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: \( 24.2793539858 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.311419862\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.220207096\) \(a_{7}=-0.796783009\) \(a_{8}=+0.353553391\) \(a_{9}=-0.903017670\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.737613143\) \(a_{12}=-0.155709931\) \(a_{13}=-1.279613609\) \(a_{14}=-0.563410669\) \(a_{15}=-0.139271196\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.117240806\) \(a_{18}=-0.638529918\) \(a_{19}=-0.829892462\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.248134055\) \(a_{22}=-1.228678037\) \(a_{23}=+0.397688032\) \(a_{24}=-0.110103548\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.904823460\) \(a_{27}=+0.592637500\) \(a_{28}=-0.398391505\) \(a_{29}=+0.172552249\) \(a_{30}=-0.098479607\)
\(a_{31}=+1.508177542\) \(a_{32}=+0.176776695\) \(a_{33}=+0.541127245\) \(a_{34}=-0.082901769\) \(a_{35}=-0.356332194\)
\(a_{36}=-0.451508835\) \(a_{37}=+0.574631832\) \(a_{38}=-0.586822588\) \(a_{39}=+0.398497093\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.265176965\) \(a_{42}=+0.175457273\) \(a_{43}=+0.983977775\) \(a_{44}=-0.868806572\) \(a_{45}=-0.403841779\)
\(a_{46}=+0.281207904\) \(a_{47}=-1.775283798\) \(a_{48}=-0.077854965\) \(a_{49}=-0.365136836\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.036511116\) \(a_{52}=-0.639806804\) \(a_{53}=-0.039714237\) \(a_{54}=+0.419057995\) \(a_{55}=-0.777084221\)
\(a_{56}=-0.281705334\) \(a_{57}=+0.258444996\) \(a_{58}=+0.122012865\) \(a_{59}=+1.741269361\) \(a_{60}=-0.069635598\)
\(a_{61}=-1.007225726\) \(a_{62}=+1.066442567\) \(a_{63}=+0.719509136\) \(a_{64}=+0.125000000\) \(a_{65}=-0.572260603\)
\(a_{66}=+0.382634744\) \(a_{67}=+0.354353012\) \(a_{68}=-0.058620403\) \(a_{69}=-0.123847952\) \(a_{70}=-0.251964911\)
\(a_{71}=-0.881183484\) \(a_{72}=-0.319264959\) \(a_{73}=+1.626697898\) \(a_{74}=+0.406326065\) \(a_{75}=-0.062283972\)
\(a_{76}=-0.414946231\) \(a_{77}=+1.384500629\) \(a_{78}=+0.281779997\) \(a_{79}=-0.610543174\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.718458581\) \(a_{82}=+0.894615211\) \(a_{83}=+1.062387331\) \(a_{84}=+0.124067027\) \(a_{85}=-0.052431683\)
\(a_{86}=+0.695777357\) \(a_{87}=-0.053736197\) \(a_{88}=-0.614339018\) \(a_{89}=-0.512103444\) \(a_{90}=-0.285559260\)
\(a_{91}=+1.019574382\) \(a_{92}=+0.198844016\) \(a_{93}=-0.469676442\) \(a_{94}=-1.255315212\) \(a_{95}=-0.371139192\)
\(a_{96}=-0.055051774\) \(a_{97}=+0.128654212\) \(a_{98}=-0.258190733\) \(a_{99}=+1.569095371\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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