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: \( 19.3181145352 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.261644964\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.185010928\) \(a_{7}=+1.410994377\) \(a_{8}=-0.353553391\) \(a_{9}=-0.931541913\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.020465553\) \(a_{12}=+0.130822482\) \(a_{13}=+1.674179913\) \(a_{14}=-0.997723692\) \(a_{15}=-0.117011185\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.887409579\) \(a_{18}=+0.658699604\) \(a_{19}=-0.046363663\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.369179572\) \(a_{22}=+0.014471331\) \(a_{23}=+0.504224029\) \(a_{24}=-0.092505464\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.183823969\) \(a_{27}=-0.505378213\) \(a_{28}=+0.705497188\) \(a_{29}=+1.940578748\) \(a_{30}=+0.082739402\)
\(a_{31}=+0.922672257\) \(a_{32}=-0.176776695\) \(a_{33}=-0.005354709\) \(a_{34}=+0.627493331\) \(a_{35}=-0.631015868\)
\(a_{36}=-0.465770957\) \(a_{37}=-1.635100183\) \(a_{38}=+0.032784060\) \(a_{39}=+0.438040742\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.634715406\) \(a_{42}=-0.261049379\) \(a_{43}=-0.522240533\) \(a_{44}=-0.010232776\) \(a_{45}=+0.416598208\)
\(a_{46}=-0.356540230\) \(a_{47}=-0.607994073\) \(a_{48}=+0.065411241\) \(a_{49}=+0.990905131\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.232186247\) \(a_{52}=+0.837089956\) \(a_{53}=-1.157515970\) \(a_{54}=+0.357356362\) \(a_{55}=+0.009152473\)
\(a_{56}=-0.498861846\) \(a_{57}=-0.012130819\) \(a_{58}=-1.372196392\) \(a_{59}=-1.422238441\) \(a_{60}=-0.058505592\)
\(a_{61}=+1.707980601\) \(a_{62}=-0.652427809\) \(a_{63}=-1.314400401\) \(a_{64}=+0.125000000\) \(a_{65}=-0.748716018\)
\(a_{66}=+0.003786351\) \(a_{67}=+0.903577888\) \(a_{68}=-0.443704790\) \(a_{69}=+0.131927678\) \(a_{70}=+0.446195600\)
\(a_{71}=+0.368694406\) \(a_{72}=+0.329349802\) \(a_{73}=-0.197203404\) \(a_{74}=+1.156190427\) \(a_{75}=+0.052328993\)
\(a_{76}=-0.023181831\) \(a_{77}=-0.028876780\) \(a_{78}=-0.309741579\) \(a_{79}=+0.430478032\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.799312249\) \(a_{82}=+0.448811568\) \(a_{83}=+1.460568555\) \(a_{84}=+0.184589786\) \(a_{85}=+0.396861629\)
\(a_{86}=+0.369279823\) \(a_{87}=+0.507742656\) \(a_{88}=+0.007235666\) \(a_{89}=+0.090675481\) \(a_{90}=-0.294579418\)
\(a_{91}=+2.362258443\) \(a_{92}=+0.252112014\) \(a_{93}=+0.241412549\) \(a_{94}=+0.429916732\) \(a_{95}=+0.020734460\)
\(a_{96}=-0.046252732\) \(a_{97}=+0.312457949\) \(a_{98}=-0.700675738\) \(a_{99}=+0.019064520\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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