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: \( 8.03886120386 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.661540492\) \(a_{3}=-0.577350269\) \(a_{4}=+1.760716805\) \(a_{5}=-0.521652738\)
\(a_{6}=+0.959290851\) \(a_{7}=+0.721608936\) \(a_{8}=-1.263961753\) \(a_{9}=+0.333333223\) \(a_{10}=+0.866747725\)
\(a_{11}=-0.198852908\) \(a_{12}=-1.016533367\) \(a_{13}=+1.346761915\) \(a_{14}=-1.198446973\) \(a_{15}=+0.301176348\)
\(a_{16}=+0.339406864\) \(a_{17}=+0.508931860\) \(a_{18}=-0.553846831\) \(a_{19}=+0.318308786\) \(a_{20}=-0.918482742\)
\(a_{21}=-0.416621116\) \(a_{22}=+0.330396994\) \(a_{23}=+1.518976338\) \(a_{24}=+0.729748671\) \(a_{25}=-0.727878421\)
\(a_{26}=-2.237855767\) \(a_{27}=-0.192450090\) \(a_{28}=+1.270548989\) \(a_{29}=+1.082908922\) \(a_{30}=-0.500416698\)
\(a_{31}=-0.504720652\) \(a_{32}=+0.700023528\) \(a_{33}=+0.114805985\) \(a_{34}=-0.845610894\) \(a_{35}=-0.376429279\)
\(a_{36}=+0.586905602\) \(a_{37}=+0.383201615\) \(a_{38}=-0.528882937\) \(a_{39}=-0.777607669\) \(a_{40}=+0.659349120\)
\(a_{41}=-0.066179215\) \(a_{42}=+0.692232854\) \(a_{43}=+1.164270935\) \(a_{44}=-0.350118184\) \(a_{45}=-0.173884245\)
\(a_{46}=-2.523840691\) \(a_{47}=+0.851312461\) \(a_{48}=-0.195956645\) \(a_{49}=-0.479280534\) \(a_{50}=+1.209399473\)
\(a_{51}=-0.293831948\) \(a_{52}=+2.371431970\) \(a_{53}=-1.302435952\) \(a_{54}=+0.319763636\) \(a_{55}=+0.103730553\)
\(a_{56}=-0.912086140\) \(a_{57}=-0.183775722\) \(a_{58}=-1.799296989\) \(a_{59}=+0.240845146\) \(a_{60}=+0.530286260\)
\(a_{61}=+1.447620196\) \(a_{62}=+0.838613798\) \(a_{63}=+0.240536308\) \(a_{64}=-1.502524302\) \(a_{65}=-0.702591107\)
\(a_{66}=-0.190754787\) \(a_{67}=+1.096404007\) \(a_{68}=+0.896084865\) \(a_{69}=-0.876981393\) \(a_{70}=+0.625452513\)
\(a_{71}=+0.235827696\) \(a_{72}=-0.421320624\) \(a_{73}=-1.679507533\) \(a_{74}=-0.636704966\) \(a_{75}=+0.420240862\)
\(a_{76}=+0.560451612\) \(a_{77}=-0.143491892\) \(a_{78}=+1.292026602\) \(a_{79}=+0.343297043\) \(a_{80}=-0.177052400\)
\(a_{81}=+0.111110976\) \(a_{82}=+0.109959193\) \(a_{83}=+1.073501141\) \(a_{84}=-0.733551387\) \(a_{85}=-0.265485553\)
\(a_{86}=-1.934483864\) \(a_{87}=-0.625218272\) \(a_{88}=+0.251339097\) \(a_{89}=-0.711346491\) \(a_{90}=+0.288915491\)
\(a_{91}=+0.971901506\) \(a_{92}=+2.674486538\) \(a_{93}=+0.291402945\) \(a_{94}=-1.414487803\) \(a_{95}=-0.166048958\)
\(a_{96}=-0.404163527\) \(a_{97}=+0.007157953\) \(a_{98}=+0.796351560\) \(a_{99}=-0.066280248\) \(a_{100}=-1.281597764\)

Showing 100 of 5000 available coefficients

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