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: \( 8.77828239355 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.038771004\) \(a_{3}=+0.577350269\) \(a_{4}=-0.998496809\) \(a_{5}=-0.948536556\)
\(a_{6}=-0.022384449\) \(a_{7}=-1.098864722\) \(a_{8}=+0.077483732\) \(a_{9}=+0.333333313\) \(a_{10}=+0.036775815\)
\(a_{11}=-0.469644046\) \(a_{12}=-0.576479742\) \(a_{13}=+1.019645653\) \(a_{14}=+0.042679660\) \(a_{15}=-0.547637836\)
\(a_{16}=+0.995492687\) \(a_{17}=-1.535206091\) \(a_{18}=-0.012923668\) \(a_{19}=+0.673280894\) \(a_{20}=+0.947110724\)
\(a_{21}=-0.634429843\) \(a_{22}=+0.018208551\) \(a_{23}=-0.578280613\) \(a_{24}=+0.044735251\) \(a_{25}=-0.100278402\)
\(a_{26}=-0.039533230\) \(a_{27}=+0.192450090\) \(a_{28}=+1.097212918\) \(a_{29}=-0.308658219\) \(a_{30}=+0.021232469\)
\(a_{31}=-0.927522842\) \(a_{32}=-0.116079978\) \(a_{33}=-0.271148820\) \(a_{34}=+0.059521481\) \(a_{35}=+1.042313358\)
\(a_{36}=-0.332832270\) \(a_{37}=+0.267290781\) \(a_{38}=-0.026103776\) \(a_{39}=+0.588700806\) \(a_{40}=-0.073496148\)
\(a_{41}=-1.567547158\) \(a_{42}=+0.024597482\) \(a_{43}=+0.149111243\) \(a_{44}=+0.468937569\) \(a_{45}=-0.316178853\)
\(a_{46}=+0.022420520\) \(a_{47}=+0.660150454\) \(a_{48}=+0.574747972\) \(a_{49}=+0.207503671\) \(a_{50}=+0.003887888\)
\(a_{51}=-0.886351641\) \(a_{52}=-1.018126949\) \(a_{53}=+0.182548130\) \(a_{54}=-0.007461524\) \(a_{55}=+0.445474052\)
\(a_{56}=-0.085144051\) \(a_{57}=+0.388718962\) \(a_{58}=+0.011966868\) \(a_{59}=-0.562627846\) \(a_{60}=+0.546814630\)
\(a_{61}=+1.281703294\) \(a_{62}=+0.035960993\) \(a_{63}=-0.366288237\) \(a_{64}=-0.990992150\) \(a_{65}=-0.967184511\)
\(a_{66}=+0.010512709\) \(a_{67}=-0.478978632\) \(a_{68}=+1.532898391\) \(a_{69}=-0.333870473\) \(a_{70}=-0.040411550\)
\(a_{71}=+0.084436576\) \(a_{72}=+0.025827932\) \(a_{73}=+1.005272919\) \(a_{74}=-0.010363159\) \(a_{75}=-0.057895801\)
\(a_{76}=-0.672268805\) \(a_{77}=+0.516074780\) \(a_{78}=-0.022824509\) \(a_{79}=-0.471492281\) \(a_{80}=-0.944261280\)
\(a_{81}=+0.111111221\) \(a_{82}=+0.060775554\) \(a_{83}=-1.021955959\) \(a_{84}=+0.633475859\) \(a_{85}=+1.456199017\)
\(a_{86}=-0.005780762\) \(a_{87}=-0.178203517\) \(a_{88}=-0.036390168\) \(a_{89}=+1.032907758\) \(a_{90}=+0.012258732\)
\(a_{91}=-1.120466642\) \(a_{92}=+0.577412009\) \(a_{93}=-0.535507430\) \(a_{94}=-0.025596850\) \(a_{95}=-0.638629925\)
\(a_{96}=-0.067014507\) \(a_{97}=-0.226061111\) \(a_{98}=-0.008051917\) \(a_{99}=-0.156551988\) \(a_{100}=+0.100135739\)

Showing 100 of 5000 available coefficients

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