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: \( 5.42416298033 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.905859327\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.640539273\) \(a_{7}=+1.779314914\) \(a_{8}=-0.353553391\) \(a_{9}=-0.179418879\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.135545298\) \(a_{12}=-0.452929664\) \(a_{13}=+1.113768838\) \(a_{14}=-1.258165642\) \(a_{15}=+0.405112607\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.848420992\) \(a_{18}=+0.126868306\) \(a_{19}=+0.270004355\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.611809011\) \(a_{22}=-0.095844999\) \(a_{23}=-0.177106925\) \(a_{24}=+0.320269637\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.787553498\) \(a_{27}=+1.068387593\) \(a_{28}=+0.889657457\) \(a_{29}=+1.311458339\) \(a_{30}=-0.286457871\)
\(a_{31}=-1.035372479\) \(a_{32}=-0.176776695\) \(a_{33}=-0.122784972\) \(a_{34}=-0.599924237\) \(a_{35}=-0.795733820\)
\(a_{36}=-0.089709440\) \(a_{37}=+1.401442844\) \(a_{38}=-0.190921911\) \(a_{39}=-1.008917890\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.811855879\) \(a_{42}=+1.139721082\) \(a_{43}=+1.039735549\) \(a_{44}=+0.067772649\) \(a_{45}=+0.080238562\)
\(a_{46}=+0.125233507\) \(a_{47}=-1.400637207\) \(a_{48}=-0.226464832\) \(a_{49}=+2.165961564\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.768550069\) \(a_{52}=+0.556884419\) \(a_{53}=-0.162334863\) \(a_{54}=-0.755464112\) \(a_{55}=-0.060617700\)
\(a_{56}=-0.629082821\) \(a_{57}=-0.244585964\) \(a_{58}=-0.927341085\) \(a_{59}=+0.645789609\) \(a_{60}=+0.202556303\)
\(a_{61}=+0.313877590\) \(a_{62}=+0.732118901\) \(a_{63}=-0.319242688\) \(a_{64}=+0.125000000\) \(a_{65}=-0.498092567\)
\(a_{66}=+0.086822087\) \(a_{67}=-0.086426800\) \(a_{68}=+0.424210496\) \(a_{69}=+0.160433960\) \(a_{70}=+0.562668780\)
\(a_{71}=+0.271008500\) \(a_{72}=+0.063434153\) \(a_{73}=+0.825589800\) \(a_{74}=-0.990969738\) \(a_{75}=-0.181171865\)
\(a_{76}=+0.135002178\) \(a_{77}=+0.241177770\) \(a_{78}=+0.713412682\) \(a_{79}=-1.286257001\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.788389986\) \(a_{82}=+0.574068797\) \(a_{83}=-0.433910001\) \(a_{84}=-0.805904506\) \(a_{85}=-0.379425402\)
\(a_{86}=-0.735204057\) \(a_{87}=-1.187996768\) \(a_{88}=-0.047922500\) \(a_{89}=+1.879453003\) \(a_{90}=-0.056737231\)
\(a_{91}=+1.981745505\) \(a_{92}=-0.088553462\) \(a_{93}=+0.937901817\) \(a_{94}=+0.990400067\) \(a_{95}=-0.120749619\)
\(a_{96}=+0.160134818\) \(a_{97}=+0.310200214\) \(a_{98}=-1.531566110\) \(a_{99}=-0.024319385\) \(a_{100}=+0.099975586\)

Showing 100 of 130 available coefficients

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