Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 9.95201540908 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.423900208\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.299742711\) \(a_{7}=+0.516637335\) \(a_{8}=-0.353553391\) \(a_{9}=-0.820308614\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.550388015\) \(a_{12}=-0.211950104\) \(a_{13}=-1.866956592\) \(a_{14}=-0.365317763\) \(a_{15}=+0.189573936\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.745487806\) \(a_{18}=+0.580045784\) \(a_{19}=+1.100316447\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.219002674\) \(a_{22}=+0.389183098\) \(a_{23}=+0.493389701\) \(a_{24}=+0.149871356\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.320137667\) \(a_{27}=+0.771629200\) \(a_{28}=+0.258318667\) \(a_{29}=-0.607809823\) \(a_{30}=-0.134049016\)
\(a_{31}=+0.776882573\) \(a_{32}=-0.176776695\) \(a_{33}=+0.233309594\) \(a_{34}=-0.527139483\) \(a_{35}=-0.231047240\)
\(a_{36}=-0.410154307\) \(a_{37}=+1.248489895\) \(a_{38}=-0.778041221\) \(a_{39}=+0.791403287\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.802269550\) \(a_{42}=+0.154858276\) \(a_{43}=+1.071628846\) \(a_{44}=-0.275194008\) \(a_{45}=+0.366853165\)
\(a_{46}=-0.348879203\) \(a_{47}=+0.503198782\) \(a_{48}=-0.105975052\) \(a_{49}=-0.733085864\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.316012436\) \(a_{52}=-0.933478296\) \(a_{53}=+1.297445148\) \(a_{54}=-0.545624240\) \(a_{55}=+0.246141003\)
\(a_{56}=-0.182658881\) \(a_{57}=-0.466424371\) \(a_{58}=+0.429786448\) \(a_{59}=+0.174573425\) \(a_{60}=+0.094786968\)
\(a_{61}=+1.616898195\) \(a_{62}=-0.549338935\) \(a_{63}=-0.423802056\) \(a_{64}=+0.125000000\) \(a_{65}=+0.834928370\)
\(a_{66}=-0.164974796\) \(a_{67}=-0.486731595\) \(a_{68}=+0.372743903\) \(a_{69}=-0.209147997\) \(a_{70}=+0.163375070\)
\(a_{71}=-1.813984176\) \(a_{72}=+0.290022892\) \(a_{73}=-0.194381913\) \(a_{74}=-0.882815671\) \(a_{75}=-0.084780042\)
\(a_{76}=+0.550158224\) \(a_{77}=-0.284350997\) \(a_{78}=-0.559606631\) \(a_{79}=+1.437636100\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.493214836\) \(a_{82}=+0.567290239\) \(a_{83}=+1.759715060\) \(a_{84}=-0.109501337\) \(a_{85}=-0.333392282\)
\(a_{86}=-0.757756024\) \(a_{87}=+0.257650710\) \(a_{88}=+0.194591549\) \(a_{89}=-0.468639790\) \(a_{90}=-0.259404360\)
\(a_{91}=-0.964539478\) \(a_{92}=+0.246694851\) \(a_{93}=-0.329320684\) \(a_{94}=-0.355815271\) \(a_{95}=-0.492076475\)
\(a_{96}=+0.074935678\) \(a_{97}=+0.761515900\) \(a_{98}=+0.518369986\) \(a_{99}=+0.451488030\) \(a_{100}=+0.099975586\)

Showing 100 of 150 available coefficients

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