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: \( 26.9871409866 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.187998686\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.132935146\) \(a_{7}=-0.148016462\) \(a_{8}=+0.353553391\) \(a_{9}=-0.964656494\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.604768985\) \(a_{12}=+0.093999343\) \(a_{13}=+1.656539462\) \(a_{14}=-0.104663444\) \(a_{15}=-0.084075568\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.771317580\) \(a_{18}=-0.682115148\) \(a_{19}=+0.188280638\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.027826900\) \(a_{22}=-0.427636250\) \(a_{23}=-0.628837096\) \(a_{24}=+0.066467573\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.171350287\) \(a_{27}=-0.369352839\) \(a_{28}=-0.074008231\) \(a_{29}=+0.131987132\) \(a_{30}=-0.059450404\)
\(a_{31}=-0.827191844\) \(a_{32}=+0.176776695\) \(a_{33}=-0.113695774\) \(a_{34}=-0.545403891\) \(a_{35}=+0.066194974\)
\(a_{36}=-0.482328247\) \(a_{37}=+0.436043906\) \(a_{38}=+0.133134516\) \(a_{39}=+0.311427242\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.090084847\) \(a_{42}=-0.019676590\) \(a_{43}=+0.399309702\) \(a_{44}=-0.302384493\) \(a_{45}=+0.431407499\)
\(a_{46}=-0.444654975\) \(a_{47}=+0.758561460\) \(a_{48}=+0.046999671\) \(a_{49}=-0.978091127\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.145006691\) \(a_{52}=+0.828269731\) \(a_{53}=+0.872975850\) \(a_{54}=-0.261171897\) \(a_{55}=+0.270460912\)
\(a_{56}=-0.052331722\) \(a_{57}=+0.035396513\) \(a_{58}=+0.093328996\) \(a_{59}=+1.677818674\) \(a_{60}=-0.042037784\)
\(a_{61}=-0.777410743\) \(a_{62}=-0.584912962\) \(a_{63}=+0.142785041\) \(a_{64}=+0.125000000\) \(a_{65}=-0.740826969\)
\(a_{66}=-0.080395053\) \(a_{67}=-1.713187833\) \(a_{68}=-0.385658790\) \(a_{69}=-0.118220548\) \(a_{70}=+0.046806915\)
\(a_{71}=+1.122108564\) \(a_{72}=-0.341057574\) \(a_{73}=+1.579154838\) \(a_{74}=+0.308329603\) \(a_{75}=+0.037599737\)
\(a_{76}=+0.094140319\) \(a_{77}=+0.089515765\) \(a_{78}=+0.220212315\) \(a_{79}=+0.769530854\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.895218646\) \(a_{82}=+0.063699606\) \(a_{83}=-0.482852838\) \(a_{84}=-0.013913450\) \(a_{85}=+0.344943708\)
\(a_{86}=+0.282354598\) \(a_{87}=+0.024813407\) \(a_{88}=-0.213818125\) \(a_{89}=+0.843235013\) \(a_{90}=+0.305051168\)
\(a_{91}=-0.245195110\) \(a_{92}=-0.314418548\) \(a_{93}=-0.155510980\) \(a_{94}=+0.536383952\) \(a_{95}=-0.084201661\)
\(a_{96}=+0.033233786\) \(a_{97}=-0.396345071\) \(a_{98}=-0.691614869\) \(a_{99}=+0.583394329\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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