_n^{m1,\ge})_{m\ge\max_i n_i}$ (resp. $(\omega_n^{m1,\le})_{m\ge\max_i n_i}$) converges to $\omega_n$. By Lemma 17, this implies that the sequence $(\omega_n^{Mm,\ge})_{m\ge\max_i n_i}$ (resp. $(\omega_n^{Mm,\le})_{m\ge\max_i n_i}$) also converges to $\omega_n$. Since this is a subsequence of the converging sequence $(\omega_n^{m,\ge})_{m\ge|n|}$ (resp. $(\omega_n^{m,\le})_{m\ge|n|}$), it implies that the sequence $(\omega_n^{m,\ge})_{m\ge|n|}$ (resp. $(\omega_n^{m,\le})_{m\ge|n|}$) also converges to $\omega_n$.

With similar proofs to the single-mode case using multi-index notations, we obtain the following result:

**Theorem 8 (Generalisation of Theorem 1).** Let $\mu = (\mu_k)_{k\in\mathbb{N}^M} \in \mathbb{R}^{\mathbb{N}^M}$. Then, $\mu$ is the sequence of Laguerre moments $\int_{\mathbb{R}_+^M} \mathcal{L}_k(x)d\mu(x)$ of a non-negative distribution $\mu$ supported on $\mathbb{R}_+^M$ if and only if $\forall m \in \mathbb{N}, \forall g \in \mathcal{R}_{m,+}(\mathbb{R}_+^M), \langle f_\mu, g \rangle \ge 0$.

The proof of this theorem is identical to the univariate case, with the use of Riesz-Haviland theorem over $\mathbb{R}_+^M$ [67] rather than $\mathbb{R}_+$.

With Eq. (177), the proof of convergence of the multimode hierarchy of upper bounds is then obtained directly from its single-mode counterpart using multi-index notations:

**Theorem 9 (Generalisation of Theorem 4).** The decreasing sequence of optimal values $\omega_n^{m1,\ge}$ of $(SDP_n^{m1,\ge})$ converges to the optimal value $\omega_n$ of $(LP_n)$:

$$ \lim_{m \to +\infty} \omega_n^{m1,\ge} = \omega_n. \qquad (178) $$

With Lemma 17, we also obtain

$$ \lim_{m \to +\infty} \omega_n^{m,\ge} = \omega_n. \qquad (179) $$

On the other hand, the proof of convergence of the single-mode hierarchy of lower bounds crucially exploits analytical feasible solutions of the programs $(SDP_n^{m,\le})$ in order to obtain two results:

* Strong duality between programs $(SDP_n^{m,\le})$ and $(D-SDP_n^{m,\le})$ (Theorem 2).

* The fact that the feasible set of $(D-SDP_n^{m,\le})$ is compact with coefficients bounded independently of $m$ (Eq. (63)).

In what follows, we generalise these two results to the multimode setting by obtaining multimode analytical feasible solutions from products of single-mode ones.
**Lemma 18.** For $m, n \in \mathbb{N}$ with $m \ge n$, let $Q(m, n) \in \text{Sym}_{m+1}$ and $\mathbf{F}(m, n) = (F_k(m, n))_k \in \mathbb{R}^{m+1}$ be feasible solutions of $(\text{SDP}_n^{m,\le})$. Let $\mathbf{m} = (m_1, \dots, m_M) \in \mathbb{N}^M$ and $\mathbf{n} = (n_1, \dots, n_M) \in \mathbb{N}^M$ with $\mathbf{m} \ge \mathbf{n}$. Let $Q := Q(m_1, n_1) \otimes \dots \otimes Q(m_M, n_M) \in \text{Sym}_{\pi_m}$ and $\mathbf{F} = (F_k)_{\mathbf{k}\le\mathbf{m}} \in \mathbb{R}^{\pi_m}$, where for all $\mathbf{k} = (k_1, \dots, k_M) \le \mathbf{m}$, $F_k := \prod_{i=1}^M F_{k_i}(m_i, n_i)$. Then, $(Q, \mathbf{F})$ is a feasible solution of $(\text{SDP}_n^{m,\le})$. Moreover, if $(Q(m_i, n_i), \mathbf{F}(m_i, n_i))$ is strictly feasible for all $i = 1, \dots, M$ then $(Q, \mathbf{F})$ is a strictly feasible solution of $(\text{SDP}_n^{m,\le})$.

*Proof.* With the notations of the Lemma, we show the feasibility of $(Q, \mathbf{F})$ (resp. strict feasibility). We have $Q \ge 0$, $F_k \ge 0$ (resp. $Q > 0$, $F_k > 0$) for all $\mathbf{k} \le \mathbf{m}$, and $Q_{ij} = \prod_{p=1}^M Q_{i_p j_p}(m_p, n_p)$ for all $i = (i_1, \dots, i_M) \le \mathbf{m}$ and $j = (j_1, \dots, j_M) \le \mathbf{m}$. Hence, for all $\mathbf{r} = (r_1, \dots, r_M) \le 2\mathbf{m}$,

$$ \sum_{i+j=r} Q_{ij} = \sum_{i_1+j_1=r_1, \dots, i_M+j_M=r_M} \prod_{p=1}^{M} Q_{i_p j_p}(m_p, n_p) \\ = \prod_{p=1}^{M} \sum_{i_p+j_p=r_p} Q_{i_p j_p}(m_p, n_p). \qquad (180) $$

In particular, if $r \ne 2l$ for all $l \le m$, then at least one coefficient $r_p$ is odd, and the corresponding sum gives 0 since $(Q(m_p, n_p), \mathbf{F}(m_p, n_p))$ is feasible for $(\text{SDP}_{n_p}^{m_p,\le})$. In that case, $\sum_{i+j=r} Q_{ij} = 0$. Otherwise, for all $l = (l_1, \dots, l_M) \le m$,

$$ \begin{aligned} \sum_{i+j=2l} Q_{ij} &= \prod_{p=1}^{M} \sum_{i_p+j_p=2l_p} Q_{i_p j_p}(m_p, n_p) \\ &= \prod_{p=1}^{M} \sum_{k_p \ge l_p} \frac{(-1)^{k_p+l_p}}{l_p!} \binom{k_p}{l_p} F_{k_p}(m_p, n_p) \\ &= \sum_{l_1 \le k_1 \le m_1, \dots, l_M \le k_M \le m_M} \prod_{p=1}^{M} \frac{(-1)^{k_p+l_p}}{l_p!} \binom{k_p}{l_p} F_{k_p}(m_p, n_p) \\ &= \sum_{\mathbf{k} \ge \mathbf{l}} \frac{(-1)^{|\mathbf{k}|+|\mathbf{l}|}}{\mathbf{l}!} \binom{\mathbf{k}}{\mathbf{l}} F_{\mathbf{k}}, \end{aligned} \qquad (181) $$

