Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 18.8405820105 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.382033353\) \(a_{3}=+0.577350269\) \(a_{4}=+0.910016188\) \(a_{5}=-0.183064821\)
\(a_{6}=+0.797917328\) \(a_{7}=+0.857286001\) \(a_{8}=-0.124360630\) \(a_{9}=+0.333333333\) \(a_{10}=-0.253001689\)
\(a_{11}=+1.211160640\) \(a_{12}=+0.525398091\) \(a_{13}=+1.738262030\) \(a_{14}=+1.184797846\) \(a_{15}=-0.105692524\)
\(a_{16}=-1.081886726\) \(a_{17}=+0.210628591\) \(a_{18}=+0.460677784\) \(a_{19}=-0.930405426\) \(a_{20}=-0.166591951\)
\(a_{21}=+0.494954303\) \(a_{22}=+1.673864400\) \(a_{23}=+1.253483132\) \(a_{24}=-0.071799643\) \(a_{25}=-0.966487271\)
\(a_{26}=+2.402336101\) \(a_{27}=+0.192450090\) \(a_{28}=+0.780144138\) \(a_{29}=-0.080875952\) \(a_{30}=-0.146070593\)
\(a_{31}=+1.269688110\) \(a_{32}=-1.370842909\) \(a_{33}=+0.699263922\) \(a_{34}=+0.291095737\) \(a_{35}=-0.156938908\)
\(a_{36}=+0.303338729\) \(a_{37}=+0.653440766\) \(a_{38}=-1.285851330\) \(a_{39}=+1.003586051\) \(a_{40}=+0.022766056\)
\(a_{41}=-1.206021511\) \(a_{42}=+0.684043355\) \(a_{43}=-0.900952604\) \(a_{44}=+1.102175789\) \(a_{45}=-0.061021607\)
\(a_{46}=+1.732355496\) \(a_{47}=-1.123476364\) \(a_{48}=-0.624627592\) \(a_{49}=-0.265060712\) \(a_{50}=-1.335717644\)
\(a_{51}=+0.121606474\) \(a_{52}=+1.581846586\) \(a_{53}=+0.573610529\) \(a_{54}=+0.265972443\) \(a_{55}=-0.221720906\)
\(a_{56}=-0.106612627\) \(a_{57}=-0.537169823\) \(a_{58}=-0.111773263\) \(a_{59}=-0.948184516\) \(a_{60}=-0.096181908\)
\(a_{61}=-0.019692539\) \(a_{62}=+1.754751316\) \(a_{63}=+0.285762000\) \(a_{64}=-0.812663896\) \(a_{65}=-0.318214628\)
\(a_{66}=+0.966406062\) \(a_{67}=-1.228538364\) \(a_{68}=+0.191675427\) \(a_{69}=+0.723698824\) \(a_{70}=-0.216894806\)
\(a_{71}=-0.071711827\) \(a_{72}=-0.041453543\) \(a_{73}=-1.057286450\) \(a_{74}=+0.903076932\) \(a_{75}=-0.558001686\)
\(a_{76}=-0.846683999\) \(a_{77}=+1.038311062\) \(a_{78}=+1.386989395\) \(a_{79}=-0.118193726\) \(a_{80}=+0.198055400\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.666761952\) \(a_{83}=+0.251803006\) \(a_{84}=+0.450416428\) \(a_{85}=-0.038558685\)
\(a_{86}=-1.245146548\) \(a_{87}=-0.046693753\) \(a_{88}=-0.150620700\) \(a_{89}=+0.381220199\) \(a_{90}=-0.084333896\)
\(a_{91}=+1.490187704\) \(a_{92}=+1.140689941\) \(a_{93}=+0.733054772\) \(a_{94}=-1.552681806\) \(a_{95}=+0.170324503\)
\(a_{96}=-0.791456523\) \(a_{97}=-1.098704941\) \(a_{98}=-0.366322745\) \(a_{99}=+0.403720213\) \(a_{100}=-0.879519062\)

Showing 100 of 1228 available coefficients

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