I would like to evaluate the significance of fixed factor in mixed effect linear regression

Question

I performed the following mixed effect linear regression using lmer,

M1<- lmer(A.Moveis~D.utilizador+(1|Zona),data=d)

summary M1 gave me :

Linear mixed model fit by REML ['lmerMod']
Formula: A.Moveis ~ D.utilizador + (1 | Zona)
   Data: d
REML criterion at convergence: 257.5
Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.1187 -0.7500 -0.3055  0.5125  2.7626
Random effects:
 Groups   Name        Variance Std.Dev.
 Zona     (Intercept)   2.338   1.529

 Residual             126.826  11.262

Number of obs: 35, groups:  Zona, 4
Fixed effects:
             Estimate Std. Error t value
(Intercept)    13.306      2.898   4.592
D.utilizador  -15.914     11.112  -1.432
Correlation of Fixed Effects:
            (Intr)
D.utilizadr -0.706

I know that lme4 package don't give the p-value, but I would like to evaluate the significance of the fixed effects in the model output for my report.Is the t-value enough to evaluate the significance for a report?

Is there any statical tests I could run in order to test the significance of my model and of my fixed effect? I am sorry I am really new with linear regression and I am trying to understand.