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: \( 4.18409504645 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.582122857\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.118729801\) \(a_{7}=-1.045758593\) \(a_{8}=+0.353553391\) \(a_{9}=+1.503112736\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.612319496\) \(a_{12}=+0.791061429\) \(a_{13}=-0.829857447\) \(a_{14}=-0.739462993\) \(a_{15}=-0.707546852\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.141791910\) \(a_{18}=+1.062861208\) \(a_{19}=+0.862748096\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.654518574\) \(a_{22}=-0.432975268\) \(a_{23}=-0.179135739\) \(a_{24}=+0.559364901\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.586797828\) \(a_{27}=+0.795986159\) \(a_{28}=-0.522879297\) \(a_{29}=+0.164220373\) \(a_{30}=-0.500311177\)
\(a_{31}=+0.164618885\) \(a_{32}=+0.176776695\) \(a_{33}=-0.968764670\) \(a_{34}=+0.807368802\) \(a_{35}=+0.467677461\)
\(a_{36}=+0.751556368\) \(a_{37}=+1.106021147\) \(a_{38}=+0.610055029\) \(a_{39}=-1.312936435\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.704759291\) \(a_{42}=-1.169921303\) \(a_{43}=+1.641899639\) \(a_{44}=-0.306159748\) \(a_{45}=-0.672212451\)
\(a_{46}=-0.126668096\) \(a_{47}=+0.063187364\) \(a_{48}=+0.395530714\) \(a_{49}=+0.093611036\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.806455078\) \(a_{52}=-0.414928723\) \(a_{53}=-1.281399724\) \(a_{54}=+0.562847211\) \(a_{55}=+0.273837603\)
\(a_{56}=-0.369731496\) \(a_{57}=+1.364973483\) \(a_{58}=+0.116121340\) \(a_{59}=+0.095606950\) \(a_{60}=-0.353773426\)
\(a_{61}=-0.277998640\) \(a_{62}=+0.116403130\) \(a_{63}=-1.571893060\) \(a_{64}=+0.125000000\) \(a_{65}=+0.371123533\)
\(a_{66}=-0.685020068\) \(a_{67}=-1.249280630\) \(a_{68}=+0.570895955\) \(a_{69}=-0.283414747\) \(a_{70}=+0.330697904\)
\(a_{71}=-0.811554300\) \(a_{72}=+0.531430604\) \(a_{73}=+1.104174400\) \(a_{74}=+0.782075053\) \(a_{75}=+0.316424571\)
\(a_{76}=+0.431374048\) \(a_{77}=+0.640338375\) \(a_{78}=-0.928386257\) \(a_{79}=+0.890166998\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.243764840\) \(a_{82}=-1.205446855\) \(a_{83}=+0.546877000\) \(a_{84}=-0.827259287\) \(a_{85}=-0.510624865\)
\(a_{86}=+1.160998369\) \(a_{87}=+0.259816806\) \(a_{88}=-0.216487634\) \(a_{89}=-0.849317000\) \(a_{90}=-0.475325982\)
\(a_{91}=+0.867830557\) \(a_{92}=-0.089567869\) \(a_{93}=+0.260447301\) \(a_{94}=+0.044680214\) \(a_{95}=-0.385832678\)
\(a_{96}=+0.279682450\) \(a_{97}=-0.184670000\) \(a_{98}=+0.066192998\) \(a_{99}=-0.920385233\) \(a_{100}=+0.099975586\)

Showing 100 of 130 available coefficients

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