Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 29.9476419195 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.522111025\) \(a_{4}=+0.500000000\) \(a_{5}=+0.911300001\)
\(a_{6}=+1.076295028\) \(a_{7}=+1.395647614\) \(a_{8}=+0.353553391\) \(a_{9}=+1.316821973\) \(a_{10}=+0.644386410\)
\(a_{11}=-1.099976853\) \(a_{12}=+0.761055513\) \(a_{13}=+1.128984646\) \(a_{14}=+0.986871892\) \(a_{15}=+1.387099779\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.110429310\) \(a_{18}=+0.931133747\) \(a_{19}=+0.151471143\) \(a_{20}=+0.455650000\)
\(a_{21}=+2.124330620\) \(a_{22}=-0.777801092\) \(a_{23}=-0.431147857\) \(a_{24}=+0.538147514\) \(a_{25}=-0.169532308\)
\(a_{26}=+0.798312699\) \(a_{27}=+0.482238219\) \(a_{28}=+0.697823807\) \(a_{29}=-0.866543042\) \(a_{30}=+0.980827660\)
\(a_{31}=-1.200569806\) \(a_{32}=+0.176776695\) \(a_{33}=-1.674286895\) \(a_{34}=-0.785192095\) \(a_{35}=+1.271853672\)
\(a_{36}=+0.658410987\) \(a_{37}=-0.914580977\) \(a_{38}=+0.107106272\) \(a_{39}=+1.718439977\) \(a_{40}=+0.322193205\)
\(a_{41}=+0.777954151\) \(a_{42}=+1.502128587\) \(a_{43}=+0.630585431\) \(a_{44}=-0.549988426\) \(a_{45}=+1.200019866\)
\(a_{46}=-0.304867573\) \(a_{47}=+1.299916394\) \(a_{48}=+0.380527756\) \(a_{49}=+0.947832262\) \(a_{50}=-0.119877445\)
\(a_{51}=-1.690196695\) \(a_{52}=+0.564492323\) \(a_{53}=+1.381871164\) \(a_{54}=+0.340993915\) \(a_{55}=-1.002408907\)
\(a_{56}=+0.493435946\) \(a_{57}=+0.230555897\) \(a_{58}=-0.612738462\) \(a_{59}=+0.524259336\) \(a_{60}=+0.693549889\)
\(a_{61}=-1.525531774\) \(a_{62}=-0.848931051\) \(a_{63}=+1.837819445\) \(a_{64}=+0.125000000\) \(a_{65}=+1.028843709\)
\(a_{66}=-1.183899617\) \(a_{67}=-0.209426507\) \(a_{68}=-0.555214655\) \(a_{69}=-0.656254906\) \(a_{70}=+0.899336356\)
\(a_{71}=+0.113600854\) \(a_{72}=+0.465566874\) \(a_{73}=+0.792335904\) \(a_{74}=-0.646706411\) \(a_{75}=-0.258046996\)
\(a_{76}=+0.075735572\) \(a_{77}=-1.535180069\) \(a_{78}=+1.215120561\) \(a_{79}=-0.121679728\) \(a_{80}=+0.227825000\)
\(a_{81}=-0.582801864\) \(a_{82}=+0.550096655\) \(a_{83}=+0.216920879\) \(a_{84}=+1.062165310\) \(a_{85}=-1.011934231\)
\(a_{86}=+0.445891234\) \(a_{87}=-1.318974719\) \(a_{88}=-0.388900546\) \(a_{89}=-0.270245644\) \(a_{90}=+0.848542185\)
\(a_{91}=+1.575664727\) \(a_{92}=-0.215573928\) \(a_{93}=-1.827400539\) \(a_{94}=+0.919179697\) \(a_{95}=+0.138035653\)
\(a_{96}=+0.269073757\) \(a_{97}=-0.267835523\) \(a_{98}=+0.670218620\) \(a_{99}=-1.448473690\) \(a_{100}=-0.084766154\)

Showing 100 of 1228 available coefficients

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