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: \( 22.9495013485 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.059292330\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.749032790\) \(a_{7}=-0.342572397\) \(a_{8}=-0.353553391\) \(a_{9}=+0.122100240\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.623698325\) \(a_{12}=-0.529646165\) \(a_{13}=+0.569443485\) \(a_{14}=+0.242235265\) \(a_{15}=-0.473729932\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.742476212\) \(a_{18}=-0.086337908\) \(a_{19}=+1.805768359\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.362884313\) \(a_{22}=-1.148128097\) \(a_{23}=+0.302284917\) \(a_{24}=+0.374516395\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.402657349\) \(a_{27}=+0.929952482\) \(a_{28}=-0.171286199\) \(a_{29}=+1.275567522\) \(a_{30}=+0.334977647\)
\(a_{31}=+1.551687679\) \(a_{32}=-0.176776695\) \(a_{33}=-1.719971182\) \(a_{34}=+1.232116745\) \(a_{35}=-0.153203033\)
\(a_{36}=+0.061050120\) \(a_{37}=+0.172007611\) \(a_{38}=-1.276871052\) \(a_{39}=-0.603207116\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.398353627\) \(a_{42}=-0.256597958\) \(a_{43}=-1.120394535\) \(a_{44}=+0.811849163\) \(a_{45}=+0.054604888\)
\(a_{46}=-0.213747715\) \(a_{47}=+0.389811120\) \(a_{48}=-0.264823083\) \(a_{49}=-0.882644153\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.845791686\) \(a_{52}=+0.284721742\) \(a_{53}=-0.975295119\) \(a_{54}=-0.657575706\) \(a_{55}=+0.726139966\)
\(a_{56}=+0.121117633\) \(a_{57}=-1.912836573\) \(a_{58}=-0.901962445\) \(a_{59}=-1.008715298\) \(a_{60}=-0.236864966\)
\(a_{61}=-0.240824380\) \(a_{62}=-1.097208880\) \(a_{63}=-0.041828172\) \(a_{64}=+0.125000000\) \(a_{65}=+0.254662868\)
\(a_{66}=+1.216203287\) \(a_{67}=+0.513438238\) \(a_{68}=-0.871238106\) \(a_{69}=-0.320208094\) \(a_{70}=+0.108330904\)
\(a_{71}=-1.007756214\) \(a_{72}=-0.043168954\) \(a_{73}=+0.714523008\) \(a_{74}=-0.121627748\) \(a_{75}=-0.211858466\)
\(a_{76}=+0.902884180\) \(a_{77}=-0.556234228\) \(a_{78}=+0.426531842\) \(a_{79}=+0.982535744\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.107191772\) \(a_{82}=+0.281678551\) \(a_{83}=-0.687703540\) \(a_{84}=+0.181442156\) \(a_{85}=-0.779259052\)
\(a_{86}=+0.792238573\) \(a_{87}=-1.351198892\) \(a_{88}=-0.574064048\) \(a_{89}=-0.875603490\) \(a_{90}=-0.038611486\)
\(a_{91}=-0.195075620\) \(a_{92}=+0.151142458\) \(a_{93}=-1.643690857\) \(a_{94}=-0.275638086\) \(a_{95}=+0.807564161\)
\(a_{96}=+0.187258197\) \(a_{97}=-0.182309909\) \(a_{98}=+0.624123666\) \(a_{99}=+0.198253956\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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