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: \( 31.933075041 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.444343452\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.314198268\) \(a_{7}=+0.383974693\) \(a_{8}=+0.353553391\) \(a_{9}=-0.802558897\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.965482466\) \(a_{12}=+0.222171726\) \(a_{13}=-0.415280687\) \(a_{14}=+0.271511109\) \(a_{15}=+0.198716433\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.537503470\) \(a_{18}=-0.567494838\) \(a_{19}=+1.281831034\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.170616641\) \(a_{22}=+1.389805980\) \(a_{23}=+0.808751252\) \(a_{24}=+0.157099134\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.293647790\) \(a_{27}=-0.800955243\) \(a_{28}=+0.191987347\) \(a_{29}=+0.549590065\) \(a_{30}=+0.140513737\)
\(a_{31}=-0.198182493\) \(a_{32}=+0.176776695\) \(a_{33}=+0.873349264\) \(a_{34}=-1.087179129\) \(a_{35}=+0.171718703\)
\(a_{36}=-0.401279448\) \(a_{37}=+0.859167406\) \(a_{38}=+0.906391416\) \(a_{39}=-0.184527254\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.219548441\) \(a_{42}=+0.120644184\) \(a_{43}=-1.246265290\) \(a_{44}=+0.982741233\) \(a_{45}=-0.358915250\)
\(a_{46}=+0.571873495\) \(a_{47}=+1.361257327\) \(a_{48}=+0.111085863\) \(a_{49}=-0.852563435\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.683179599\) \(a_{52}=-0.207640344\) \(a_{53}=+1.010349381\) \(a_{54}=-0.566360883\) \(a_{55}=+0.878990480\)
\(a_{56}=+0.135755555\) \(a_{57}=+0.569573226\) \(a_{58}=+0.388618862\) \(a_{59}=+1.718273029\) \(a_{60}=+0.099358216\)
\(a_{61}=-1.405706856\) \(a_{62}=-0.140136185\) \(a_{63}=-0.308162306\) \(a_{64}=+0.125000000\) \(a_{65}=-0.185719169\)
\(a_{66}=+0.617551187\) \(a_{67}=-0.244012067\) \(a_{68}=-0.768751735\) \(a_{69}=+0.359363323\) \(a_{70}=+0.121423459\)
\(a_{71}=+1.428927891\) \(a_{72}=-0.283747419\) \(a_{73}=-1.044510387\) \(a_{74}=+0.607523099\) \(a_{75}=+0.088868690\)
\(a_{76}=+0.640915517\) \(a_{77}=+0.754695527\) \(a_{78}=-0.130480473\) \(a_{79}=+0.852147613\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.446659679\) \(a_{82}=+0.155244191\) \(a_{83}=-0.268382598\) \(a_{84}=+0.085308320\) \(a_{85}=-0.687592455\)
\(a_{86}=-0.881242638\) \(a_{87}=+0.244206747\) \(a_{88}=+0.694902990\) \(a_{89}=+0.604581721\) \(a_{90}=-0.253791407\)
\(a_{91}=-0.159457274\) \(a_{92}=+0.404375626\) \(a_{93}=-0.088061093\) \(a_{94}=+0.962554287\) \(a_{95}=+0.573252265\)
\(a_{96}=+0.078549567\) \(a_{97}=-1.181937454\) \(a_{98}=-0.602853386\) \(a_{99}=-1.577415439\) \(a_{100}=+0.099975586\)

Showing 100 of 259 available coefficients

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