Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 20.2392441753 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.857777403\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.313647000\) \(a_{7}=-1.658018023\) \(a_{8}=+0.353553391\) \(a_{9}=+2.451336880\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.220619687\) \(a_{12}=+0.928888702\) \(a_{13}=-0.652251600\) \(a_{14}=-1.172395787\) \(a_{15}=+0.830823312\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.128029369\) \(a_{18}=+1.733356931\) \(a_{19}=+1.195755863\) \(a_{20}=+0.223606798\)
\(a_{21}=-3.080228417\) \(a_{22}=+0.863108458\) \(a_{23}=+0.161576503\) \(a_{24}=+0.656823500\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.461211529\) \(a_{27}=+2.696260859\) \(a_{28}=-0.829009012\) \(a_{29}=+0.966065237\) \(a_{30}=+0.587480798\)
\(a_{31}=-0.026355483\) \(a_{32}=+0.176776695\) \(a_{33}=+2.267639672\) \(a_{34}=-0.090530435\) \(a_{35}=-0.741488202\)
\(a_{36}=+1.225668440\) \(a_{37}=+1.300619740\) \(a_{38}=+0.845527080\) \(a_{39}=-1.211738283\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.956511029\) \(a_{42}=-2.178050402\) \(a_{43}=+0.908322785\) \(a_{44}=+0.610309844\) \(a_{45}=+1.096271180\)
\(a_{46}=+0.114251841\) \(a_{47}=-0.202335568\) \(a_{48}=+0.464444351\) \(a_{49}=+1.749023765\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.237850069\) \(a_{52}=-0.326125800\) \(a_{53}=-1.346673989\) \(a_{54}=+1.906544338\) \(a_{55}=+0.545877719\)
\(a_{56}=-0.586197894\) \(a_{57}=+2.221448223\) \(a_{58}=+0.683111280\) \(a_{59}=-0.002972212\) \(a_{60}=+0.415411656\)
\(a_{61}=-0.192232739\) \(a_{62}=-0.018636141\) \(a_{63}=-4.064360727\) \(a_{64}=+0.125000000\) \(a_{65}=-0.291695783\)
\(a_{66}=+1.603463390\) \(a_{67}=-1.486711335\) \(a_{68}=-0.064014684\) \(a_{69}=+0.300173175\) \(a_{70}=-0.524311335\)
\(a_{71}=+0.354057842\) \(a_{72}=+0.866678465\) \(a_{73}=-1.085847128\) \(a_{74}=+0.919677038\) \(a_{75}=+0.371555481\)
\(a_{76}=+0.597877932\) \(a_{77}=-2.023809441\) \(a_{78}=-0.856828357\) \(a_{79}=-0.184070041\) \(a_{80}=+0.111803399\)
\(a_{81}=+2.557715618\) \(a_{82}=+0.676355435\) \(a_{83}=+0.364525742\) \(a_{84}=-1.540114209\) \(a_{85}=-0.057256474\)
\(a_{86}=+0.642281201\) \(a_{87}=+1.794734167\) \(a_{88}=+0.431554229\) \(a_{89}=-0.571262648\) \(a_{90}=+0.775180785\)
\(a_{91}=+1.081444908\) \(a_{92}=+0.080788251\) \(a_{93}=-0.048962620\) \(a_{94}=-0.143072852\) \(a_{95}=+0.534758279\)
\(a_{96}=+0.328411750\) \(a_{97}=-0.235324979\) \(a_{98}=+1.236746565\) \(a_{99}=+2.992150055\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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