Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 18.6474302826 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.087382775\) \(a_{3}=-0.577350269\) \(a_{4}=+0.182401300\) \(a_{5}=+1.547299831\)
\(a_{6}=+0.627800738\) \(a_{7}=-1.081538577\) \(a_{8}=+0.889042744\) \(a_{9}=+0.333333333\) \(a_{10}=-1.682507184\)
\(a_{11}=-0.445353913\) \(a_{12}=-0.105309439\) \(a_{13}=-1.404653609\) \(a_{14}=+1.176046419\) \(a_{15}=-0.893333974\)
\(a_{16}=-1.149131065\) \(a_{17}=-0.377810357\) \(a_{18}=-0.362460925\) \(a_{19}=+0.335582664\) \(a_{20}=+0.282229500\)
\(a_{21}=+0.624426588\) \(a_{22}=+0.484270174\) \(a_{23}=+1.283023398\) \(a_{24}=-0.513289067\) \(a_{25}=+1.394136768\)
\(a_{26}=+1.527396140\) \(a_{27}=-0.192450090\) \(a_{28}=-0.197274042\) \(a_{29}=-0.411846707\) \(a_{30}=+0.971395976\)
\(a_{31}=+0.394715603\) \(a_{32}=+0.360502583\) \(a_{33}=+0.257125202\) \(a_{34}=+0.410824474\) \(a_{35}=-1.673464457\)
\(a_{36}=+0.060800433\) \(a_{37}=+0.694179199\) \(a_{38}=-0.364906808\) \(a_{39}=+0.810977139\) \(a_{40}=+1.375615687\)
\(a_{41}=-1.437195496\) \(a_{42}=-0.678990717\) \(a_{43}=+0.203993478\) \(a_{44}=-0.081233133\) \(a_{45}=+0.515766610\)
\(a_{46}=-1.395137543\) \(a_{47}=+1.458500171\) \(a_{48}=+0.663451130\) \(a_{49}=+0.169725693\) \(a_{50}=-1.515960307\)
\(a_{51}=+0.218128911\) \(a_{52}=-0.256210644\) \(a_{53}=+1.012068234\) \(a_{54}=+0.209266913\) \(a_{55}=-0.689096035\)
\(a_{56}=-0.961534024\) \(a_{57}=-0.193748741\) \(a_{58}=+0.447835015\) \(a_{59}=+1.515956320\) \(a_{60}=-0.162945278\)
\(a_{61}=+0.294333665\) \(a_{62}=-0.429206948\) \(a_{63}=-0.360512859\) \(a_{64}=+0.757126766\) \(a_{65}=-2.173420292\)
\(a_{66}=-0.279593515\) \(a_{67}=+1.163677338\) \(a_{68}=-0.068913100\) \(a_{69}=-0.740753904\) \(a_{70}=+1.819696426\)
\(a_{71}=+0.633194360\) \(a_{72}=+0.296347581\) \(a_{73}=-0.695514342\) \(a_{74}=-0.754838504\) \(a_{75}=-0.804905238\)
\(a_{76}=+0.061210714\) \(a_{77}=+0.481667437\) \(a_{78}=-0.881842572\) \(a_{79}=+1.552029840\) \(a_{80}=-1.778050304\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.562781627\) \(a_{83}=+0.511006047\) \(a_{84}=+0.113896221\) \(a_{85}=-0.584585902\)
\(a_{86}=-0.221818995\) \(a_{87}=+0.237779807\) \(a_{88}=-0.395938665\) \(a_{89}=-0.677899049\) \(a_{90}=-0.560835728\)
\(a_{91}=+1.519187065\) \(a_{92}=+0.234025135\) \(a_{93}=-0.227889160\) \(a_{94}=-1.585947963\) \(a_{95}=+0.519246999\)
\(a_{96}=-0.208136263\) \(a_{97}=+1.202063316\) \(a_{98}=-0.184556795\) \(a_{99}=-0.148451304\) \(a_{100}=+0.254292358\)

Showing 100 of 1228 available coefficients

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