Properties

Level $65$
Weight $0$
Character 65.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 65 = 5 \cdot 13 \)
Weight: \( 0 \)
Character: 65.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.6761628246 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.820722316\) \(a_{3}=+0.809756641\) \(a_{4}=+2.315029750\) \(a_{5}=+0.447213596\)
\(a_{6}=-1.474341986\) \(a_{7}=+0.202830185\) \(a_{8}=-2.394304012\) \(a_{9}=-0.344294183\) \(a_{10}=-0.814251773\)
\(a_{11}=+0.987181302\) \(a_{12}=+1.874610714\) \(a_{13}=-0.277350098\) \(a_{14}=-0.369297444\) \(a_{15}=+0.362134179\)
\(a_{16}=+2.044332994\) \(a_{17}=+0.073967826\) \(a_{18}=+0.626864102\) \(a_{19}=-0.180345103\) \(a_{20}=+1.035312778\)
\(a_{21}=+0.164243089\) \(a_{22}=-1.797383026\) \(a_{23}=+0.557646564\) \(a_{24}=-1.938803573\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.504977513\) \(a_{27}=-1.088551142\) \(a_{28}=+0.469557912\) \(a_{29}=+0.918140946\) \(a_{30}=-0.659345780\)
\(a_{31}=+1.839060353\) \(a_{32}=-1.327858691\) \(a_{33}=+0.799376615\) \(a_{34}=-0.134674871\) \(a_{35}=+0.090708416\)
\(a_{36}=-0.797051276\) \(a_{37}=-0.624843597\) \(a_{38}=+0.328358353\) \(a_{39}=-0.224586084\) \(a_{40}=-1.070765306\)
\(a_{41}=+1.840224176\) \(a_{42}=-0.299041057\) \(a_{43}=+0.605241902\) \(a_{44}=+2.285354083\) \(a_{45}=-0.153973039\)
\(a_{46}=-1.015319543\) \(a_{47}=+1.310533708\) \(a_{48}=+1.655412218\) \(a_{49}=-0.958859916\) \(a_{50}=-0.364144463\)
\(a_{51}=+0.059895938\) \(a_{52}=-0.642073728\) \(a_{53}=-1.300675124\) \(a_{54}=+1.981949355\) \(a_{55}=+0.441480899\)
\(a_{56}=-0.485637125\) \(a_{57}=-0.146035645\) \(a_{58}=-1.671679709\) \(a_{59}=+1.306954951\) \(a_{60}=+0.838351397\)
\(a_{61}=+0.780776433\) \(a_{62}=-3.348418224\) \(a_{63}=-0.069833253\) \(a_{64}=+0.373328956\) \(a_{65}=-0.124034735\)
\(a_{66}=-1.455442841\) \(a_{67}=-1.609688854\) \(a_{68}=+0.171237718\) \(a_{69}=+0.451558008\) \(a_{70}=-0.165154838\)
\(a_{71}=+1.560539776\) \(a_{72}=+0.824344943\) \(a_{73}=+0.059209395\) \(a_{74}=+1.137666680\) \(a_{75}=+0.161951328\)
\(a_{76}=-0.417504278\) \(a_{77}=+0.200230166\) \(a_{78}=+0.408908894\) \(a_{79}=+1.331862825\) \(a_{80}=+0.914253509\)
\(a_{81}=-0.537167333\) \(a_{82}=-3.350537223\) \(a_{83}=+1.599476944\) \(a_{84}=+0.380227637\) \(a_{85}=+0.033079417\)
\(a_{86}=-1.101977437\) \(a_{87}=+0.743470728\) \(a_{88}=-2.363612151\) \(a_{89}=+0.141020621\) \(a_{90}=+0.280342149\)
\(a_{91}=-0.056254972\) \(a_{92}=+1.290968385\) \(a_{93}=+1.489191333\) \(a_{94}=-2.386117967\) \(a_{95}=-0.080652782\)
\(a_{96}=-1.075242393\) \(a_{97}=+0.286538276\) \(a_{98}=+1.745817647\) \(a_{99}=-0.339880780\) \(a_{100}=+0.463005950\)

Showing 100 of 586 available coefficients

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