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: \( 27.6399081653 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.949613473\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.378584907\) \(a_{7}=-0.912654027\) \(a_{8}=+0.353553391\) \(a_{9}=+2.800992694\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.337435767\) \(a_{12}=-0.974806736\) \(a_{13}=+0.963720050\) \(a_{14}=-0.645343851\) \(a_{15}=-0.871893651\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.105504669\) \(a_{18}=+1.980600928\) \(a_{19}=+0.792262890\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.779322587\) \(a_{22}=+0.945709900\) \(a_{23}=+1.730947576\) \(a_{24}=-0.689292454\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.681452982\) \(a_{27}=-3.511239620\) \(a_{28}=-0.456327014\) \(a_{29}=+0.244908930\) \(a_{30}=-0.616521913\)
\(a_{31}=+1.493186802\) \(a_{32}=+0.176776695\) \(a_{33}=-2.607482790\) \(a_{34}=+0.074603067\) \(a_{35}=-0.408151289\)
\(a_{36}=+1.400496347\) \(a_{37}=-1.221948163\) \(a_{38}=+0.560214462\) \(a_{39}=-1.878881593\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.800219198\) \(a_{42}=+1.258171067\) \(a_{43}=-0.353569945\) \(a_{44}=+0.668717883\) \(a_{45}=+1.252642014\)
\(a_{46}=+1.223964769\) \(a_{47}=+0.675063777\) \(a_{48}=-0.487403368\) \(a_{49}=-0.167062627\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.205693325\) \(a_{52}=+0.481860025\) \(a_{53}=-0.255165920\) \(a_{54}=-2.482821346\) \(a_{55}=+0.598119458\)
\(a_{56}=-0.322671926\) \(a_{57}=-1.544606404\) \(a_{58}=+0.173176765\) \(a_{59}=+0.125752442\) \(a_{60}=-0.435946826\)
\(a_{61}=-0.984048303\) \(a_{62}=+1.055842513\) \(a_{63}=-2.556337262\) \(a_{64}=+0.125000000\) \(a_{65}=+0.430988709\)
\(a_{66}=-1.843768763\) \(a_{67}=-0.495139402\) \(a_{68}=+0.052752335\) \(a_{69}=-3.374678715\) \(a_{70}=-0.288606544\)
\(a_{71}=+1.118386290\) \(a_{72}=+0.990300464\) \(a_{73}=+0.245830002\) \(a_{74}=-0.864047833\) \(a_{75}=-0.389922695\)
\(a_{76}=+0.396131445\) \(a_{77}=-1.220616139\) \(a_{78}=-1.328569916\) \(a_{79}=-0.934261128\) \(a_{80}=+0.111803399\)
\(a_{81}=+4.044567376\) \(a_{82}=+0.565840421\) \(a_{83}=+0.756154041\) \(a_{84}=+0.889661294\) \(a_{85}=+0.047183123\)
\(a_{86}=-0.250011706\) \(a_{87}=-0.477477750\) \(a_{88}=+0.472854950\) \(a_{89}=+0.144008212\) \(a_{90}=+0.885751662\)
\(a_{91}=-0.879542984\) \(a_{92}=+0.865473788\) \(a_{93}=-2.911137106\) \(a_{94}=+0.477342174\) \(a_{95}=+0.354310735\)
\(a_{96}=-0.344646227\) \(a_{97}=-0.510324765\) \(a_{98}=-0.118131116\) \(a_{99}=+3.746147811\) \(a_{100}=+0.099975586\)

Showing 100 of 228 available coefficients

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