Properties

Level $33$
Weight $0$
Character 33.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.41355464648 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.326908378\) \(a_{3}=-0.577350268\) \(a_{4}=-0.893130912\) \(a_{5}=+1.540386280\)
\(a_{6}=+0.188740639\) \(a_{7}=+0.011699861\) \(a_{8}=+0.618880355\) \(a_{9}=+0.333333333\) \(a_{10}=-0.503565179\)
\(a_{11}=-0.301511344\) \(a_{12}=+0.515649373\) \(a_{13}=+0.445598871\) \(a_{14}=-0.003824783\) \(a_{15}=-0.889342435\)
\(a_{16}=+0.690813739\) \(a_{17}=-0.040456097\) \(a_{18}=-0.108969459\) \(a_{19}=-1.803019859\) \(a_{20}=-1.375766606\)
\(a_{21}=-0.006754917\) \(a_{22}=+0.098566583\) \(a_{23}=+1.572437061\) \(a_{24}=-0.357310738\) \(a_{25}=+1.372789898\)
\(a_{26}=-0.145670004\) \(a_{27}=-0.192450090\) \(a_{28}=-0.010449505\) \(a_{29}=+0.060253115\) \(a_{30}=+0.290733493\)
\(a_{31}=+0.921278861\) \(a_{32}=-0.844713153\) \(a_{33}=+0.174077654\) \(a_{34}=+0.013225438\) \(a_{35}=+0.018022303\)
\(a_{36}=-0.297710301\) \(a_{37}=+0.403513376\) \(a_{38}=+0.589422332\) \(a_{39}=-0.257266668\) \(a_{40}=+0.953314850\)
\(a_{41}=+0.187236646\) \(a_{42}=+0.002208230\) \(a_{43}=-1.661854456\) \(a_{44}=+0.269289129\) \(a_{45}=+0.513462055\)
\(a_{46}=-0.514042827\) \(a_{47}=-0.272593017\) \(a_{48}=-0.398841499\) \(a_{49}=-0.999863080\) \(a_{50}=-0.448776581\)
\(a_{51}=+0.023357417\) \(a_{52}=-0.397978224\) \(a_{53}=+0.375197480\) \(a_{54}=+0.062913522\) \(a_{55}=-0.464443927\)
\(a_{56}=+0.007240942\) \(a_{57}=+1.040974001\) \(a_{58}=-0.019697197\) \(a_{59}=-0.413809479\) \(a_{60}=+0.794299170\)
\(a_{61}=+0.793824524\) \(a_{62}=-0.301173801\) \(a_{63}=+0.003900071\) \(a_{64}=-0.414670015\) \(a_{65}=+0.686394491\)
\(a_{66}=-0.056907442\) \(a_{67}=-0.724346547\) \(a_{68}=+0.036132530\) \(a_{69}=-0.907847081\) \(a_{70}=-0.005891882\)
\(a_{71}=+0.580643184\) \(a_{72}=+0.206293396\) \(a_{73}=+0.238458161\) \(a_{74}=-0.131911933\) \(a_{75}=-0.792580610\)
\(a_{76}=+1.610332780\) \(a_{77}=-0.003527664\) \(a_{78}=+0.084102626\) \(a_{79}=+0.387241412\) \(a_{80}=+1.064120007\)
\(a_{81}=+0.111111114\) \(a_{82}=-0.061209224\) \(a_{83}=+0.752607587\) \(a_{84}=+0.006033026\) \(a_{85}=-0.062318018\)
\(a_{86}=+0.543274166\) \(a_{87}=-0.034787164\) \(a_{88}=-0.186599473\) \(a_{89}=-0.369996533\) \(a_{90}=-0.167855074\)
\(a_{91}=+0.005213429\) \(a_{92}=-1.404392163\) \(a_{93}=-0.531900675\) \(a_{94}=+0.089112960\) \(a_{95}=-2.777347228\)
\(a_{96}=+0.487695301\) \(a_{97}=+0.540585751\) \(a_{98}=+0.326863542\) \(a_{99}=-0.100503746\) \(a_{100}=-1.226081053\)

Showing 100 of 2000 available coefficients

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