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: \( 12.580463057 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.819926422\) \(a_{3}=+0.577350269\) \(a_{4}=-0.327720662\) \(a_{5}=-1.553787521\)
\(a_{6}=+0.473384741\) \(a_{7}=+0.321628847\) \(a_{8}=-1.088633252\) \(a_{9}=+0.333333333\) \(a_{10}=-1.273991443\)
\(a_{11}=-1.256795019\) \(a_{12}=-0.189209613\) \(a_{13}=-0.297390460\) \(a_{14}=+0.263711990\) \(a_{15}=-0.897079644\)
\(a_{16}=-0.564878505\) \(a_{17}=+0.704557186\) \(a_{18}=+0.273308807\) \(a_{19}=-0.717431211\) \(a_{20}=+0.509208275\)
\(a_{21}=+0.185692501\) \(a_{22}=-1.030479443\) \(a_{23}=+0.439308592\) \(a_{24}=-0.628522701\) \(a_{25}=+1.414255661\)
\(a_{26}=-0.243838296\) \(a_{27}=+0.192450090\) \(a_{28}=-0.105404419\) \(a_{29}=-1.377242401\) \(a_{30}=-0.735539303\)
\(a_{31}=+1.837156934\) \(a_{32}=+0.625474440\) \(a_{33}=-0.725610942\) \(a_{34}=+0.577685053\) \(a_{35}=-0.499742889\)
\(a_{36}=-0.109240221\) \(a_{37}=-0.343278065\) \(a_{38}=-0.588240806\) \(a_{39}=-0.171698462\) \(a_{40}=+1.691504763\)
\(a_{41}=-0.506045036\) \(a_{42}=+0.152254188\) \(a_{43}=-0.193906372\) \(a_{44}=+0.411877696\) \(a_{45}=-0.517929174\)
\(a_{46}=+0.360200722\) \(a_{47}=-0.454675885\) \(a_{48}=-0.326132757\) \(a_{49}=-0.896554885\) \(a_{50}=+1.159585584\)
\(a_{51}=+0.406776281\) \(a_{52}=+0.097460998\) \(a_{53}=-0.897313115\) \(a_{54}=+0.157794914\) \(a_{55}=+1.952792417\)
\(a_{56}=-0.350135858\) \(a_{57}=-0.414209103\) \(a_{58}=-1.129237434\) \(a_{59}=-0.897387200\) \(a_{60}=+0.293991535\)
\(a_{61}=-0.848491065\) \(a_{62}=+1.506333512\) \(a_{63}=+0.107209616\) \(a_{64}=+1.077721525\) \(a_{65}=+0.462081586\)
\(a_{66}=-0.594947584\) \(a_{67}=-0.449236711\) \(a_{68}=-0.230897948\) \(a_{69}=+0.253634934\) \(a_{70}=-0.409752399\)
\(a_{71}=-0.685607043\) \(a_{72}=-0.362877751\) \(a_{73}=+0.706463310\) \(a_{74}=-0.281462755\) \(a_{75}=+0.816520887\)
\(a_{76}=+0.235117032\) \(a_{77}=-0.404221533\) \(a_{78}=-0.140780106\) \(a_{79}=+0.030002467\) \(a_{80}=+0.877701173\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.414919696\) \(a_{83}=+0.239835535\) \(a_{84}=-0.060855270\) \(a_{85}=-1.094732163\)
\(a_{86}=-0.158988957\) \(a_{87}=-0.795151271\) \(a_{88}=+1.368188849\) \(a_{89}=-0.053642738\) \(a_{90}=-0.424663814\)
\(a_{91}=-0.095649351\) \(a_{92}=-0.143970503\) \(a_{93}=+1.060683051\) \(a_{94}=-0.372800771\) \(a_{95}=+1.114735663\)
\(a_{96}=+0.361117837\) \(a_{97}=+0.328825466\) \(a_{98}=-0.735109039\) \(a_{99}=-0.418931673\) \(a_{100}=-0.463480802\)

Showing 100 of 1228 available coefficients

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