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: \( 24.5944725418 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.425420351\) \(a_{3}=+0.577350269\) \(a_{4}=-0.819017525\) \(a_{5}=+0.072841156\)
\(a_{6}=+0.245616554\) \(a_{7}=+0.054287395\) \(a_{8}=-0.773847074\) \(a_{9}=+0.333333333\) \(a_{10}=+0.030988110\)
\(a_{11}=+1.814078306\) \(a_{12}=-0.472859989\) \(a_{13}=-0.810684222\) \(a_{14}=+0.023094963\) \(a_{15}=+0.042054861\)
\(a_{16}=+0.489807232\) \(a_{17}=-0.857952124\) \(a_{18}=+0.141806784\) \(a_{19}=-0.846709249\) \(a_{20}=-0.059658184\)
\(a_{21}=+0.031342842\) \(a_{22}=+0.771745829\) \(a_{23}=-0.629163459\) \(a_{24}=-0.446780816\) \(a_{25}=-0.994694166\)
\(a_{26}=-0.344881566\) \(a_{27}=+0.192450090\) \(a_{28}=-0.044462328\) \(a_{29}=+0.511780700\) \(a_{30}=+0.017890994\)
\(a_{31}=+0.031822624\) \(a_{32}=+0.982221038\) \(a_{33}=+1.047358598\) \(a_{34}=-0.364990293\) \(a_{35}=+0.003954357\)
\(a_{36}=-0.273005842\) \(a_{37}=-1.222706993\) \(a_{38}=-0.360207346\) \(a_{39}=-0.468048754\) \(a_{40}=-0.056367916\)
\(a_{41}=-0.751266041\) \(a_{42}=+0.013333883\) \(a_{43}=-1.664304153\) \(a_{44}=-1.485761925\) \(a_{45}=+0.024280385\)
\(a_{46}=-0.267658940\) \(a_{47}=+0.195774952\) \(a_{48}=+0.282790337\) \(a_{49}=-0.997052879\) \(a_{50}=-0.423163141\)
\(a_{51}=-0.495338890\) \(a_{52}=+0.663964585\) \(a_{53}=-1.074640705\) \(a_{54}=+0.081872185\) \(a_{55}=+0.132139562\)
\(a_{56}=-0.042010142\) \(a_{57}=-0.488847813\) \(a_{58}=+0.217721925\) \(a_{59}=+1.448067303\) \(a_{60}=-0.034443668\)
\(a_{61}=-1.747663155\) \(a_{62}=+0.013537992\) \(a_{63}=+0.018095798\) \(a_{64}=-0.071950413\) \(a_{65}=-0.059051176\)
\(a_{66}=+0.445567662\) \(a_{67}=+0.036152876\) \(a_{68}=+0.702677825\) \(a_{69}=-0.363247693\) \(a_{70}=+0.001682264\)
\(a_{71}=+0.310914430\) \(a_{72}=-0.257949025\) \(a_{73}=-0.412828992\) \(a_{74}=-0.520164438\) \(a_{75}=-0.574286944\)
\(a_{76}=+0.693469714\) \(a_{77}=+0.098481586\) \(a_{78}=-0.199117465\) \(a_{79}=+1.259158898\) \(a_{80}=+0.035678125\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.319603863\) \(a_{83}=-0.415317100\) \(a_{84}=-0.025670337\) \(a_{85}=-0.062494225\)
\(a_{86}=-0.708028856\) \(a_{87}=+0.295476725\) \(a_{88}=-1.403819188\) \(a_{89}=+1.822675585\) \(a_{90}=+0.010329370\)
\(a_{91}=-0.044009935\) \(a_{92}=+0.515295900\) \(a_{93}=+0.018372801\) \(a_{94}=+0.083286649\) \(a_{95}=-0.061675281\)
\(a_{96}=+0.567085581\) \(a_{97}=-1.740532666\) \(a_{98}=-0.424166585\) \(a_{99}=+0.604692769\) \(a_{100}=+0.814671954\)

Showing 100 of 1228 available coefficients

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