where we used the feasibility of $(Q(m_p, n_p), \mathbf{F}(m_p, n_p))$ in the second line. Finally,

$$ \begin{aligned} \sum_{\mathbf{k} \le \mathbf{m}} F_{\mathbf{k}} &= \sum_{k_1 \le m_1, \dots, k_M \le m_M} \prod_{i=1}^{M} F_{k_i}(m_i, n_i) \\ &= \prod_{i=1}^{M} \sum_{k_i=0}^{m_i} F_{k_i}(m_i, n_i) \\ &= 1, \end{aligned} \qquad (182) $$

since $\sum_{k=0}^m F_k(m, n) = 1$ for all $m, n \in \mathbb{N}$ with $m \ge n$. This shows that $(Q, \mathbf{F})$ is a feasible solution of $(\text{SDP}_n^{m,\le})$ (resp. strictly feasible). $\square$

A direct consequence of this construction is the following result:

**Theorem 10 (Generalisation of Theorem 2).** *Strong duality holds between the programs $(\text{SDP}_n^{m,\le})$ and $(\text{D-SDP}_n^{m,\le})$).*

*Proof.* The proof of Theorem 2 gives a strictly feasible solution $(Q(m, n), \mathbf{F}(m, n))$ of $(\text{SDP}_n^{m,\le})$ for all $m \ge n$. By Lemma 18, the program $(\text{SDP}_n^{m,\le})$ thus has a strictly feasible solution, for all $\mathbf{m} \ge \mathbf{n}$. By Slater condition, this implies that strong duality holds between the programs $(\text{SDP}_n^{m,\le})$ and $(\text{D-SDP}_n^{m,\le})$. $\square$
In particular, strong duality holds between the programs $(SDP_n^{m,\le})$ and $(D-SDP_n^{m,\le})$. Note that the multimode generalisation of Theorem 3 is a direct consequence of Theorem 10:

**Theorem 11** (Generalisation of Theorem 3). *Strong duality holds between the programs $(SDP_n^{m,\ge})$ and $(D-SDP_n^{m,\ge})$.*

*Proof.* The strictly feasible solution of $(SDP_n^{m,\le})$ derived in the proof of Theorem 10 yields a strictly feasible solution for $(SDP_n^{m,\ge})$. With Slater condition, this shows again that strong duality holds between the programs $(SDP_n^{m,\ge})$ and $(D-SDP_n^{m,\ge})$. $\square$

In particular, strong duality holds between the programs $(SDP_n^{m,1,\le})$ and $(D-SDP_n^{m,1,\le})$. We recall the following definition from the main text: for all $n \in \mathbb{N}$, $F^n = (F_k^n)_{k \in \mathbb{N}} \in \mathbb{R}^\mathbb{N}$ where

• if $n$ is even:

$$F_k^n := \begin{cases} \frac{1}{2^n} \binom{k}{2} \binom{n-k}{\frac{n-k}{2}} & \text{when } k \le n, k \text{ even,} \\ 0 & \text{otherwise,} \end{cases} \qquad (183)$$

• if $n$ is odd:

$$F_k^n := \begin{cases} \frac{1}{2^n} \binom{\lfloor \frac{n}{2} \rfloor}{\lfloor \frac{k}{2} \rfloor}^2 & \text{when } k \le n, \\ 0 & \text{otherwise.} \end{cases} \qquad (184)$$

Let us define, for all $n = (n_1, \dots, n_M) \in \mathbb{N}^m$, $F^n = (F_k^n)_{k \in \mathbb{N}^M} \in \mathbb{R}^{\mathbb{N}^M}$ where

$$F_k^n := \begin{cases} \prod_{i=1}^{M} F_{k_i}^{n_i} & \text{when } k \le n, \\ 0 & \text{otherwise.} \end{cases} \qquad (185)$$

By (60), for all $n \in \mathbb{N}$, $F_n^n \ge \frac{1}{n+1}$, so for all $n = (n_1, \dots, n_M) \in \mathbb{N}^M$,

$$F_n^n \ge \frac{1}{\pi_n}. \qquad (186)$$

Like in the single-mode case, the program $(SDP_n^{m,\le})$ is equivalent to

$$(SDP_n^{m,\le}) \quad \left\{ \begin{array}{ll} \displaystyle \sup_{F \in \mathbb{R}^{\pi_m}} & F_n \\ \text{subject to} & \displaystyle \sum_{k \le m} F_k = 1 \\ \text{and} & \forall k \le m, F_k \ge 0 \\ \text{and} & \displaystyle \sum_{k \le m} F_k \mathcal{L}_k \in \mathcal{R}_{m,+}(\mathbb{R}_+^M), \end{array} \right.$$

with the dual program given by

$$(D-SDP_n^{m,\le}) \quad \left\{ \begin{array}{ll} \displaystyle \inf_{y, \mu \in \mathbb{R} \times \mathbb{R}^{\pi_m}} & y \\ \text{subject to} & y \ge 1 + \mu_n \\ \text{and} & \forall k \le m, k \ne n, y \ge \mu_k \\ \text{and} & \forall g \in \mathcal{R}_{m,+}(\mathbb{R}_+^M), \left\langle \sum_{k \le m} \mu_k \mathcal{L}_k, g \right\rangle \ge 0, \end{array} \right.$$

for all $m \ge n$. Moreover, adding the condition $\mu_k \le 1$ for all $k \le m$ does not change the optimal value of the program. We enforce this condition in what follows. With Lemma 7 and Lemma 18, we thus obtain the following result:
**Lemma 19 (Generalisation of Lemma 7).** For all $m \ge n$, $F^m$ (defined in Eq. (185)) is a feasible solution of $(SDP_n^{m,\le})$.

