Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 22.7859084942 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.267693067\) \(a_{3}=-0.585495820\) \(a_{4}=-0.928340422\) \(a_{5}=+0.038341628\)
\(a_{6}=-0.156733172\) \(a_{7}=+0.992993253\) \(a_{8}=-0.516203362\) \(a_{9}=-0.657194645\) \(a_{10}=+0.010263788\)
\(a_{11}=+1.575383460\) \(a_{12}=+0.543539436\) \(a_{13}=+1.411859039\) \(a_{14}=+0.265817404\) \(a_{15}=-0.022448863\)
\(a_{16}=+0.790156361\) \(a_{17}=-0.380388579\) \(a_{18}=-0.175926450\) \(a_{19}=+0.536611239\) \(a_{20}=-0.035594083\)
\(a_{21}=-0.581393399\) \(a_{22}=+0.421719230\) \(a_{23}=+0.067953251\) \(a_{24}=+0.302234910\) \(a_{25}=-0.998529920\)
\(a_{26}=+0.377944876\) \(a_{27}=+0.970280537\) \(a_{28}=-0.921835776\) \(a_{29}=-0.042068133\) \(a_{30}=-0.006009405\)
\(a_{31}=+0.188220401\) \(a_{32}=+0.727722741\) \(a_{33}=-0.922380430\) \(a_{34}=-0.101827385\) \(a_{35}=+0.038072978\)
\(a_{36}=+0.610100354\) \(a_{37}=-0.115955466\) \(a_{38}=+0.143647108\) \(a_{39}=-0.826637565\) \(a_{40}=-0.019792077\)
\(a_{41}=+0.712092793\) \(a_{42}=-0.155634982\) \(a_{43}=+0.909530077\) \(a_{44}=-1.462492146\) \(a_{45}=-0.025197913\)
\(a_{46}=+0.018190614\) \(a_{47}=+1.160264205\) \(a_{48}=-0.462633246\) \(a_{49}=-0.013964399\) \(a_{50}=-0.267299537\)
\(a_{51}=+0.222715923\) \(a_{52}=-1.310685815\) \(a_{53}=+1.390857805\) \(a_{54}=+0.259737373\) \(a_{55}=+0.060402767\)
\(a_{56}=-0.512586456\) \(a_{57}=-0.314183636\) \(a_{58}=-0.011261347\) \(a_{59}=-0.105578665\) \(a_{60}=+0.020840189\)
\(a_{61}=+1.103596977\) \(a_{62}=+0.050385296\) \(a_{63}=-0.652589849\) \(a_{64}=-0.595350028\) \(a_{65}=+0.054132974\)
\(a_{66}=-0.246914846\) \(a_{67}=+0.807163983\) \(a_{68}=+0.353130094\) \(a_{69}=-0.039786344\) \(a_{70}=+0.010191872\)
\(a_{71}=-0.893040241\) \(a_{72}=+0.339246085\) \(a_{73}=-0.335219322\) \(a_{74}=-0.031040474\) \(a_{75}=+0.584635094\)
\(a_{76}=-0.498157904\) \(a_{77}=+1.564345147\) \(a_{78}=-0.221285145\) \(a_{79}=-1.573933132\) \(a_{80}=+0.030295881\)
\(a_{81}=+0.089099447\) \(a_{82}=+0.190622304\) \(a_{83}=+0.127902083\) \(a_{84}=+0.539730993\) \(a_{85}=-0.014584718\)
\(a_{86}=+0.243474896\) \(a_{87}=+0.024630716\) \(a_{88}=-0.813218238\) \(a_{89}=-0.868184495\) \(a_{90}=-0.006745307\)
\(a_{91}=+1.401966500\) \(a_{92}=-0.063083750\) \(a_{93}=-0.110202259\) \(a_{94}=+0.310594684\) \(a_{95}=+0.020574549\)
\(a_{96}=-0.426078623\) \(a_{97}=-0.166293045\) \(a_{98}=-0.003738173\) \(a_{99}=-1.035333573\) \(a_{100}=+0.926975686\)

Showing 100 of 5000 available coefficients

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