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: \( 10.2641383944 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.949911716\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.671689016\) \(a_{7}=-1.170229306\) \(a_{8}=-0.353553391\) \(a_{9}=-0.097667732\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.080420801\) \(a_{12}=+0.474955858\) \(a_{13}=+0.856648241\) \(a_{14}=+0.827477078\) \(a_{15}=+0.424813434\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.809348683\) \(a_{18}=+0.069061515\) \(a_{19}=-1.322186046\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.111614529\) \(a_{22}=-0.056866093\) \(a_{23}=+0.183706177\) \(a_{24}=-0.335844508\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.605741780\) \(a_{27}=-1.042687439\) \(a_{28}=-0.585114653\) \(a_{29}=-1.521978498\) \(a_{30}=-0.300388460\)
\(a_{31}=+1.574309325\) \(a_{32}=-0.176776695\) \(a_{33}=+0.076392661\) \(a_{34}=+0.572295942\) \(a_{35}=-0.523342456\)
\(a_{36}=-0.048833866\) \(a_{37}=-1.710014160\) \(a_{38}=+0.934926719\) \(a_{39}=+0.813740200\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.966216708\) \(a_{42}=+0.786030171\) \(a_{43}=-0.492739272\) \(a_{44}=+0.040210400\) \(a_{45}=-0.043678337\)
\(a_{46}=-0.129899883\) \(a_{47}=-0.831729083\) \(a_{48}=+0.237477929\) \(a_{49}=+0.369436630\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.768809796\) \(a_{52}=+0.428324120\) \(a_{53}=+1.421048112\) \(a_{54}=+0.737291359\) \(a_{55}=+0.035965275\)
\(a_{56}=+0.413738539\) \(a_{57}=-1.255960016\) \(a_{58}=+1.076201317\) \(a_{59}=-1.700552831\) \(a_{60}=+0.212406717\)
\(a_{61}=-0.236859645\) \(a_{62}=-1.113204800\) \(a_{63}=+0.114293642\) \(a_{64}=+0.125000000\) \(a_{65}=+0.383104740\)
\(a_{66}=-0.054017768\) \(a_{67}=-0.364358190\) \(a_{68}=-0.404674341\) \(a_{69}=+0.174504650\) \(a_{70}=+0.370058999\)
\(a_{71}=+1.391805966\) \(a_{72}=+0.034530758\) \(a_{73}=+0.110379641\) \(a_{74}=+1.209162608\) \(a_{75}=+0.189982343\)
\(a_{76}=-0.661093023\) \(a_{77}=-0.094110779\) \(a_{78}=-0.575401214\) \(a_{79}=-1.014692423\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.892793277\) \(a_{82}=+0.683218386\) \(a_{83}=+1.139842182\) \(a_{84}=-0.555807264\) \(a_{85}=-0.361951735\)
\(a_{86}=+0.348419280\) \(a_{87}=-1.445745216\) \(a_{88}=-0.028433047\) \(a_{89}=+0.387069765\) \(a_{90}=+0.030885249\)
\(a_{91}=-1.002474877\) \(a_{92}=+0.091853088\) \(a_{93}=+1.495454885\) \(a_{94}=+0.588121275\) \(a_{95}=-0.591299575\)
\(a_{96}=-0.167922254\) \(a_{97}=+1.627782528\) \(a_{98}=-0.261231146\) \(a_{99}=-0.007854661\) \(a_{100}=+0.099975586\)

Showing 100 of 150 available coefficients

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