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: \( 28.1553130021 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.984265534\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.695980833\) \(a_{7}=-0.423643941\) \(a_{8}=-0.353553391\) \(a_{9}=-0.031221359\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.197746094\) \(a_{12}=-0.492132767\) \(a_{13}=-0.709079392\) \(a_{14}=+0.299561504\) \(a_{15}=+0.440176928\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.563536677\) \(a_{18}=+0.022076835\) \(a_{19}=-0.734980319\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.416978130\) \(a_{22}=+0.846934385\) \(a_{23}=-0.327877780\) \(a_{24}=+0.347990417\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.501394846\) \(a_{27}=+1.014995641\) \(a_{28}=-0.211821971\) \(a_{29}=-1.840298811\) \(a_{30}=-0.311252091\)
\(a_{31}=+0.399986392\) \(a_{32}=-0.176776695\) \(a_{33}=+1.178900199\) \(a_{34}=-1.105587387\) \(a_{35}=+0.189459330\)
\(a_{36}=-0.015610680\) \(a_{37}=-0.225064219\) \(a_{38}=+0.519709568\) \(a_{39}=+0.697922406\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.148445777\) \(a_{42}=-0.294848063\) \(a_{43}=+0.437242374\) \(a_{44}=-0.598873047\) \(a_{45}=+0.013962616\)
\(a_{46}=+0.231844602\) \(a_{47}=-1.128181142\) \(a_{48}=-0.246066383\) \(a_{49}=-0.820525811\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.538935262\) \(a_{52}=-0.354539696\) \(a_{53}=+1.562774496\) \(a_{54}=-0.717710301\) \(a_{55}=+0.535648337\)
\(a_{56}=+0.149780752\) \(a_{57}=+0.723415796\) \(a_{58}=+1.301287769\) \(a_{59}=+0.796642034\) \(a_{60}=+0.220088464\)
\(a_{61}=+0.804162647\) \(a_{62}=-0.282833090\) \(a_{63}=+0.013226740\) \(a_{64}=+0.125000000\) \(a_{65}=+0.317109944\)
\(a_{66}=-0.833608325\) \(a_{67}=-1.061500998\) \(a_{68}=+0.781768339\) \(a_{69}=+0.322718799\) \(a_{70}=-0.133967977\)
\(a_{71}=+1.491836913\) \(a_{72}=+0.011038417\) \(a_{73}=-0.116718807\) \(a_{74}=+0.159144435\) \(a_{75}=-0.196853107\)
\(a_{76}=-0.367490160\) \(a_{77}=+0.507417876\) \(a_{78}=-0.493505666\) \(a_{79}=+1.497239746\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.967803868\) \(a_{82}=-0.104967016\) \(a_{83}=+0.271218185\) \(a_{84}=+0.208489065\) \(a_{85}=-0.699234859\)
\(a_{86}=-0.309177048\) \(a_{87}=+1.811342692\) \(a_{88}=+0.423467193\) \(a_{89}=-0.145492922\) \(a_{90}=-0.009873061\)
\(a_{91}=+0.300397188\) \(a_{92}=-0.163938890\) \(a_{93}=-0.393692820\) \(a_{94}=+0.797744536\) \(a_{95}=+0.328693191\)
\(a_{96}=+0.173995208\) \(a_{97}=+0.583148277\) \(a_{98}=+0.580199365\) \(a_{99}=+0.037395261\) \(a_{100}=+0.099975586\)

Showing 100 of 240 available coefficients

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