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: \( 29.5726130963 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.334120239\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.943365468\) \(a_{7}=+0.481981975\) \(a_{8}=-0.353553391\) \(a_{9}=+0.779876812\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.036665738\) \(a_{12}=+0.667060119\) \(a_{13}=+0.782866273\) \(a_{14}=-0.340812723\) \(a_{15}=-0.596636709\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.561650217\) \(a_{18}=-0.551456182\) \(a_{19}=-1.398226222\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.643021908\) \(a_{22}=+0.025926592\) \(a_{23}=-0.693005321\) \(a_{24}=-0.471682734\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.553570050\) \(a_{27}=-0.293670801\) \(a_{28}=+0.240990988\) \(a_{29}=-0.102306177\) \(a_{30}=+0.421885863\)
\(a_{31}=-0.337148574\) \(a_{32}=-0.176776695\) \(a_{33}=-0.048916503\) \(a_{34}=-0.397146677\) \(a_{35}=-0.215548892\)
\(a_{36}=+0.389938406\) \(a_{37}=+1.618530385\) \(a_{38}=+0.988695243\) \(a_{39}=+1.044437739\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.244624336\) \(a_{42}=-0.454685151\) \(a_{43}=-0.503490033\) \(a_{44}=-0.018332869\) \(a_{45}=-0.348771513\)
\(a_{46}=+0.490028762\) \(a_{47}=-0.099093618\) \(a_{48}=+0.333530060\) \(a_{49}=-0.767693376\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.749308921\) \(a_{52}=+0.391433136\) \(a_{53}=+1.308128237\) \(a_{54}=+0.207656615\) \(a_{55}=+0.016397416\)
\(a_{56}=-0.170406361\) \(a_{57}=-1.865401902\) \(a_{58}=+0.072341391\) \(a_{59}=-1.102580552\) \(a_{60}=-0.298318354\)
\(a_{61}=-0.131247196\) \(a_{62}=+0.238400043\) \(a_{63}=+0.375886566\) \(a_{64}=+0.125000000\) \(a_{65}=-0.350108441\)
\(a_{66}=+0.034589191\) \(a_{67}=-1.246996828\) \(a_{68}=+0.280825108\) \(a_{69}=-0.924552424\) \(a_{70}=+0.152416083\)
\(a_{71}=-0.341629689\) \(a_{72}=-0.275728091\) \(a_{73}=-1.414789184\) \(a_{74}=-1.144473811\) \(a_{75}=+0.266824048\)
\(a_{76}=-0.699113111\) \(a_{77}=-0.017672225\) \(a_{78}=-0.738529008\) \(a_{79}=-0.953921412\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.171668970\) \(a_{82}=+0.172975527\) \(a_{83}=+1.843637817\) \(a_{84}=+0.321510954\) \(a_{85}=-0.251177613\)
\(a_{86}=+0.356021217\) \(a_{87}=-0.136488741\) \(a_{88}=+0.012963296\) \(a_{89}=-1.176789441\) \(a_{90}=+0.246618702\)
\(a_{91}=+0.377327432\) \(a_{92}=-0.346502660\) \(a_{93}=-0.449796736\) \(a_{94}=+0.070069770\) \(a_{95}=+0.625305776\)
\(a_{96}=-0.235841367\) \(a_{97}=+1.234912963\) \(a_{98}=+0.542841192\) \(a_{99}=-0.028594759\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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