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: \( 25.7447796785 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.123394886\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.087253360\) \(a_{7}=+0.474302819\) \(a_{8}=-0.353553391\) \(a_{9}=-0.984773702\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.305394814\) \(a_{12}=+0.061697443\) \(a_{13}=-0.923837776\) \(a_{14}=-0.335382740\) \(a_{15}=-0.055183870\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.705208549\) \(a_{18}=+0.696340163\) \(a_{19}=+1.251934666\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.058526542\) \(a_{22}=-0.923053525\) \(a_{23}=-0.214428818\) \(a_{24}=-0.043626680\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.653251956\) \(a_{27}=-0.244910924\) \(a_{28}=+0.237151410\) \(a_{29}=-0.854907227\) \(a_{30}=+0.039020889\)
\(a_{31}=+1.618121999\) \(a_{32}=-0.176776695\) \(a_{33}=+0.161079044\) \(a_{34}=+0.498657747\) \(a_{35}=-0.212114669\)
\(a_{36}=-0.492386851\) \(a_{37}=-0.039838429\) \(a_{38}=-0.885251492\) \(a_{39}=-0.113996857\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.522928049\) \(a_{42}=-0.041384515\) \(a_{43}=-1.871477229\) \(a_{44}=+0.652697407\) \(a_{45}=+0.440404188\)
\(a_{46}=+0.151624071\) \(a_{47}=+0.934095257\) \(a_{48}=+0.030848721\) \(a_{49}=-0.775036835\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.087019128\) \(a_{52}=-0.461918888\) \(a_{53}=-0.481080874\) \(a_{54}=+0.173178175\) \(a_{55}=-0.583790308\)
\(a_{56}=-0.167691370\) \(a_{57}=+0.154482335\) \(a_{58}=+0.604510697\) \(a_{59}=+0.416567357\) \(a_{60}=-0.027591935\)
\(a_{61}=+0.481218641\) \(a_{62}=-1.144185039\) \(a_{63}=-0.467080943\) \(a_{64}=+0.125000000\) \(a_{65}=+0.413152814\)
\(a_{66}=-0.113900084\) \(a_{67}=-1.526163237\) \(a_{68}=-0.352604274\) \(a_{69}=-0.026459419\) \(a_{70}=+0.149987721\)
\(a_{71}=+1.458438542\) \(a_{72}=+0.348170081\) \(a_{73}=+1.075580833\) \(a_{74}=+0.028170023\) \(a_{75}=+0.024678977\)
\(a_{76}=+0.625967333\) \(a_{77}=+0.619152441\) \(a_{78}=+0.080607950\) \(a_{79}=-0.419118528\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.954552947\) \(a_{82}=-0.369765970\) \(a_{83}=+1.430999720\) \(a_{84}=+0.029263271\) \(a_{85}=+0.315378851\)
\(a_{86}=+1.323334239\) \(a_{87}=-0.105491179\) \(a_{88}=-0.461526763\) \(a_{89}=+0.202552280\) \(a_{90}=-0.311412788\)
\(a_{91}=-0.438178862\) \(a_{92}=-0.107214409\) \(a_{93}=+0.199667979\) \(a_{94}=-0.660505091\) \(a_{95}=-0.559882203\)
\(a_{96}=-0.021813340\) \(a_{97}=-0.397424524\) \(a_{98}=+0.548033802\) \(a_{99}=-1.285518484\) \(a_{100}=+0.099975586\)

Showing 100 of 228 available coefficients

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