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: \( 24.9540594028 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.068845122\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.755787633\) \(a_{7}=-0.420215629\) \(a_{8}=+0.353553391\) \(a_{9}=+0.142429894\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.401210133\) \(a_{12}=+0.534422561\) \(a_{13}=+1.215813372\) \(a_{14}=-0.297137321\) \(a_{15}=-0.478002070\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.266957379\) \(a_{18}=+0.100713144\) \(a_{19}=+0.829228641\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.449145425\) \(a_{22}=-0.990805187\) \(a_{23}=-0.246645340\) \(a_{24}=+0.377893817\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.859709880\) \(a_{27}=-0.916609624\) \(a_{28}=-0.210107815\) \(a_{29}=+0.265801770\) \(a_{30}=-0.337998505\)
\(a_{31}=+0.767349848\) \(a_{32}=+0.176776695\) \(a_{33}=-1.497676615\) \(a_{34}=+0.188767373\) \(a_{35}=+0.187926142\)
\(a_{36}=+0.071214947\) \(a_{37}=+0.268261185\) \(a_{38}=+0.586353196\) \(a_{39}=+1.299516191\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.740748737\) \(a_{42}=-0.317593776\) \(a_{43}=-1.775721970\) \(a_{44}=-0.700605066\) \(a_{45}=-0.063696585\)
\(a_{46}=-0.174404593\) \(a_{47}=-1.525392611\) \(a_{48}=+0.267211280\) \(a_{49}=-0.823418825\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.285336093\) \(a_{52}=+0.607906686\) \(a_{53}=-0.493380817\) \(a_{54}=-0.648140881\) \(a_{55}=+0.626640222\)
\(a_{56}=-0.148568661\) \(a_{57}=+0.886316988\) \(a_{58}=+0.187950234\) \(a_{59}=-0.879403591\) \(a_{60}=-0.239001035\)
\(a_{61}=-1.739281977\) \(a_{62}=+0.542598281\) \(a_{63}=-0.059851267\) \(a_{64}=+0.125000000\) \(a_{65}=-0.543728270\)
\(a_{66}=-1.059017290\) \(a_{67}=+0.042588016\) \(a_{68}=+0.133478690\) \(a_{69}=-0.263625669\) \(a_{70}=+0.132883850\)
\(a_{71}=-0.812502162\) \(a_{72}=+0.050356572\) \(a_{73}=-0.653763395\) \(a_{74}=+0.189689303\) \(a_{75}=+0.213769024\)
\(a_{76}=+0.414614321\) \(a_{77}=+0.588810398\) \(a_{78}=+0.918896711\) \(a_{79}=-0.583861481\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.122143619\) \(a_{82}=-0.523788455\) \(a_{83}=-1.172977473\) \(a_{84}=-0.224572713\) \(a_{85}=-0.119386970\)
\(a_{86}=-1.255625047\) \(a_{87}=+0.284100925\) \(a_{88}=-0.495402593\) \(a_{89}=+0.672497931\) \(a_{90}=-0.045040287\)
\(a_{91}=-0.510903781\) \(a_{92}=-0.123322670\) \(a_{93}=+0.820178142\) \(a_{94}=-1.078615459\) \(a_{95}=-0.370842322\)
\(a_{96}=+0.188946908\) \(a_{97}=+0.633734953\) \(a_{98}=-0.582245035\) \(a_{99}=-0.199574210\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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