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: \( 22.3042312641 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.902537950\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.345297486\) \(a_{7}=-1.019354701\) \(a_{8}=-0.353553391\) \(a_{9}=+2.619650652\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.364912905\) \(a_{12}=-0.951268975\) \(a_{13}=-1.794570474\) \(a_{14}=+0.720792621\) \(a_{15}=+0.850840837\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.458324110\) \(a_{18}=-1.852372740\) \(a_{19}=-0.275660990\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.939361003\) \(a_{22}=+0.258032389\) \(a_{23}=-1.317524786\) \(a_{24}=+0.672648743\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.268952952\) \(a_{27}=-3.081446832\) \(a_{28}=-0.509677350\) \(a_{29}=-0.536067964\) \(a_{30}=-0.601635326\)
\(a_{31}=+0.680656219\) \(a_{32}=-0.176776695\) \(a_{33}=+0.694260649\) \(a_{34}=+0.324084086\) \(a_{35}=+0.455869281\)
\(a_{36}=+1.309825326\) \(a_{37}=-0.526899672\) \(a_{38}=+0.194921755\) \(a_{39}=+3.414238432\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.503809548\) \(a_{42}=-1.371335317\) \(a_{43}=+0.916823482\) \(a_{44}=-0.182456452\) \(a_{45}=-1.171543387\)
\(a_{46}=+0.931630710\) \(a_{47}=+1.326159285\) \(a_{48}=-0.475634488\) \(a_{49}=+0.039084006\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.871979013\) \(a_{52}=-0.897285237\) \(a_{53}=+0.497650202\) \(a_{54}=+2.178911951\) \(a_{55}=+0.163194012\)
\(a_{56}=+0.360396311\) \(a_{57}=+0.524455495\) \(a_{58}=+0.379057293\) \(a_{59}=+1.918790414\) \(a_{60}=+0.425420419\)
\(a_{61}=-0.665072795\) \(a_{62}=-0.481296628\) \(a_{63}=-2.670353207\) \(a_{64}=+0.125000000\) \(a_{65}=+0.802556314\)
\(a_{66}=-0.490916413\) \(a_{67}=+1.069407227\) \(a_{68}=-0.229162055\) \(a_{69}=+2.506640906\) \(a_{70}=-0.322348260\)
\(a_{71}=-1.616307171\) \(a_{72}=-0.926186370\) \(a_{73}=+0.773946161\) \(a_{74}=+0.372574331\) \(a_{75}=-0.380507590\)
\(a_{76}=-0.137830495\) \(a_{77}=+0.371975685\) \(a_{78}=-2.414231148\) \(a_{79}=+1.711580552\) \(a_{80}=-0.111803399\)
\(a_{81}=+3.242918887\) \(a_{82}=-0.356247148\) \(a_{83}=-0.239478199\) \(a_{84}=+0.969680502\) \(a_{85}=+0.204968773\)
\(a_{86}=-0.648292101\) \(a_{87}=+1.019889645\) \(a_{88}=+0.129016195\) \(a_{89}=-0.701849483\) \(a_{90}=+0.828406273\)
\(a_{91}=+1.829303849\) \(a_{92}=-0.658762393\) \(a_{93}=-1.294974289\) \(a_{94}=-0.937736224\) \(a_{95}=+0.123279342\)
\(a_{96}=+0.336324372\) \(a_{97}=-0.566517334\) \(a_{98}=-0.027636566\) \(a_{99}=-0.955944328\) \(a_{100}=+0.099975586\)

Showing 100 of 196 available coefficients

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