Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 23.028056402 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.340154845\) \(a_{4}=+0.500000000\) \(a_{5}=+1.714712200\)
\(a_{6}=+0.240525798\) \(a_{7}=+0.900172097\) \(a_{8}=+0.353553391\) \(a_{9}=-0.884294681\) \(a_{10}=+1.212484625\)
\(a_{11}=-0.126988074\) \(a_{12}=+0.170077423\) \(a_{13}=+0.713500118\) \(a_{14}=+0.636517795\) \(a_{15}=+0.583267663\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.695500058\) \(a_{18}=-0.625290766\) \(a_{19}=-0.864776901\) \(a_{20}=+0.857356100\)
\(a_{21}=+0.306197900\) \(a_{22}=-0.089794128\) \(a_{23}=+1.526490868\) \(a_{24}=+0.120262899\) \(a_{25}=+1.940237928\)
\(a_{26}=+0.504520772\) \(a_{27}=-0.640951965\) \(a_{28}=+0.450086049\) \(a_{29}=+1.445538190\) \(a_{30}=+0.412432520\)
\(a_{31}=-0.625858959\) \(a_{32}=+0.176776696\) \(a_{33}=-0.043195608\) \(a_{34}=-0.491792808\) \(a_{35}=+1.543536077\)
\(a_{36}=-0.442147341\) \(a_{37}=-0.032169185\) \(a_{38}=-0.611489611\) \(a_{39}=+0.242700522\) \(a_{40}=+0.606242313\)
\(a_{41}=-1.145406077\) \(a_{42}=+0.216514612\) \(a_{43}=+1.402768023\) \(a_{44}=-0.063494037\) \(a_{45}=-1.516310878\)
\(a_{46}=+1.079392045\) \(a_{47}=-0.953543452\) \(a_{48}=+0.085038711\) \(a_{49}=-0.189690195\) \(a_{50}=+1.371955396\)
\(a_{51}=-0.236577715\) \(a_{52}=+0.356750059\) \(a_{53}=-0.827230268\) \(a_{54}=-0.453221481\) \(a_{55}=-0.217747999\)
\(a_{56}=+0.318258897\) \(a_{57}=-0.294158053\) \(a_{58}=+1.022149857\) \(a_{59}=+0.293752544\) \(a_{60}=+0.291633832\)
\(a_{61}=-0.692927959\) \(a_{62}=-0.442549114\) \(a_{63}=-0.796017398\) \(a_{64}=+0.125000000\) \(a_{65}=+1.223447357\)
\(a_{66}=-0.030543908\) \(a_{67}=-0.469773494\) \(a_{68}=-0.347750029\) \(a_{69}=+0.519243265\) \(a_{70}=+1.091444828\)
\(a_{71}=-0.685114339\) \(a_{72}=-0.312645383\) \(a_{73}=-0.755995915\) \(a_{74}=-0.022747049\) \(a_{75}=+0.659981332\)
\(a_{76}=-0.432388451\) \(a_{77}=-0.114311121\) \(a_{78}=+0.171615185\) \(a_{79}=+0.723121209\) \(a_{80}=+0.428678050\)
\(a_{81}=+0.666271765\) \(a_{82}=-0.809924404\) \(a_{83}=-1.206715229\) \(a_{84}=+0.153098950\) \(a_{85}=-1.192582435\)
\(a_{86}=+0.991906782\) \(a_{87}=+0.491706819\) \(a_{88}=-0.044897064\) \(a_{89}=+0.994533047\) \(a_{90}=-1.072193705\)
\(a_{91}=+0.642272898\) \(a_{92}=+0.763245434\) \(a_{93}=-0.212888957\) \(a_{94}=-0.674257041\) \(a_{95}=-1.482843502\)
\(a_{96}=+0.060131449\) \(a_{97}=+0.797191538\) \(a_{98}=-0.134131223\) \(a_{99}=+0.112294878\) \(a_{100}=+0.970118964\)

Showing 100 of 1228 available coefficients

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