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: \( 8.42338862095 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.149114123\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.105439608\) \(a_{7}=-1.326421961\) \(a_{8}=-0.353553391\) \(a_{9}=-0.977764978\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.676059340\) \(a_{12}=-0.074557062\) \(a_{13}=-0.575060667\) \(a_{14}=+0.937921963\) \(a_{15}=-0.066685863\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.377595706\) \(a_{18}=+0.691384247\) \(a_{19}=+0.528604624\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.197788248\) \(a_{22}=-1.185152925\) \(a_{23}=+0.044105341\) \(a_{24}=+0.052719804\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.406629297\) \(a_{27}=+0.294912690\) \(a_{28}=-0.663210981\) \(a_{29}=+1.307099680\) \(a_{30}=+0.047154026\)
\(a_{31}=+0.610190729\) \(a_{32}=-0.176776695\) \(a_{33}=-0.249924119\) \(a_{34}=-0.974107265\) \(a_{35}=-0.593193934\)
\(a_{36}=-0.488882489\) \(a_{37}=+1.432141805\) \(a_{38}=-0.373779914\) \(a_{39}=+0.085749667\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.230826198\) \(a_{42}=-0.139857411\) \(a_{43}=-0.187406776\) \(a_{44}=+0.838029670\) \(a_{45}=-0.437269792\)
\(a_{46}=-0.031187186\) \(a_{47}=+0.513203201\) \(a_{48}=-0.037278531\) \(a_{49}=+0.759395219\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.205418976\) \(a_{52}=-0.287530334\) \(a_{53}=-1.144537578\) \(a_{54}=-0.208534763\) \(a_{55}=+0.749556524\)
\(a_{56}=+0.468960982\) \(a_{57}=-0.078822415\) \(a_{58}=-0.924259048\) \(a_{59}=-1.250664591\) \(a_{60}=-0.033342932\)
\(a_{61}=+1.435261915\) \(a_{62}=-0.431470002\) \(a_{63}=+1.296928940\) \(a_{64}=+0.125000000\) \(a_{65}=-0.257174949\)
\(a_{66}=+0.176723039\) \(a_{67}=-0.857066486\) \(a_{68}=+0.688797853\) \(a_{69}=-0.006576729\) \(a_{70}=+0.419451454\)
\(a_{71}=+1.599390521\) \(a_{72}=+0.345692123\) \(a_{73}=-1.085886316\) \(a_{74}=-1.012677182\) \(a_{75}=-0.029822825\)
\(a_{76}=+0.264302312\) \(a_{77}=-2.223161917\) \(a_{78}=-0.060634171\) \(a_{79}=-0.504495262\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.933789331\) \(a_{82}=-0.163218770\) \(a_{83}=+0.070617810\) \(a_{84}=+0.098894124\) \(a_{85}=+0.616079529\)
\(a_{86}=+0.132516602\) \(a_{87}=-0.194907023\) \(a_{88}=-0.592576462\) \(a_{89}=+1.498002780\) \(a_{90}=+0.309196435\)
\(a_{91}=+0.762773098\) \(a_{92}=+0.022052670\) \(a_{93}=-0.090988055\) \(a_{94}=-0.362889463\) \(a_{95}=+0.236399175\)
\(a_{96}=+0.026359902\) \(a_{97}=+0.020356000\) \(a_{98}=-0.536973509\) \(a_{99}=-1.638792124\) \(a_{100}=+0.099975586\)

Showing 100 of 136 available coefficients

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