In particular, for all $m \in \mathbb{N}^M$, $\sum_{k \le m} F_k^m \mathcal{L}_k \in \mathcal{R}_{m,+}(\mathbb{R}_+^M)$. For $m, n \in \mathbb{N}^M$ with $m \ge n$, let $\mu \in \mathbb{R}^{\pi_m}$ be a feasible solution of $(D-SDP_n^{m,\le})$. Then, for all $l \le m$

$$ \left\langle \sum_{k \le m} \mu_k \mathcal{L}_k, \sum_{k \le l} F_k^l \mathcal{L}_k \right\rangle \ge 0, \qquad (187) $$

so that

$$ \sum_{k \le l} \mu_k F_k^l \ge 0. \qquad (188) $$

Hence, for all $l \ge m$,

$$ \begin{aligned} \mu_l &\ge -\frac{1}{F_l^l} \sum_{\substack{k \le l \\ k \ne l}} \mu_k F_k^l \\ &\ge -\frac{1}{F_l^l} \sum_{\substack{k \le l \\ k \ne l}} F_k^l \\ &= 1 - \frac{1}{F_l^l} \\ &\ge 1 - \pi_l, \end{aligned} \qquad (189) $$

where we used $F_l^l > 0$ in the first line, $\mu_k \le 1$ and $F_k^l \ge 0$ in the second line, $\sum_{k \le l} F_k^l = 1$ in the third line, and Eq. (186) in the last line.

With these additional results, the proof of convergence of the multimode hierarchy of lower bounds $(SDP_n^{m,\le})$ is then obtained directly from its single-mode counterpart using multi-index notations:

**Theorem 12 (Generalisation of Theorem 5).** The increasing sequence of optimal values $\omega_n^{m,\le}$ of $(SDP_n^{m,\le})$ converges to the optimal value $\omega_n$ of $(LP_n)$:

$$ \lim_{m \to +\infty} \omega_n^{m,\le} = \omega_n. \qquad (190) $$

With Lemma 17, we also obtain

$$ \lim_{m \to +\infty} \omega_n^{m,\le} = \omega_n. \qquad (191) $$

Like in the single-mode case, this result implies strong duality between the linear programs:

**Theorem 13 (Generalisation of Theorem 6).** Strong duality holds between the programs $(LP_n)$ and $(D-LP_n)$.

## I Bounds on threshold values of several witness for $n = 3$

Below, we provide tables of numerical upper bounds and lower bounds obtained on the threshold values for witnesses of the form:

$$ \hat{\Omega}_{(a_1,a_2,a_3)} = a_1 |1\rangle\langle 1| + a_2 |2\rangle\langle 2| + a_3 |3\rangle\langle 3| \qquad (192) $$

