Properties

Level $55$
Weight $0$
Character 55.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 55 = 5 \cdot 11 \)
Weight: \( 0 \)
Character: 55.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.3436234845 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.049953693\) \(a_{3}=-0.480803662\) \(a_{4}=-0.997504629\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.024017918\) \(a_{7}=+1.509095127\) \(a_{8}=-0.099782732\) \(a_{9}=-0.768827839\) \(a_{10}=-0.022339970\)
\(a_{11}=+0.301511345\) \(a_{12}=+0.479603878\) \(a_{13}=+1.798220060\) \(a_{14}=+0.075384874\) \(a_{15}=+0.215021934\)
\(a_{16}=+0.992520113\) \(a_{17}=-0.025340817\) \(a_{18}=-0.038405790\) \(a_{19}=-1.052785516\) \(a_{20}=+0.446097631\)
\(a_{21}=-0.725578463\) \(a_{22}=+0.015061605\) \(a_{23}=+0.375508855\) \(a_{24}=+0.047975903\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.089827732\) \(a_{27}=+0.850458902\) \(a_{28}=-1.505329374\) \(a_{29}=-0.287255591\) \(a_{30}=+0.010741140\)
\(a_{31}=+0.183342255\) \(a_{32}=+0.149362777\) \(a_{33}=-0.144967759\) \(a_{34}=-0.001265867\) \(a_{35}=-0.674887858\)
\(a_{36}=+0.766909328\) \(a_{37}=+1.600486107\) \(a_{38}=-0.052590524\) \(a_{39}=-0.864590790\) \(a_{40}=+0.044624194\)
\(a_{41}=+1.609956034\) \(a_{42}=-0.036245324\) \(a_{43}=+0.236248360\) \(a_{44}=-0.300758962\) \(a_{45}=+0.343830262\)
\(a_{46}=+0.018758054\) \(a_{47}=-0.118960071\) \(a_{48}=-0.477207305\) \(a_{49}=+1.277368103\) \(a_{50}=+0.009990739\)
\(a_{51}=+0.012183958\) \(a_{52}=-1.793732833\) \(a_{53}=-0.068177048\) \(a_{54}=+0.042483563\) \(a_{55}=-0.134839972\)
\(a_{56}=-0.150581635\) \(a_{57}=+0.506183131\) \(a_{58}=-0.014349477\) \(a_{59}=+0.940741497\) \(a_{60}=-0.214485375\)
\(a_{61}=+0.899810625\) \(a_{62}=+0.009158623\) \(a_{63}=-1.160234345\) \(a_{64}=-0.985058890\) \(a_{65}=-0.804188459\)
\(a_{66}=-0.007241675\) \(a_{67}=-0.091439608\) \(a_{68}=+0.025277582\) \(a_{69}=-0.180546032\) \(a_{70}=-0.033713141\)
\(a_{71}=-1.109295335\) \(a_{72}=+0.076715742\) \(a_{73}=-1.137520841\) \(a_{74}=+0.079950191\) \(a_{75}=-0.096160732\)
\(a_{76}=+1.050158425\) \(a_{77}=+0.455009301\) \(a_{78}=-0.043189503\) \(a_{79}=+1.659043897\) \(a_{80}=-0.443868488\)
\(a_{81}=+0.359924084\) \(a_{82}=+0.080423249\) \(a_{83}=-0.957816703\) \(a_{84}=+0.723767876\) \(a_{85}=+0.011332758\)
\(a_{86}=+0.011801478\) \(a_{87}=+0.138113540\) \(a_{88}=-0.030085626\) \(a_{89}=-0.834402681\) \(a_{90}=+0.017175591\)
\(a_{91}=+2.713685131\) \(a_{92}=-0.374571821\) \(a_{93}=-0.088151628\) \(a_{94}=-0.005942495\) \(a_{95}=+0.470819996\)
\(a_{96}=-0.071814170\) \(a_{97}=-0.043309511\) \(a_{98}=+0.063809254\) \(a_{99}=-0.231810315\) \(a_{100}=-0.199500926\)

Showing 100 of 478 available coefficients

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