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: \( 30.6130320107 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.851287294\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.309057799\) \(a_{7}=+0.950982218\) \(a_{8}=-0.353553391\) \(a_{9}=+2.427264643\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.485894316\) \(a_{12}=+0.925643647\) \(a_{13}=-0.576910720\) \(a_{14}=-0.672445975\) \(a_{15}=+0.827920847\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.147551057\) \(a_{18}=-1.716335289\) \(a_{19}=-1.247947463\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.760541297\) \(a_{22}=+0.343579166\) \(a_{23}=-0.271997782\) \(a_{24}=-0.654528900\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.407937482\) \(a_{27}=+2.642276899\) \(a_{28}=+0.475491109\) \(a_{29}=-0.140351046\) \(a_{30}=-0.585428445\)
\(a_{31}=+1.930984909\) \(a_{32}=-0.176776695\) \(a_{33}=-0.899529973\) \(a_{34}=-0.811441134\) \(a_{35}=+0.425292177\)
\(a_{36}=+1.213632322\) \(a_{37}=-1.113258574\) \(a_{38}=+0.882432113\) \(a_{39}=-1.068027485\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.726569126\) \(a_{42}=-1.244890690\) \(a_{43}=+1.023348735\) \(a_{44}=-0.242947158\) \(a_{45}=+1.085505748\)
\(a_{46}=+0.192331476\) \(a_{47}=+0.466606101\) \(a_{48}=+0.462821823\) \(a_{49}=-0.095632821\) \(a_{50}=-0.141421356\)
\(a_{51}=+2.124446690\) \(a_{52}=-0.288455360\) \(a_{53}=+0.930533316\) \(a_{54}=-1.868371913\) \(a_{55}=-0.217298544\)
\(a_{56}=-0.336222988\) \(a_{57}=-2.310309281\) \(a_{58}=+0.099243177\) \(a_{59}=+1.232127291\) \(a_{60}=+0.413960423\)
\(a_{61}=+0.099233892\) \(a_{62}=-1.365412524\) \(a_{63}=+2.308285515\) \(a_{64}=+0.125000000\) \(a_{65}=-0.258002317\)
\(a_{66}=+0.636063744\) \(a_{67}=+1.572495913\) \(a_{68}=+0.573775528\) \(a_{69}=-0.503546038\) \(a_{70}=-0.300726982\)
\(a_{71}=+1.408179400\) \(a_{72}=-0.858167645\) \(a_{73}=+1.539552231\) \(a_{74}=+0.787192687\) \(a_{75}=+0.370257459\)
\(a_{76}=-0.623973731\) \(a_{77}=-0.462076855\) \(a_{78}=+0.755209477\) \(a_{79}=+1.215157390\) \(a_{80}=+0.111803399\)
\(a_{81}=+2.464349005\) \(a_{82}=+1.220868737\) \(a_{83}=+0.673203393\) \(a_{84}=+0.880270649\) \(a_{85}=+0.513200434\)
\(a_{86}=-0.723616830\) \(a_{87}=-0.259830109\) \(a_{88}=+0.171789583\) \(a_{89}=-0.502258352\) \(a_{90}=-0.767568476\)
\(a_{91}=-0.548631836\) \(a_{92}=-0.135998891\) \(a_{93}=+3.574807826\) \(a_{94}=-0.329940338\) \(a_{95}=-0.558099072\)
\(a_{96}=-0.327264450\) \(a_{97}=-0.045690701\) \(a_{98}=+0.067622616\) \(a_{99}=-1.179394094\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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