where $\forall i \in \{1, 2, 3\}$, $0 \le a_i \le 1$ and $\max_i a_i = 1$. We focused on these particular witnesses for experimental considerations as it is challenging to obtain fidelities with higher Fock states. We vary each $a_i$ from 0 to 1 with a step of 0.1.
<table><caption>Table 2: Upper and lower bounds on the threshold values of witnesses of the form $\hat{\Omega}_{(1,a_2,a_3)}$.</caption><thead><tr><th>a<sub>1</sub></th><th>a<sub>2</sub></th><th>a<sub>3</sub></th><th>ω<sup>≤</sup><sub>a</sub></th><th>ω<sup>≥</sup><sub>a</sub></th><th>a<sub>1</sub></th><th>a<sub>2</sub></th><th>a<sub>3</sub></th><th>ω<sup>≤</sup><sub>a</sub></th><th>ω<sup>≥</sup><sub>a</sub></th><th>a<sub>1</sub></th><th>a<sub>2</sub></th><th>a<sub>3</sub></th><th>ω<sup>≤</sup><sub>a</sub></th><th>ω<sup>≥</sup><sub>a</sub></th></tr></thead><tbody><tr><td>1.0</td><td>0.0</td><td>0.0</td><td>0.500</td><td>0.529</td><td>1.0</td><td>0.3</td><td>0.8</td><td>0.589</td><td>0.590</td><td>1.0</td><td>0.7</td><td>0.5</td><td>0.705</td><td>0.715</td></tr><tr><td>1.0</td><td>0.0</td><td>0.1</td><td>0.500</td><td>0.529</td><td>1.0</td><td>0.3</td><td>0.9</td><td>0.606</td><td>0.610</td><td>1.0</td><td>0.7</td><td>0.6</td><td>0.718</td><td>0.720</td></tr><tr><td>1.0</td><td>0.0</td><td>0.2</td><td>0.500</td><td>0.529</td><td>1.0</td><td>0.3</td><td>1.0</td><td>0.626</td><td>0.633</td><td>1.0</td><td>0.7</td><td>0.7</td><td>0.735</td><td>0.738</td></tr><tr><td>1.0</td><td>0.0</td><td>0.3</td><td>0.500</td><td>0.529</td><td>1.0</td><td>0.4</td><td>0.0</td><td>0.610</td><td>0.615</td><td>1.0</td><td>0.7</td><td>0.8</td><td>0.754</td><td>0.758</td></tr><tr><td>1.0</td><td>0.0</td><td>0.4</td><td>0.500</td><td>0.529</td><td>1.0</td><td>0.4</td><td>0.1</td><td>0.610</td><td>0.615</td><td>1.0</td><td>0.7</td><td>0.9</td><td>0.774</td><td>0.781</td></tr><tr><td>1.0</td><td>0.0</td><td>0.5</td><td>0.500</td><td>0.528</td><td>1.0</td><td>0.4</td><td>0.2</td><td>0.610</td><td>0.615</td><td>1.0</td><td>0.7</td><td>1.0</td><td>0.795</td><td>0.805</td></tr><tr><td>1.0</td><td>0.0</td><td>0.6</td><td>0.500</td><td>0.529</td><td>1.0</td><td>0.4</td><td>0.3</td><td>0.610</td><td>0.615</td><td>1.0</td><td>0.8</td><td>0.0</td><td>0.739</td><td>0.751</td></tr><tr><td>1.0</td><td>0.0</td><td>0.7</td><td>0.500</td><td>0.529</td><td>1.0</td><td>0.4</td><td>0.4</td><td>0.610</td><td>0.615</td><td>1.0</td><td>0.8</td><td>0.1</td><td>0.739</td><td>0.751</td></tr><tr><td>1.0</td><td>0.0</td><td>0.8</td><td>0.500</td><td>0.529</td><td>1.0</td><td>0.4</td><td>0.5</td><td>0.610</td><td>0.615</td><td>1.0</td><td>0.8</td><td>0.2</td><td>0.739</td><td>0.751</td></tr><tr><td>1.0</td><td>0.0</td><td>0.9</td><td>0.500</td><td>0.530</td><td>1.0</td><td>0.4</td><td>0.6</td><td>0.610</td><td>0.615</td><td>1.0</td><td>0.8</td><td>0.3</td><td>0.739</td><td>0.751</td></tr><tr><td>1.0</td><td>0.0</td><td>1.0</td><td>0.500</td><td>0.563</td><td>1.0</td><td>0.4</td><td>0.7</td><td>0.614</td><td>0.615</td><td>1.0</td><td>0.8</td><td>0.4</td><td>0.739</td><td>0.751</td></tr><tr><td>1.0</td><td>0.1</td><td>0.0</td><td>0.526</td><td>0.529</td><td>1.0</td><td>0.4</td><td>0.8</td><td>0.629</td><td>0.631</td><td>1.0</td><td>0.8</td><td>0.5</td><td>0.742</td><td>0.751</td></tr><tr><td>1.0</td><td>0.1</td><td>0.1</td><td>0.526</td><td>0.529</td><td>1.0</td><td>0.4</td><td>0.9</td><td>0.648</td><td>0.653</td><td>1.0</td><td>0.8</td><td>0.6</td><td>0.759</td><td>0.761</td></tr><tr><td>1.0</td><td>0.1</td><td>0.2</td><td>0.526</td><td>0.529</td><td>1.0</td><td>0.4</td><td>1.0</td><td>0.669</td><td>0.677</td><td>1.0</td><td>0.8</td><td>0.7</td><td>0.777</td><td>0.780</td></tr><tr><td>1.0</td><td>0.1</td><td>0.3</td><td>0.526</td><td>0.529</td><td>1.0</td><td>0.5</td><td>0.0</td><td>0.640</td><td>0.649</td><td>1.0</td><td>0.8</td><td>0.8</td><td>0.796</td><td>0.801</td></tr><tr><td>1.0</td><td>0.1</td><td>0.4</td><td>0.526</td><td>0.529</td><td>1.0</td><td>0.5</td><td>0.1</td><td>0.640</td><td>0.649</td><td>1.0</td><td>0.8</td><td>0.9</td><td>0.816</td><td>0.824</td></tr><tr><td>1.0</td><td>0.1</td><td>0.5</td><td>0.526</td><td>0.529</td><td>1.0</td><td>0.5</td><td>0.2</td><td>0.640</td><td>0.649</td><td>1.0</td><td>0.8</td><td>1.0</td><td>0.837</td><td>0.848</td></tr><tr><td>1.0</td><td>0.1</td><td>0.6</td><td>0.526</td><td>0.529</td><td>1.0</td><td>0.5</td><td>0.3</td><td>0.640</td><td>0.649</td><td>1.0</td><td>0.9</td><td>0.0</td><td>0.773</td><td>0.790</td></tr><tr><td>1.0</td><td>0.1</td><td>0.7</td><td>0.526</td><td>0.529</td><td>1.0</td><td>0.5</td><td>0.4</td><td>0.640</td><td>0.649</td><td>1.0</td><td>0.9</td><td>0.1</td><td>0.773</td><td>0.790</td></tr><tr><td>1.0</td><td>0.1</td><td>0.8</td><td>0.526</td><td>0.529</td><td>1.0</td><td>0.5</td><td>0.5</td><td>0.640</td><td>0.649</td><td>1.0</td><td>0.9</td><td>0.2</td><td>0.773</td><td>0.790</td></tr><tr><td>1.0</td><td>0