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: \( 26.3274378838 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.270411735\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.898316752\) \(a_{7}=-0.663820994\) \(a_{8}=+0.353553391\) \(a_{9}=+0.613945975\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.524879009\) \(a_{12}=-0.635205867\) \(a_{13}=-1.656262041\) \(a_{14}=-0.469392326\) \(a_{15}=-0.568145400\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.657032391\) \(a_{18}=+0.434125362\) \(a_{19}=+1.044108370\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.843325980\) \(a_{22}=-0.371145507\) \(a_{23}=-1.078337146\) \(a_{24}=-0.449158376\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.171154121\) \(a_{27}=+0.490447563\) \(a_{28}=-0.331910497\) \(a_{29}=+0.337664577\) \(a_{30}=-0.401739465\)
\(a_{31}=-1.179622253\) \(a_{32}=+0.176776695\) \(a_{33}=+0.666812452\) \(a_{34}=-0.464592059\) \(a_{35}=-0.296869773\)
\(a_{36}=+0.306972988\) \(a_{37}=-0.963041987\) \(a_{38}=+0.738296109\) \(a_{39}=+2.104134732\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.268291585\) \(a_{42}=+0.596321519\) \(a_{43}=-1.161055687\) \(a_{44}=-0.262439504\) \(a_{45}=+0.274564987\)
\(a_{46}=-0.762499508\) \(a_{47}=+0.720890735\) \(a_{48}=-0.317602934\) \(a_{49}=-0.559341688\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.834701659\) \(a_{52}=-0.828131021\) \(a_{53}=-1.038586860\) \(a_{54}=+0.346798798\) \(a_{55}=-0.234733029\)
\(a_{56}=-0.234696163\) \(a_{57}=-1.326447525\) \(a_{58}=+0.238764912\) \(a_{59}=-0.958630842\) \(a_{60}=-0.284072700\)
\(a_{61}=-0.942002729\) \(a_{62}=-0.834118895\) \(a_{63}=-0.407550227\) \(a_{64}=+0.125000000\) \(a_{65}=-0.740702902\)
\(a_{66}=+0.471507607\) \(a_{67}=-0.758682946\) \(a_{68}=-0.328516195\) \(a_{69}=+1.369932164\) \(a_{70}=-0.209918630\)
\(a_{71}=+1.100054486\) \(a_{72}=+0.217062681\) \(a_{73}=+0.238653253\) \(a_{74}=-0.680973519\) \(a_{75}=-0.254082347\)
\(a_{76}=+0.522054185\) \(a_{77}=+0.348425705\) \(a_{78}=+1.487847938\) \(a_{79}=+1.228866978\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.237016315\) \(a_{82}=+0.896817580\) \(a_{83}=-1.528766801\) \(a_{84}=+0.421662990\) \(a_{85}=-0.293833818\)
\(a_{86}=-0.820990349\) \(a_{87}=-0.428973041\) \(a_{88}=-0.185572753\) \(a_{89}=+0.871476531\) \(a_{90}=+0.194146764\)
\(a_{91}=+1.099461514\) \(a_{92}=-0.539168573\) \(a_{93}=+1.498605953\) \(a_{94}=+0.509746727\) \(a_{95}=+0.466939458\)
\(a_{96}=-0.224579188\) \(a_{97}=+0.860155563\) \(a_{98}=-0.395514301\) \(a_{99}=-0.322247355\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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