Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 11.8899755746 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.488750540\) \(a_{3}=-0.577350269\) \(a_{4}=+1.216378171\) \(a_{5}=+1.057513449\)
\(a_{6}=-0.859530525\) \(a_{7}=+1.386814926\) \(a_{8}=+0.322133117\) \(a_{9}=+0.333333337\) \(a_{10}=+1.574373703\)
\(a_{11}=+0.861334626\) \(a_{12}=-0.702276581\) \(a_{13}=-0.353920085\) \(a_{14}=+2.064613771\) \(a_{15}=-0.610516577\)
\(a_{16}=-0.737004538\) \(a_{17}=+0.460365023\) \(a_{18}=+0.496250180\) \(a_{19}=-1.266938866\) \(a_{20}=+1.286336274\)
\(a_{21}=-0.800677971\) \(a_{22}=+1.282312288\) \(a_{23}=-0.952129145\) \(a_{24}=-0.185983643\) \(a_{25}=+0.118334695\)
\(a_{26}=-0.526901010\) \(a_{27}=-0.192450090\) \(a_{28}=+1.686891403\) \(a_{29}=+0.267884280\) \(a_{30}=-0.908965090\)
\(a_{31}=+0.240097945\) \(a_{32}=-1.419047965\) \(a_{33}=-0.497291739\) \(a_{34}=+0.685368677\) \(a_{35}=+1.466575435\)
\(a_{36}=+0.405459390\) \(a_{37}=+0.220691365\) \(a_{38}=-1.886155921\) \(a_{39}=+0.204336745\) \(a_{40}=+0.340660105\)
\(a_{41}=+0.022892898\) \(a_{42}=-1.192009761\) \(a_{43}=+0.773790922\) \(a_{44}=+1.047708554\) \(a_{45}=+0.352504481\)
\(a_{46}=-1.417482778\) \(a_{47}=-0.160735579\) \(a_{48}=+0.425393017\) \(a_{49}=+0.923255635\) \(a_{50}=+0.176170831\)
\(a_{51}=-0.265791862\) \(a_{52}=-0.430502519\) \(a_{53}=-1.602546078\) \(a_{54}=-0.286510214\) \(a_{55}=+0.910872848\)
\(a_{56}=+0.446739123\) \(a_{57}=+0.731467558\) \(a_{58}=+0.398812754\) \(a_{59}=+0.793769311\) \(a_{60}=-0.742666465\)
\(a_{61}=-1.147027943\) \(a_{62}=+0.357445946\) \(a_{63}=+0.462271643\) \(a_{64}=-1.375806108\) \(a_{65}=-0.374276879\)
\(a_{66}=-0.740343346\) \(a_{67}=+1.197390979\) \(a_{68}=+0.559977966\) \(a_{69}=+0.549712017\) \(a_{70}=+2.183364968\)
\(a_{71}=-1.833468319\) \(a_{72}=+0.107377712\) \(a_{73}=-1.114499862\) \(a_{74}=+0.328554383\) \(a_{75}=-0.068320578\)
\(a_{76}=-1.541076776\) \(a_{77}=+1.194511640\) \(a_{78}=+0.304206444\) \(a_{79}=+0.568227169\) \(a_{80}=-0.779178384\)
\(a_{81}=+0.111111136\) \(a_{82}=+0.034081864\) \(a_{83}=+0.160210076\) \(a_{84}=-0.973927283\) \(a_{85}=+0.486842155\)
\(a_{86}=+1.151981760\) \(a_{87}=-0.154662936\) \(a_{88}=+0.277464318\) \(a_{89}=-0.060755639\) \(a_{90}=+0.524791181\)
\(a_{91}=-0.490823383\) \(a_{92}=-1.158148782\) \(a_{93}=-0.138620980\) \(a_{94}=-0.239296064\) \(a_{95}=-1.339804786\)
\(a_{96}=+0.819289159\) \(a_{97}=-0.185456093\) \(a_{98}=+1.374495634\) \(a_{99}=+0.287108813\) \(a_{100}=+0.143941142\)

Showing 100 of 5000 available coefficients

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