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: \( 31.5042508761 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.753046963\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.532484614\) \(a_{7}=-1.035528297\) \(a_{8}=-0.353553391\) \(a_{9}=-0.432920272\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.538427533\) \(a_{12}=-0.376523481\) \(a_{13}=+0.650763591\) \(a_{14}=+0.732229081\) \(a_{15}=-0.336772840\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.347704040\) \(a_{18}=+0.306120860\) \(a_{19}=-0.326143530\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.779801439\) \(a_{22}=+1.087832541\) \(a_{23}=+0.212599112\) \(a_{24}=+0.266242307\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.460159348\) \(a_{27}=+1.079056259\) \(a_{28}=-0.517764148\) \(a_{29}=+0.808616783\) \(a_{30}=+0.238134359\)
\(a_{31}=+0.639535537\) \(a_{32}=-0.176776695\) \(a_{33}=+1.158508182\) \(a_{34}=+0.952970666\) \(a_{35}=-0.463102333\)
\(a_{36}=-0.216460136\) \(a_{37}=+0.532610497\) \(a_{38}=+0.230618301\) \(a_{39}=-0.490055546\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.633404720\) \(a_{42}=-0.551402885\) \(a_{43}=-0.066545041\) \(a_{44}=-0.769213767\) \(a_{45}=-0.193607831\)
\(a_{46}=-0.150330273\) \(a_{47}=+0.268053541\) \(a_{48}=-0.188261741\) \(a_{49}=+0.072318853\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.014884434\) \(a_{52}=+0.325381796\) \(a_{53}=-1.382365920\) \(a_{54}=-0.763007998\) \(a_{55}=-0.688005709\)
\(a_{56}=+0.366114540\) \(a_{57}=+0.245601394\) \(a_{58}=-0.571778411\) \(a_{59}=+0.738510093\) \(a_{60}=-0.168386420\)
\(a_{61}=-1.519039726\) \(a_{62}=-0.452219915\) \(a_{63}=+0.448301192\) \(a_{64}=+0.125000000\) \(a_{65}=+0.291030326\)
\(a_{66}=-0.819188991\) \(a_{67}=-0.886601650\) \(a_{68}=-0.673852020\) \(a_{69}=-0.160097115\) \(a_{70}=+0.327462800\)
\(a_{71}=+0.488086898\) \(a_{72}=+0.153060430\) \(a_{73}=+1.641594797\) \(a_{74}=-0.376612494\) \(a_{75}=-0.150609393\)
\(a_{76}=-0.163071765\) \(a_{77}=+1.593085243\) \(a_{78}=+0.346521600\) \(a_{79}=+1.291035731\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.379659767\) \(a_{82}=-0.447884772\) \(a_{83}=+1.336129966\) \(a_{84}=+0.389900719\) \(a_{85}=-0.602711569\)
\(a_{86}=+0.047054450\) \(a_{87}=-0.608926413\) \(a_{88}=+0.543916271\) \(a_{89}=-0.971942675\) \(a_{90}=+0.136901410\)
\(a_{91}=-0.673884113\) \(a_{92}=+0.106299556\) \(a_{93}=-0.481600294\) \(a_{94}=-0.189542477\) \(a_{95}=-0.145855820\)
\(a_{96}=+0.133121153\) \(a_{97}=-0.140827704\) \(a_{98}=-0.051137151\) \(a_{99}=+0.666016466\) \(a_{100}=+0.099975586\)

Showing 100 of 256 available coefficients

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