.1</td><td>0.9</td><td>0.526</td><td>0.528</td><td>1.0</td><td>0.5</td><td>0.6</td><td>0.640</td><td>0.649</td><td>1.0</td><td>0.9</td><td>0.3</td><td>0.773</td><td>0.790</td></tr><tr><td>1.0</td><td>0.1</td><td>1.0</td><td>0.542</td><td>0.563</td><td>1.0</td><td>0.5</td><td>0.7</td><td>0.654</td><td>0.655</td><td>1.0</td><td>0.9</td><td>0.4</td><td>0.773</td><td>0.790</td></tr><tr><td>1.0</td><td>0.2</td><td>0.0</td><td>0.552</td><td>0.555</td><td>1.0</td><td>0.5</td><td>0.8</td><td>0.671</td><td>0.673</td><td>1.0</td><td>0.9</td><td>0.5</td><td>0.783</td><td>0.790</td></tr><tr><td>1.0</td><td>0.2</td><td>0.1</td><td>0.552</td><td>0.555</td><td>1.0</td><td>0.5</td><td>0.9</td><td>0.690</td><td>0.696</td><td>1.0</td><td>0.9</td><td>0.6</td><td>0.800</td><td>0.803</td></tr><tr><td>1.0</td><td>0.2</td><td>0.2</td><td>0.552</td><td>0.555</td><td>1.0</td><td>0.5</td><td>1.0</td><td>0.711</td><td>0.719</td><td>1.0</td><td>0.9</td><td>0.7</td><td>0.818</td><td>0.822</td></tr><tr><td>1.0</td><td>0.2</td><td>0.3</td><td>0.552</td><td>0.555</td><td>1.0</td><td>0.6</td><td>0.0</td><td>0.672</td><td>0.682</td><td>1.0</td><td>0.9</td><td>0.8</td><td>0.838</td><td>0.844</td></tr><tr><td>1.0</td><td>0.2</td><td>0.4</td><td>0.552</td><td>0.555</td><td>1.0</td><td>0.6</td><td>0.1</td><td>0.672</td><td>0.682</td><td>1.0</td><td>0.9</td><td>0.9</td><td>0.858</td><td>0.867</td></tr><tr><td>1.0</td><td>0.2</td><td>0.5</td><td>0.552</td><td>0.555</td><td>1.0</td><td>0.6</td><td>0.2</td><td>0.672</td><td>0.682</td><td>1.0</td><td>0.9</td><td>1.0</td><td>0.879</td><td>0.891</td></tr><tr><td>1.0</td><td>0.2</td><td>0.6</td><td>0.552</td><td>0.555</td><td>1.0</td><td>0.6</td><td>0.3</td><td>0.672</td><td>0.683</td><td>1.0</td><td>1.0</td><td>0.0</td><td>0.809</td><td>0.830</td></tr><tr><td>1.0</td><td>0.2</td><td>0.7</td><td>0.552</td><td>0.555</td><td>1.0</td><td>0.6</td><td>0.4</td><td>0.672</td><td>0.682</td><td>1.0</td><td>1.0</td><td>0.1</td><td>0.809</td><td>0.830</td></tr><tr><td>1.0</td><td>0.2</td><td>0.8</td><td>0.552</td><td>0.555</td><td>1.0</td><td>0.6</td><td>0.5</td><td>0.672</td><td>0.682</td><td>1.0</td><td>1.0</td><td>0.2</td><td>0.809</td><td>0.830</td></tr><tr><td>1.0</td><td>0.2</td><td>0.9</td><td>0.565</td><td>0.567</td><td>1.0</td><td>0.6</td><td>0.6</td><td>0.678</td><td>0.682</td><td>1.0</td><td>1.0</td><td>0.3</td><td>0.809</td><td>0.830</td></tr><tr><td>1.0</td><td>0.2</td><td>1.0</td><td>0.584</td><td>0.594</td><td>1.0</td><td>0.6</td><td>0.7</td><td>0.694</td><td>0.696</td><td>1.0</td><td>1.0</td><td>0.4</td><td>0.809</td><td>0.830</td></tr><tr><td>1.0</td><td>0.3</td><td>0.0</td><td>0.581</td><td>0.585</td><td>1.0</td><td>0.6</td><td>0.8</td><td>0.712</td><td>0.716</td><td>1.0</td><td>1.0</td><td>0.5</td><td>0.824</td><td>0.830</td></tr><tr><td>1.0</td><td>0.3</td><td>0.1</td><td>0.581</td><td>0.585</td><td>1.0</td><td>0.6</td><td>0.9</td><td>0.732</td><td>0.739</td><td>1.0</td><td>1.0</td><td>0.6</td><td>0.841</td><td>0.845</td></tr><tr><td>1.0</td><td>0.3</td><td>0.2</td><td>0.581</td><td>0.584</td><td>1.0</td><td>0.6</td><td>1.0</td><td>0.753</td><td>0.762</td><td>1.0</td><td>1.0</td><td>0.7</td><td>0.860</td><td>0.865</td></tr><tr><td>1.0</td><td>0.3</td><td>0.3</td><td>0.581</td><td>0.584</td><td>1.0</td><td>0.7</td><td>0.0</td><td>0.705</td><td>0.716</td><td>1.0</td><td>1.0</td><td>0.8</td><td>0.879</td><td>0.887</td></tr><tr><td>1.0</td><td>0.3</td><td>0.4</td><td>0.581</td><td>0.584</td><td>1.0</td><td>0.7</td><td>0.1</td><td>0.705</td><td>0.715</td><td>1.0</td><td>1.0</td><td>0.9</td><td>0.900</td><td>0.910</td></tr><tr><td>1.0</td><td>0.3</td><td>0.5</td><td>0.581</td><td>0.584</td><td>1.0</td><td>0.7</td><td>0.2</td><td>0.705</td><td>0.715</td><td>1.0</td><td>1.0</td><td>1.0</td><td>0.922</td><td>0.934</td></tr><tr><td>1.0</td><td>0.3</td><td>0.6</td><td>0.581</td><td>0.584</td><td>1.0</td><td>0.7</td><td>0.3</td><td>0.705</td><td>0.715</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1.0</td><td>0.3</td><td>0.7</td><td>0.581</td><td>0.584</td><td>1.0</td><td>0.7</td><td>0.4</td><td>0.705</td><td>0.715</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>
