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: \( 30.6967542171 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.307781802\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.924741381\) \(a_{7}=-1.177173122\) \(a_{8}=-0.353553391\) \(a_{9}=+0.710293243\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.291955603\) \(a_{12}=+0.653890901\) \(a_{13}=+1.467967388\) \(a_{14}=+0.832387097\) \(a_{15}=-0.584857802\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.905828944\) \(a_{18}=-0.502253168\) \(a_{19}=+0.968552670\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.539485587\) \(a_{22}=+0.206443787\) \(a_{23}=+0.011416738\) \(a_{24}=-0.462370690\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.038009695\) \(a_{27}=-0.378873225\) \(a_{28}=-0.588586561\) \(a_{29}=+1.045050202\) \(a_{30}=+0.413556918\)
\(a_{31}=+1.378443878\) \(a_{32}=-0.176776695\) \(a_{33}=-0.381814225\) \(a_{34}=+1.347624570\) \(a_{35}=+0.526447824\)
\(a_{36}=+0.355146621\) \(a_{37}=-0.951315924\) \(a_{38}=-0.684870161\) \(a_{39}=+1.919781037\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.445830164\) \(a_{42}=+1.088580698\) \(a_{43}=+0.465524978\) \(a_{44}=-0.145977802\) \(a_{45}=-0.317652795\)
\(a_{46}=-0.008072853\) \(a_{47}=-0.326708462\) \(a_{48}=+0.326945451\) \(a_{49}=+0.385736560\) \(a_{50}=-0.141421356\)
\(a_{51}=-2.492408411\) \(a_{52}=+0.733983694\) \(a_{53}=+0.531952325\) \(a_{54}=+0.267903827\) \(a_{55}=+0.130566515\)
\(a_{56}=+0.416193549\) \(a_{57}=+1.266655556\) \(a_{58}=-0.738962084\) \(a_{59}=+1.164156239\) \(a_{60}=-0.292428901\)
\(a_{61}=-0.192220470\) \(a_{62}=-0.974707014\) \(a_{63}=-0.836138114\) \(a_{64}=+0.125000000\) \(a_{65}=-0.656494974\)
\(a_{66}=+0.269983428\) \(a_{67}=-0.376875358\) \(a_{68}=-0.952914472\) \(a_{69}=+0.014930602\) \(a_{70}=-0.372254827\)
\(a_{71}=+0.256393692\) \(a_{72}=-0.251126584\) \(a_{73}=-1.427793791\) \(a_{74}=+0.672681941\) \(a_{75}=+0.261556360\)
\(a_{76}=+0.484276335\) \(a_{77}=+0.343682289\) \(a_{78}=-1.357490190\) \(a_{79}=-0.921773135\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.205776752\) \(a_{82}=-1.022356314\) \(a_{83}=-1.913776487\) \(a_{84}=-0.769742794\) \(a_{85}=+0.852312614\)
\(a_{86}=-0.329175869\) \(a_{87}=+1.366697637\) \(a_{88}=+0.103221893\) \(a_{89}=-0.719612388\) \(a_{90}=+0.224614445\)
\(a_{91}=-1.728051754\) \(a_{92}=+0.005708369\) \(a_{93}=+1.802703819\) \(a_{94}=+0.231017769\) \(a_{95}=-0.433149922\)
\(a_{96}=-0.231185345\) \(a_{97}=-0.506115795\) \(a_{98}=-0.272756937\) \(a_{99}=-0.207374092\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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