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: \( 12.657894507 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.270748838\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.191448339\) \(a_{7}=+1.110518447\) \(a_{8}=-0.353553391\) \(a_{9}=-0.926695067\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.403726282\) \(a_{12}=+0.135374419\) \(a_{13}=+0.015421970\) \(a_{14}=-0.785255125\) \(a_{15}=-0.121082561\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.434902067\) \(a_{18}=+0.655272366\) \(a_{19}=+0.259963704\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.300671579\) \(a_{22}=+0.285477591\) \(a_{23}=+1.783044511\) \(a_{24}=-0.095724170\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.010904979\) \(a_{27}=-0.521650450\) \(a_{28}=+0.555259224\) \(a_{29}=-0.585006517\) \(a_{30}=+0.085618300\)
\(a_{31}=-1.759695378\) \(a_{32}=-0.176776695\) \(a_{33}=-0.109308422\) \(a_{34}=-0.307522201\) \(a_{35}=-0.496638948\)
\(a_{36}=-0.463347533\) \(a_{37}=-0.923238286\) \(a_{38}=-0.183822098\) \(a_{39}=+0.004175480\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.575302159\) \(a_{42}=-0.212606912\) \(a_{43}=-1.869003697\) \(a_{44}=-0.201863141\) \(a_{45}=+0.414430633\)
\(a_{46}=-1.260802865\) \(a_{47}=-0.470790966\) \(a_{48}=+0.067687209\) \(a_{49}=+0.233251222\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.117749229\) \(a_{52}=+0.007710985\) \(a_{53}=+0.723008522\) \(a_{54}=+0.368862571\) \(a_{55}=+0.180551882\)
\(a_{56}=-0.392627562\) \(a_{57}=+0.070384871\) \(a_{58}=+0.413662075\) \(a_{59}=-0.975643155\) \(a_{60}=-0.060541281\)
\(a_{61}=-1.500858457\) \(a_{62}=+1.244292535\) \(a_{63}=-1.029111967\) \(a_{64}=+0.125000000\) \(a_{65}=-0.006896915\)
\(a_{66}=+0.077292726\) \(a_{67}=-0.667035496\) \(a_{68}=+0.217451033\) \(a_{69}=+0.482757229\) \(a_{70}=+0.351176768\)
\(a_{71}=+1.243715709\) \(a_{72}=+0.327636183\) \(a_{73}=-0.772151522\) \(a_{74}=+0.652828052\) \(a_{75}=+0.054149768\)
\(a_{76}=+0.129981852\) \(a_{77}=-0.448345483\) \(a_{78}=-0.002952510\) \(a_{79}=-1.351076907\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.785458815\) \(a_{82}=-0.406800058\) \(a_{83}=-1.027489912\) \(a_{84}=+0.150335790\) \(a_{85}=-0.194494117\)
\(a_{86}=+1.321585188\) \(a_{87}=-0.158389828\) \(a_{88}=+0.142738796\) \(a_{89}=-0.618166067\) \(a_{90}=-0.293046711\)
\(a_{91}=+0.017126369\) \(a_{92}=+0.891522255\) \(a_{93}=-0.476435427\) \(a_{94}=+0.332899485\) \(a_{95}=-0.116259303\)
\(a_{96}=-0.047862085\) \(a_{97}=+1.326524579\) \(a_{98}=-0.164933520\) \(a_{99}=+0.374131191\) \(a_{100}=+0.099975586\)

Showing 100 of 162 available coefficients

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