<table><caption>Table 3: Upper and lower bounds on the threshold values of witnesses of the form $\hat{\Omega}_{(a_1,1,a_3)}$.</caption><thead><tr><th>a<sub>1</sub></th><th>a<sub>2</sub></th><th>a<sub>3</sub></th><th>ω<sup>≤</sup><sub>a</sub></th><th>ω<sup>≥</sup><sub>a</sub></th><th>a<sub>1</sub></th><th>a<sub>2</sub></th><th>a<sub>3</sub></th><th>ω<sup>≤</sup><sub>a</sub></th><th>ω<sup>≥</sup><sub>a</sub></th><th>a<sub>1</sub></th><th>a<sub>2</sub></th><th>a<sub>3</sub></th><th>ω<sup>≤</sup><sub>a</sub></th><th>ω<sup>≥</sup><sub>a</sub></th></tr></thead><tbody><tr><td>0.0</td><td>1.0</td><td>0.0</td><td>0.500</td><td>0.546</td><td>0.3</td><td>1.0</td><td>0.4</td><td>0.594</td><td>0.603</td><td>0.6</td><td>1.0</td><td>0.8</td><td>0.767</td><td>0.779</td></tr><tr><td>0.0</td><td>1.0</td><td>0.1</td><td>0.500</td><td>0.551</td><td>0.3</td><td>1.0</td><td>0.5</td><td>0.617</td><td>0.629</td><td>0.6</td><td>1.0</td><td>0.9</td><td>0.792</td><td>0.806</td></tr><tr><td>0.0</td><td>1.0</td><td>0.2</td><td>0.500</td><td>0.546</td><td>0.3</td><td>1.0</td><td>0.6</td><td>0.642</td><td>0.655</td><td>0.6</td><td>1.0</td><td>1.0</td><td>0.817</td><td>0.849</td></tr><tr><td>0.0</td><td>1.0</td><td>0.3</td><td>0.500</td><td>0.546</td><td>0.3</td><td>1.0</td><td>0.7</td><td>0.667</td><td>0.683</td><td>0.7</td><td>1.0</td><td>0.0</td><td>0.680</td><td>0.701</td></tr><tr><td>0.0</td><td>1.0</td><td>0.4</td><td>0.517</td><td>0.546</td><td>0.3</td><td>1.0</td><td>0.8</td><td>0.693</td><td>0.712</td><td>0.7</td><td>1.0</td><td>0.1</td><td>0.680</td><td>0.702</td></tr><tr><td>0.0</td><td>1.0</td><td>0.5</td><td>0.543</td><td>0.559</td><td>0.3</td><td>1.0</td><td>0.9</td><td>0.719</td><td>0.741</td><td>0.7</td><td>1.0</td><td>0.2</td><td>0.680</td><td>0.702</td></tr><tr><td>0.0</td><td>1.0</td><td>0.6</td><td>0.569</td><td>0.588</td><td>0.3</td><td>1.0</td><td>1.0</td><td>0.747</td><td>0.789</td><td>0.7</td><td>1.0</td><td>0.3</td><td>0.691</td><td>0.702</td></tr><tr><td>0.0</td><td>1.0</td><td>0.7</td><td>0.597</td><td>0.618</td><td>0.4</td><td>1.0</td><td>0.0</td><td>0.570</td><td>0.603</td><td>0.7</td><td>1.0</td><td>0.4</td><td>0.710</td><td>0.714</td></tr><tr><td>0.0</td><td>1.0</td><td>0.8</td><td>0.625</td><td>0.650</td><td>0.4</td><td>1.0</td><td>0.1</td><td>0.570</td><td>0.600</td><td>0.7</td><td>1.0</td><td>0.5</td><td>0.729</td><td>0.735</td></tr><tr><td>0.0</td><td>1.0</td><td>0.9</td><td>0.654</td><td>0.682</td><td>0.4</td><td>1.0</td><td>0.2</td><td>0.579</td><td>0.603</td><td>0.7</td><td>1.0</td><td>0.6</td><td>0.750</td><td>0.759</td></tr><tr><td>0.0</td><td>1.0</td><td>1.0</td><td>0.683</td><td>0.740</td><td>0.4</td><td>1.0</td><td>0.3</td><td>0.600</td><td>0.607</td><td>0.7</td><td>1.0</td><td>0.7</td><td>0.772</td><td>0.782</td></tr><tr><td>0.1</td><td>1.0</td><td>0.0</td><td>0.505</td><td>0.551</td><td>0.4</td><td>1.0</td><td>0.4</td><td>0.622</td><td>0.631</td><td>0.7</td><td>1.0</td><td>0.8</td><td>0.794</td><td>0.806</td></tr><tr><td>0.1</td><td>1.0</td><td>0.1</td><td>0.505</td><td>0.551</td><td>0.4</td><td>1.0</td><td>0.5</td><td>0.644</td><td>0.653</td><td>0.7</td><td>1.0</td><td>0.9</td><td>0.817</td><td>0.830</td></tr><tr><td>0.1</td><td>1.0</td><td>0.2</td><td>0.505</td><td>0.551</td><td>0.4</td><td>1.0</td><td>0.6</td><td>0.667</td><td>0.679</td><td>0.7</td><td>1.0</td><td>1.0</td><td>0.842</td><td>0.870</td></tr><tr><td>0.1</td><td>1.0</td><td>0.3</td><td>0.517</td><td>0.551</td><td>0.4</td><td>1.0</td><td>0.7</td><td>0.692</td><td>0.705</td><td>0.8</td><td>1.0</td><td>0.0</td><td>0.722</td><td>0.744</td></tr><tr><td>0.1</td><td>1.0</td><td>0.4</td><td>0.542</td><td>0.556</td><td>0.4</td><td>1.0</td><td>0.8</td><td>0.717</td><td>0.733</td><td>0.8</td><td>1.0</td><td>0.1</td><td>0.722</td><td>0.744</td></tr><tr><td>0.1</td><td>1.0</td><td>0.5</td><td>0.567</td><td>0.583</td><td>0.4</td><td>1.0</td><td>0.9</td><td>0.743</td><td>0.763</td><td>0.8</td><td>1.0</td><td>0.2</td><td>0.722</td><td>0.744</td></tr><tr><td>0.1</td><td>1.0</td><td>0.6</td><td>0.593</td><td>0.610</td><td>0.4</td><td>1.0</td><td>1.0</td><td>0.769</td><td>0.813</td><td>0.8</td><td>1.0</td><td>0.3</td><td>0.724</td><td>0.744</td></tr><tr><td>0.1</td><td>1.0</td><td>0.7</td><td>0.619</td><td>0.641</td><td>0.5</td><td>1.0</td><td>0.0</td><td>0.604</td><td>0.632</td><td>0.8</td><td>1.0</td><td>0.4</td><td>0.741</td><td>0.745</td></tr><tr><td>0.1</td><td>1.0</td><td>0.8</td><td>0.647</td><td>0.671</td><td>0.5</td><td>1.0</td><td>0.1</td><td>0.604</td><td>0.638</td><td>0.8</td><td>1.0</td><td>0.5</td><td>0.760</td><td>0.764</td></tr><tr><td>0.1</td><td>1.0</td><td>0.9</td><td>0.675</td><td>0.701</td><td>0.5</td><td>1.0</td><td>0.2</td><td>0.610</td><td>0.632</td><td>0.8</td><td>1.0</td><td>0.6</td><td>0.779</td><td>0.786</td></tr><tr><td>0.1</td><td>1.0</td><td>1.0</td><td>0.704</td><td>0.750</td><td>0.5</td><td>1.0</td><td>0.3</td><td>0.629</td><td>0.635</td><td>0.8</td><td>1.0</td><td>0.7</td><td>0.800</td><td>0.809</td></tr><tr><td>0.2</td><td>1.0</td><td>0.0</td><td>0.519</td><td>0.556</td><td>0.5</td><td>1.0</td><td>0.4</td><td>0.650</td><td>0.658</td><td>0.8</td><td>1.0</td><td>0.8</td><td>0.822</td><td>0.832</td></tr><tr><td>0.2</td><td>1.0</td><td>0.1</td><td>0.519</td><td>0.556</td><td>0.5</td><td>1.0</td><td>0.5</td><td>0.672</td><td>0.681</td><td>0.8</td><td>1.0</td><td>0.9</td><td>0.844</td><td>0.857</td></tr><tr><td>0.2</td><td>1.0</td><td>0.2</td><td>0.522</td><td>0.556</td><td>0.5</td><td>1.0</td><td>0.6</td><td>0.694</td><td>0.705</td><td>0.8</td><td>1.0</td><td>1.0</td><td>0.867</td><td>0.891</td></tr><