Properties

Level 10
Weight 0
Character 10.1
Symmetry odd
Fricke sign +1

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: \(+1\)
Spectral parameter: \( 29.2898614134 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.189379667\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.133911647\) \(a_{7}=-0.440081514\) \(a_{8}=+0.353553391\) \(a_{9}=-0.964135342\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.057789313\) \(a_{12}=+0.094689834\) \(a_{13}=+0.604354224\) \(a_{14}=-0.311184623\) \(a_{15}=+0.084693162\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.860940585\) \(a_{18}=-0.681746638\) \(a_{19}=+0.803920890\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.083342491\) \(a_{22}=-0.040863215\) \(a_{23}=+0.107410075\) \(a_{24}=+0.066955824\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.427342970\) \(a_{27}=-0.371967298\) \(a_{28}=-0.220040757\) \(a_{29}=+0.729074186\) \(a_{30}=+0.059887109\)
\(a_{31}=+0.429105653\) \(a_{32}=+0.176776695\) \(a_{33}=-0.010944121\) \(a_{34}=-0.608776926\) \(a_{35}=-0.196810436\)
\(a_{36}=-0.482067671\) \(a_{37}=+0.262411534\) \(a_{38}=+0.568457913\) \(a_{39}=+0.114452402\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.482519795\) \(a_{42}=-0.058932040\) \(a_{43}=-0.520494235\) \(a_{44}=-0.028894657\) \(a_{45}=-0.431174433\)
\(a_{46}=+0.075950393\) \(a_{47}=-0.595578086\) \(a_{48}=+0.047344917\) \(a_{49}=-0.806328261\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.163044642\) \(a_{52}=+0.302177112\) \(a_{53}=+0.259178771\) \(a_{54}=-0.263020599\) \(a_{55}=-0.025844166\)
\(a_{56}=-0.155592311\) \(a_{57}=+0.152246271\) \(a_{58}=+0.515533301\) \(a_{59}=-1.548894773\) \(a_{60}=+0.042346581\)
\(a_{61}=-0.802149185\) \(a_{62}=+0.303423517\) \(a_{63}=+0.424298141\) \(a_{64}=+0.125000000\) \(a_{65}=+0.270275425\)
\(a_{66}=-0.007738662\) \(a_{67}=-0.278566402\) \(a_{68}=-0.430470293\) \(a_{69}=+0.020341284\) \(a_{70}=-0.139165994\)
\(a_{71}=-1.173620897\) \(a_{72}=-0.340873319\) \(a_{73}=+0.025746641\) \(a_{74}=+0.185552975\) \(a_{75}=+0.037875933\)
\(a_{76}=+0.401960445\) \(a_{77}=+0.025432008\) \(a_{78}=+0.080930070\) \(a_{79}=+1.338947124\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.893692298\) \(a_{82}=-0.341193019\) \(a_{83}=+0.584926337\) \(a_{84}=-0.041671245\) \(a_{85}=-0.385024335\)
\(a_{86}=-0.368045003\) \(a_{87}=+0.138071827\) \(a_{88}=-0.020431608\) \(a_{89}=-0.996190874\) \(a_{90}=-0.304886365\)
\(a_{91}=-0.265965122\) \(a_{92}=+0.053705038\) \(a_{93}=+0.081263886\) \(a_{94}=-0.421137303\) \(a_{95}=+0.359524351\)
\(a_{96}=+0.033477912\) \(a_{97}=-1.674351985\) \(a_{98}=-0.570160181\) \(a_{99}=+0.055716719\) \(a_{100}=+0.099975586\)

Showing 100 of 240 available coefficients

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