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: \( 21.3799613173 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.882094500\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.330841784\) \(a_{7}=+0.237223920\) \(a_{8}=+0.353553391\) \(a_{9}=+2.542279706\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.271719771\) \(a_{12}=-0.941047250\) \(a_{13}=-1.066818031\) \(a_{14}=+0.167742643\) \(a_{15}=-0.841698248\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.624263638\) \(a_{18}=+1.797663220\) \(a_{19}=+0.700775163\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.446477835\) \(a_{22}=-0.899241674\) \(a_{23}=+1.262741327\) \(a_{24}=-0.665420892\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.754354264\) \(a_{27}=-2.902716152\) \(a_{28}=+0.118611960\) \(a_{29}=+1.388665568\) \(a_{30}=-0.595170539\)
\(a_{31}=+0.215487140\) \(a_{32}=+0.176776695\) \(a_{33}=+2.393496786\) \(a_{34}=-0.441421052\) \(a_{35}=+0.106089762\)
\(a_{36}=+1.271139853\) \(a_{37}=+1.543012340\) \(a_{38}=+0.495522870\) \(a_{39}=+2.007852349\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.414178042\) \(a_{42}=-0.315707505\) \(a_{43}=+0.210300980\) \(a_{44}=-0.635859885\) \(a_{45}=+1.136942048\)
\(a_{46}=+0.892892955\) \(a_{47}=+0.043786079\) \(a_{48}=-0.470523625\) \(a_{49}=-0.943724812\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.174923160\) \(a_{52}=-0.533409016\) \(a_{53}=+1.502402398\) \(a_{54}=-2.052530275\) \(a_{55}=-0.568730371\)
\(a_{56}=+0.083871321\) \(a_{57}=-1.318925081\) \(a_{58}=+0.981934840\) \(a_{59}=-1.589223501\) \(a_{60}=-0.420849124\)
\(a_{61}=-1.333968581\) \(a_{62}=+0.152372418\) \(a_{63}=+0.603089558\) \(a_{64}=+0.125000000\) \(a_{65}=-0.477095528\)
\(a_{66}=+1.692457808\) \(a_{67}=+0.358680746\) \(a_{68}=-0.312131819\) \(a_{69}=-2.376598506\) \(a_{70}=+0.075016790\)
\(a_{71}=-0.605989851\) \(a_{72}=+0.898831610\) \(a_{73}=+0.709825895\) \(a_{74}=+1.091074489\) \(a_{75}=-0.376418900\)
\(a_{76}=+0.350387582\) \(a_{77}=-0.301682349\) \(a_{78}=+1.419766012\) \(a_{79}=-0.119869826\) \(a_{80}=+0.111803399\)
\(a_{81}=+2.920906398\) \(a_{82}=-0.999974883\) \(a_{83}=-0.360398211\) \(a_{84}=-0.223238918\) \(a_{85}=-0.279179186\)
\(a_{86}=+0.148705249\) \(a_{87}=-2.613599827\) \(a_{88}=-0.449620837\) \(a_{89}=+0.345009541\) \(a_{90}=+0.803939432\)
\(a_{91}=-0.253074755\) \(a_{92}=+0.631370663\) \(a_{93}=-0.405567161\) \(a_{94}=+0.030961434\) \(a_{95}=+0.313396180\)
\(a_{96}=-0.332710446\) \(a_{97}=-0.646856530\) \(a_{98}=-0.667314214\) \(a_{99}=-3.233067365\) \(a_{100}=+0.099975586\)

Showing 100 of 207 available coefficients

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