tr><td>0.2</td><td>1.0</td><td>0.3</td><td>0.544</td><td>0.556</td><td>0.5</td><td>1.0</td><td>0.7</td><td>0.717</td><td>0.729</td><td>0.9</td><td>1.0</td><td>0.0</td><td>0.765</td><td>0.787</td></tr><tr><td>0.2</td><td>1.0</td><td>0.4</td><td>0.567</td><td>0.578</td><td>0.5</td><td>1.0</td><td>0.8</td><td>0.742</td><td>0.756</td><td>0.9</td><td>1.0</td><td>0.1</td><td>0.765</td><td>0.787</td></tr><tr><td>0.2</td><td>1.0</td><td>0.5</td><td>0.592</td><td>0.605</td><td>0.5</td><td>1.0</td><td>0.9</td><td>0.767</td><td>0.784</td><td>0.9</td><td>1.0</td><td>0.2</td><td>0.765</td><td>0.787</td></tr><tr><td>0.2</td><td>1.0</td><td>0.6</td><td>0.617</td><td>0.633</td><td>0.5</td><td>1.0</td><td>1.0</td><td>0.793</td><td>0.831</td><td>0.9</td><td>1.0</td><td>0.3</td><td>0.765</td><td>0.787</td></tr><tr><td>0.2</td><td>1.0</td><td>0.7</td><td>0.643</td><td>0.660</td><td>0.6</td><td>1.0</td><td>0.0</td><td>0.641</td><td>0.665</td><td>0.9</td><td>1.0</td><td>0.4</td><td>0.774</td><td>0.787</td></tr><tr><td>0.2</td><td>1.0</td><td>0.8</td><td>0.669</td><td>0.690</td><td>0.6</td><td>1.0</td><td>0.1</td><td>0.641</td><td>0.665</td><td>0.9</td><td>1.0</td><td>0.5</td><td>0.791</td><td>0.795</td></tr><tr><td>0.2</td><td>1.0</td><td>0.9</td><td>0.697</td><td>0.722</td><td>0.6</td><td>1.0</td><td>0.2</td><td>0.641</td><td>0.665</td><td>0.9</td><td>1.0</td><td>0.6</td><td>0.810</td><td>0.815</td></tr><tr><td>0.2</td><td>1.0</td><td>1.0</td><td>0.725</td><td>0.770</td><td>0.6</td><td>1.0</td><td>0.3</td><td>0.660</td><td>0.665</td><td>0.9</td><td>1.0</td><td>0.7</td><td>0.829</td><td>0.836</td></tr><tr><td>0.3</td><td>1.0</td><td>0.0</td><td>0.542</td><td>0.575</td><td>0.6</td><td>1.0</td><td>0.4</td><td>0.679</td><td>0.685</td><td>0.9</td><td>1.0</td><td>0.8</td><td>0.850</td><td>0.860</td></tr><tr><td>0.3</td><td>1.0</td><td>0.1</td><td>0.542</td><td>0.575</td><td>0.6</td><td>1.0</td><td>0.5</td><td>0.700</td><td>0.708</td><td>0.9</td><td>1.0</td><td>0.9</td><td>0.872</td><td>0.883</td></tr><tr><td>0.3</td><td>1.0</td><td>0.2</td><td>0.550</td><td>0.575</td><td>0.6</td><td>1.0</td><td>0.6</td><td>0.722</td><td>0.732</td><td>0.9</td><td>1.0</td><td>1.0</td><td>0.894</td><td>0.913</td></tr><tr><td>0.3</td><td>1.0</td><td>0.3</td><td>0.572</td><td>0.580</td><td>0.6</td><td>1.0</td><td>0.7</td><td>0.744</td><td>0.756</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>
<table><caption>Table 4: Upper and lower bounds on the threshold values of witnesses of the form $\hat{\Omega}_{(a_1,a_2,1)}$.</caption><thead><tr><th>a<sub>1</sub></th><th>a<sub>2</sub></th><th>a<sub>3</sub></th><th>ω<sup>≤</sup><sub>a</sub></th><th>ω<sup>≥</sup><sub>a</sub></th><th>a<sub>1</sub></th><th>a<sub>2</sub></th><th>a<sub>3</sub></th><th>ω<sup>≤</sup><sub>a</sub></th><th>ω<sup>≥</sup><sub>a</sub></th><th>a<sub>1</sub></th><th>a<sub>2</sub></th><th>a<sub>3</sub></th><th>ω<sup>≤</sup><sub>a</sub></th><th>ω<sup>≥</sup><sub>a</sub></th></tr></thead><tbody><tr><td>0.0</td><td>0.0</td><td>1.0</td><td>0.377</td><td>0.428</td><td>0.3</td><td>0.4</td><td>1.0</td><td>0.529</td><td>0.547</td><td>0.6</td><td>0.8</td><td>1.0</td><td>0.734</td><td>0.752</td></tr><tr><td>0.0</td><td>0.1</td><td>1.0</td><td>0.401</td><td>0.437</td><td>0.3</td><td>0.5</td><td>1.0</td><td>0.561</td><td>0.583</td><td>0.6</td><td>0.9</td><td>1.0</td><td>0.775</td><td>0.793</td></tr><tr><td>0.0</td><td>0.2</td><td>1.0</td><td>0.429</td><td>0.452</td><td>0.3</td><td>0.6</td><td>1.0</td><td>0.594</td><td>0.621</td><td>0.7</td><td>0.0</td><td>1.0</td><td>0.463</td><td>0.521</td></tr><tr><td>0.0</td><td>0.3</td><td>1.0</td><td>0.458</td><td>0.474</td><td>0.3</td><td>0.7</td><td>1.0</td><td>0.628</td><td>0.657</td><td>0.7</td><td>0.1</td><td>1.0</td><td>0.490</td><td>0.522</td></tr><tr><td>0.0</td><td>0.4</td><td>1.0</td><td>0.488</td><td>0.510</td><td>0.3</td><td>0.8</td><td>1.0</td><td>0.667</td><td>0.694</td><td>0.7</td><td>0.2</td><td>1.0</td><td>0.521</td><td>0.542</td></tr><tr><td>0.0</td><td>0.5</td><td>1.0</td><td>0.519</td><td>0.533</td><td>0.3</td><td>0.9</td><td>1.0</td><td>0.707</td><td>0.733</td><td>0.7</td><td>0.3</td><td>1.0</td><td>0.555</td><td>0.580</td></tr><tr><td>0.0</td><td>0.6</td><td>1.0</td><td>0.550</td><td>0.572</td><td>0.4</td><td>0.0</td><td>1.0</td><td>0.426</td><td>0.480</td><td>0.7</td><td>0.4</td><td>1.0</td><td>0.594</td><td>0.615</td></tr><tr><td>0.0</td><td>0.7</td><td>1.0</td><td>0.583</td><td>0.605</td><td>0.4</td><td>0.1</td><td>1.0</td><td>0.451</td><td>0.485</td><td>0.7</td><td>0.5</td><td>1.0</td><td>0.635</td><td>0.653</td></tr><tr><td>0.0</td><td>0.8</td><td>1.0</td><td>0.616</td><td>0.642</td><td>0.4</td><td>0.2</td><td>1.0</td><td>0.480</td><td>0.501</td><td>0.7</td><td>0.6</td><td>1.0</td><td>0.676</td><td>0.692</td></tr><tr><td>0.0</td><td>0.9</td><td>1.0</td><td>0.649</td><td>0.678</td><td>0.4</td><td>0.3</td><td>1.0</td