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: \( 11.1924559787 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.530177261\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.081998718\) \(a_{7}=+1.291037956\) \(a_{8}=+0.353553391\) \(a_{9}=+1.341442450\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.140191718\) \(a_{12}=-0.765088631\) \(a_{13}=-1.675699147\) \(a_{14}=+0.912901694\) \(a_{15}=+0.684316075\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.937309026\) \(a_{18}=+0.948543053\) \(a_{19}=+0.563488712\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.975516924\) \(a_{22}=+0.806237295\) \(a_{23}=-0.802406871\) \(a_{24}=-0.540999359\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.184898230\) \(a_{27}=-0.522467473\) \(a_{28}=+0.645518978\) \(a_{29}=-0.694427415\) \(a_{30}=+0.483884537\)
\(a_{31}=-1.452647880\) \(a_{32}=+0.176776695\) \(a_{33}=-1.744695440\) \(a_{34}=-0.662777569\) \(a_{35}=-0.577369726\)
\(a_{36}=+0.670721225\) \(a_{37}=-0.369438871\) \(a_{38}=+0.398446690\) \(a_{39}=+2.564116732\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.905485737\) \(a_{42}=-1.396901413\) \(a_{43}=-0.134424451\) \(a_{44}=+0.570095859\) \(a_{45}=-0.599911301\)
\(a_{46}=-0.567387340\) \(a_{47}=-0.786436665\) \(a_{48}=-0.382544315\) \(a_{49}=+0.666779004\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.434248959\) \(a_{52}=-0.837849574\) \(a_{53}=+1.408516449\) \(a_{54}=-0.369440293\) \(a_{55}=-0.509909238\)
\(a_{56}=+0.456450847\) \(a_{57}=-0.862237615\) \(a_{58}=-0.491034334\) \(a_{59}=+0.525918607\) \(a_{60}=+0.342158037\)
\(a_{61}=-0.271376015\) \(a_{62}=-1.027177167\) \(a_{63}=+1.731853119\) \(a_{64}=+0.125000000\) \(a_{65}=+0.749395441\)
\(a_{66}=-1.233685976\) \(a_{67}=-1.250161656\) \(a_{68}=-0.468654513\) \(a_{69}=+1.227824748\) \(a_{70}=-0.408262049\)
\(a_{71}=-1.045565153\) \(a_{72}=+0.474271527\) \(a_{73}=+0.336600709\) \(a_{74}=-0.261232731\) \(a_{75}=-0.306035452\)
\(a_{76}=+0.281744356\) \(a_{77}=+1.472030784\) \(a_{78}=+1.813104329\) \(a_{79}=+0.168143721\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.541974603\) \(a_{82}=-0.640275105\) \(a_{83}=-1.436963554\) \(a_{84}=-0.987758462\) \(a_{85}=+0.419177340\)
\(a_{86}=-0.095052441\) \(a_{87}=+1.062597039\) \(a_{88}=+0.403118648\) \(a_{89}=+0.579507021\) \(a_{90}=-0.424201349\)
\(a_{91}=-2.163391198\) \(a_{92}=-0.401203436\) \(a_{93}=+2.222808746\) \(a_{94}=-0.556094699\) \(a_{95}=-0.251999813\)
\(a_{96}=-0.270499679\) \(a_{97}=-1.547955348\) \(a_{98}=+0.471483955\) \(a_{99}=+1.529501350\) \(a_{100}=+0.099975586\)

Showing 100 of 150 available coefficients

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