Properties

Level $33$
Weight $0$
Character 33.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.7874911756 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.500121034\) \(a_{3}=-0.577350269\) \(a_{4}=-0.749878951\) \(a_{5}=-0.487547535\)
\(a_{6}=-0.288745014\) \(a_{7}=-0.020598324\) \(a_{8}=-0.875151270\) \(a_{9}=+0.333333333\) \(a_{10}=-0.243832777\)
\(a_{11}=-0.301511345\) \(a_{12}=+0.432942815\) \(a_{13}=+0.205144252\) \(a_{14}=-0.010301655\) \(a_{15}=+0.281485701\)
\(a_{16}=+0.312197393\) \(a_{17}=-0.350312890\) \(a_{18}=+0.166707011\) \(a_{19}=-0.660510586\) \(a_{20}=+0.365601634\)
\(a_{21}=+0.011892448\) \(a_{22}=-0.150792165\) \(a_{23}=-1.187619368\) \(a_{24}=+0.505268822\) \(a_{25}=-0.762297401\)
\(a_{26}=+0.102596956\) \(a_{27}=-0.192450090\) \(a_{28}=+0.015446250\) \(a_{29}=-1.437586612\) \(a_{30}=+0.140776920\)
\(a_{31}=+1.263991705\) \(a_{32}=+1.031287753\) \(a_{33}=+0.174077656\) \(a_{34}=-0.175198844\) \(a_{35}=+0.010042662\)
\(a_{36}=-0.249959650\) \(a_{37}=+1.529576404\) \(a_{38}=-0.330335237\) \(a_{39}=-0.118440089\) \(a_{40}=+0.426677845\)
\(a_{41}=-0.078410487\) \(a_{42}=+0.005947663\) \(a_{43}=+1.045281011\) \(a_{44}=+0.226097011\) \(a_{45}=-0.162515845\)
\(a_{46}=-0.593953426\) \(a_{47}=-0.430549956\) \(a_{48}=-0.180247249\) \(a_{49}=-0.999575709\) \(a_{50}=-0.381240964\)
\(a_{51}=+0.202253241\) \(a_{52}=-0.153833357\) \(a_{53}=-1.255549586\) \(a_{54}=-0.096248338\) \(a_{55}=+0.147001113\)
\(a_{56}=+0.018026650\) \(a_{57}=+0.381345965\) \(a_{58}=-0.718967303\) \(a_{59}=+1.890416433\) \(a_{60}=-0.211080202\)
\(a_{61}=-1.835723785\) \(a_{62}=+0.632148838\) \(a_{63}=-0.006866108\) \(a_{64}=+0.203571304\) \(a_{65}=-0.100017575\)
\(a_{66}=+0.087059897\) \(a_{67}=+0.285845526\) \(a_{68}=+0.262692262\) \(a_{69}=+0.685672362\) \(a_{70}=+0.005022547\)
\(a_{71}=-0.773877612\) \(a_{72}=-0.291717090\) \(a_{73}=+0.235641200\) \(a_{74}=+0.764973333\) \(a_{75}=+0.440112610\)
\(a_{76}=+0.495302986\) \(a_{77}=+0.006210628\) \(a_{78}=-0.059234380\) \(a_{79}=+0.378723150\) \(a_{80}=-0.152211070\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.039214734\) \(a_{83}=-0.919254125\) \(a_{84}=-0.008917896\) \(a_{85}=+0.170794186\)
\(a_{86}=+0.522767020\) \(a_{87}=+0.829991017\) \(a_{88}=+0.263868036\) \(a_{89}=-0.661984600\) \(a_{90}=-0.081277592\)
\(a_{91}=-0.004225628\) \(a_{92}=+0.890570766\) \(a_{93}=-0.729765951\) \(a_{94}=-0.215327089\) \(a_{95}=+0.322030308\)
\(a_{96}=-0.595414262\) \(a_{97}=-0.415617501\) \(a_{98}=-0.499908837\) \(a_{99}=-0.100503782\) \(a_{100}=+0.571630776\)

Showing 100 of 282 available coefficients

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