><td>0.511</td><td>0.528</td><td>0.7</td><td>0.7</td><td>1.0</td><td>0.717</td><td>0.733</td></tr><tr><td>0.1</td><td>0.0</td><td>1.0</td><td>0.390</td><td>0.440</td><td>0.4</td><td>0.4</td><td>1.0</td><td>0.543</td><td>0.567</td><td>0.7</td><td>0.8</td><td>1.0</td><td>0.758</td><td>0.774</td></tr><tr><td>0.1</td><td>0.1</td><td>1.0</td><td>0.414</td><td>0.448</td><td>0.4</td><td>0.5</td><td>1.0</td><td>0.576</td><td>0.602</td><td>0.7</td><td>0.9</td><td>1.0</td><td>0.800</td><td>0.815</td></tr><tr><td>0.1</td><td>0.2</td><td>1.0</td><td>0.441</td><td>0.464</td><td>0.4</td><td>0.6</td><td>1.0</td><td>0.610</td><td>0.637</td><td>0.8</td><td>0.0</td><td>1.0</td><td>0.475</td><td>0.535</td></tr><tr><td>0.1</td><td>0.3</td><td>1.0</td><td>0.471</td><td>0.486</td><td>0.4</td><td>0.7</td><td>1.0</td><td>0.649</td><td>0.674</td><td>0.8</td><td>0.1</td><td>1.0</td><td>0.504</td><td>0.535</td></tr><tr><td>0.1</td><td>0.4</td><td>1.0</td><td>0.501</td><td>0.519</td><td>0.4</td><td>0.8</td><td>1.0</td><td>0.689</td><td>0.713</td><td>0.8</td><td>0.2</td><td>1.0</td><td>0.537</td><td>0.562</td></tr><tr><td>0.1</td><td>0.5</td><td>1.0</td><td>0.532</td><td>0.549</td><td>0.4</td><td>0.9</td><td>1.0</td><td>0.729</td><td>0.752</td><td>0.8</td><td>0.3</td><td>1.0</td><td>0.576</td><td>0.597</td></tr><tr><td>0.1</td><td>0.6</td><td>1.0</td><td>0.565</td><td>0.588</td><td>0.5</td><td>0.0</td><td>1.0</td><td>0.439</td><td>0.494</td><td>0.8</td><td>0.4</td><td>1.0</td><td>0.617</td><td>0.633</td></tr><tr><td>0.1</td><td>0.7</td><td>1.0</td><td>0.597</td><td>0.623</td><td>0.5</td><td>0.1</td><td>1.0</td><td>0.464</td><td>0.497</td><td>0.8</td><td>0.5</td><td>1.0</td><td>0.658</td><td>0.672</td></tr><tr><td>0.1</td><td>0.8</td><td>1.0</td><td>0.631</td><td>0.659</td><td>0.5</td><td>0.2</td><td>1.0</td><td>0.494</td><td>0.513</td><td>0.8</td><td>0.6</td><td>1.0</td><td>0.700</td><td>0.713</td></tr><tr><td>0.1</td><td>0.9</td><td>1.0</td><td>0.665</td><td>0.696</td><td>0.5</td><td>0.3</td><td>1.0</td><td>0.525</td><td>0.544</td><td>0.8</td><td>0.7</td><td>1.0</td><td>0.742</td><td>0.754</td></tr><tr><td>0.2</td><td>0.0</td><td>1.0</td><td>0.402</td><td>0.453</td><td>0.5</td><td>0.4</td><td>1.0</td><td>0.558</td><td>0.583</td><td>0.8</td><td>0.8</td><td>1.0</td><td>0.784</td><td>0.808</td></tr><tr><td>0.2</td><td>0.1</td><td>1.0</td><td>0.426</td><td>0.460</td><td>0.5</td><td>0.5</td><td>1.0</td><td>0.592</td><td>0.617</td><td>0.8</td><td>0.9</td><td>1.0</td><td>0.825</td><td>0.849</td></tr><tr><td>0.2</td><td>0.2</td><td>1.0</td><td>0.454</td><td>0.476</td><td>0.5</td><td>0.6</td><td>1.0</td><td>0.631</td><td>0.655</td><td>0.9</td><td>0.0</td><td>1.0</td><td>0.488</td><td>0.549</td></tr><tr><td>0.2</td><td>0.3</td><td>1.0</td><td>0.484</td><td>0.499</td><td>0.5</td><td>0.7</td><td>1.0</td><td>0.671</td><td>0.693</td><td>0.9</td><td>0.1</td><td>1.0</td><td>0.518</td><td>0.549</td></tr><tr><td>0.2</td><td>0.4</td><td>1.0</td><td>0.515</td><td>0.530</td><td>0.5</td><td>0.8</td><td>1.0</td><td>0.711</td><td>0.732</td><td>0.9</td><td>0.2</td><td>1.0</td><td>0.559</td><td>0.578</td></tr><tr><td>0.2</td><td>0.5</td><td>1.0</td><td>0.547</td><td>0.570</td><td>0.5</td><td>0.9</td><td>1.0</td><td>0.752</td><td>0.773</td><td>0.9</td><td>0.3</td><td>1.0</td><td>0.600</td><td>0.613</td></tr><tr><td>0.2</td><td>0.6</td><td>1.0</td><td>0.579</td><td>0.604</td><td>0.6</td><td>0.0</td><td>1.0</td><td>0.451</td><td>0.506</td><td>0.9</td><td>0.4</td><td>1.0</td><td>0.642</td><td>0.652</td></tr><tr><td>0.2</td><td>0.7</td><td>1.0</td><td>0.613</td><td>0.640</td><td>0.6</td><td>0.1</td><td>1.0</td><td>0.477</td><td>0.509</td><td>0.9</td><td>0.5</td><td>1.0</td><td>0.684</td><td>0.693</td></tr><tr><td>0.2</td><td>0.8</td><td>1.0</td><td>0.646</td><td>0.676</td><td>0.6</td><td>0.2</td><td>1.0</td><td>0.507</td><td>0.527</td><td>0.9</td><td>0.6</td><td>1.0</td><td>0.726</td><td>0.736</td></tr><tr><td>0.2</td><td>0.9</td><td>1.0</td><td>0.685</td><td>0.714</td><td>0.6</td><td>0.3</td><td>1.0</td><td>0.540</td><td>0.564</td><td>0.9</td><td>0.7</td><td>1.0</td><td>0.768</td><td>0.779</td></tr><tr><td>0.3</td><td>0.0</td><td>1.0</td><td>0.414</td><td>0.466</td><td>0.6</td><td>0.4</td><td>1.0</td><td>0.573</td><td>0.598</td><td>0.9</td><td>0.8</td><td>1.0</td><td>0.810</td><td>0.821</td></tr><tr><td>0.3</td><td>0.1</td><td>1.0</td><td>0.439</td><td>0.505</td><td>0.6</td><td>0.5</td><td>1.0</td><td>0.613</td><td>0.635</td><td>0.9</td><td>0.9</td><td>1.0</td><td>0.852</td><td>0.866</td></tr><tr><td>0.3</td><td>0.2</td><td>1.0</td><td>0.467</td><td>0.488</td><td>0.6</td><td>0.6</td><td>1.0</td><td>0.653</td><td>0.673</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.3</td><td>0.3</td><td>1.0</td><td>0.497</td><td>0.513</td><td>0.6</td><td>0.7</td><td>1.0</td><td>0.693</td><td>0.712</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>