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: \( 26.4098588141 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.611223824\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.139307292\) \(a_{7}=+0.082420231\) \(a_{8}=-0.353553391\) \(a_{9}=+1.596042211\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.617568533\) \(a_{12}=-0.805611912\) \(a_{13}=-1.896360034\) \(a_{14}=-0.058279904\) \(a_{15}=-0.720561199\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.706995149\) \(a_{18}=-1.128572270\) \(a_{19}=+1.017429057\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.132797439\) \(a_{22}=-0.436686898\) \(a_{23}=-0.179344272\) \(a_{24}=+0.569653646\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.340929040\) \(a_{27}=-0.960357410\) \(a_{28}=+0.041210115\) \(a_{29}=+1.484286985\) \(a_{30}=+0.509513710\)
\(a_{31}=+1.478376138\) \(a_{32}=-0.176776695\) \(a_{33}=-0.995041133\) \(a_{34}=-1.207027846\) \(a_{35}=+0.036859448\)
\(a_{36}=+0.798021105\) \(a_{37}=+0.220576829\) \(a_{38}=-0.719430986\) \(a_{39}=+3.055460466\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.469221701\) \(a_{42}=+0.093901970\) \(a_{43}=+1.192453467\) \(a_{44}=+0.308784266\) \(a_{45}=+0.713771776\)
\(a_{46}=+0.126815551\) \(a_{47}=-0.948439691\) \(a_{48}=-0.402805956\) \(a_{49}=-0.993206906\) \(a_{50}=-0.141421356\)
\(a_{51}=-2.750351252\) \(a_{52}=-0.948180017\) \(a_{53}=+0.973504569\) \(a_{54}=+0.679075237\) \(a_{55}=+0.276185044\)
\(a_{56}=-0.029139952\) \(a_{57}=-1.639305936\) \(a_{58}=-1.049549392\) \(a_{59}=+0.374975125\) \(a_{60}=-0.360280600\)
\(a_{61}=-0.149647461\) \(a_{62}=-1.045369792\) \(a_{63}=+0.131546167\) \(a_{64}=+0.125000000\) \(a_{65}=-0.848077989\)
\(a_{66}=+0.703600333\) \(a_{67}=-1.090583533\) \(a_{68}=+0.853497575\) \(a_{69}=+0.288963763\) \(a_{70}=-0.026063565\)
\(a_{71}=+0.339768182\) \(a_{72}=-0.564286135\) \(a_{73}=+0.187658560\) \(a_{74}=-0.155971372\) \(a_{75}=-0.322244765\)
\(a_{76}=+0.508714529\) \(a_{77}=+0.050900141\) \(a_{78}=-2.160536815\) \(a_{79}=-0.692919240\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.048691472\) \(a_{82}=-0.331789846\) \(a_{83}=-0.390440372\) \(a_{84}=-0.066398720\) \(a_{85}=+0.763391438\)
\(a_{86}=-0.843191933\) \(a_{87}=-2.391518552\) \(a_{88}=-0.218343449\) \(a_{89}=+1.651531612\) \(a_{90}=-0.504712863\)
\(a_{91}=-0.156298431\) \(a_{92}=-0.089672136\) \(a_{93}=-2.381994855\) \(a_{94}=+0.670648137\) \(a_{95}=+0.455008107\)
\(a_{96}=+0.284826823\) \(a_{97}=-0.482384657\) \(a_{98}=+0.702303338\) \(a_{99}=+0.985665447\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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