Properties

Level $22$
Weight $0$
Character 22.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 7.43473012516 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.488164970\) \(a_{4}=+0.500000000\) \(a_{5}=-0.063098950\)
\(a_{6}=-1.052291542\) \(a_{7}=+1.036755394\) \(a_{8}=+0.353553391\) \(a_{9}=+1.214634979\) \(a_{10}=-0.044617696\)
\(a_{11}=-0.301511345\) \(a_{12}=-0.744082485\) \(a_{13}=+0.349492947\) \(a_{14}=+0.733096770\) \(a_{15}=+0.093901647\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.827381409\) \(a_{18}=+0.858876630\) \(a_{19}=-0.611544802\) \(a_{20}=-0.031549475\)
\(a_{21}=-1.542863060\) \(a_{22}=-0.213200716\) \(a_{23}=-0.423342346\) \(a_{24}=-0.526145771\) \(a_{25}=-0.996018522\)
\(a_{26}=+0.247128833\) \(a_{27}=-0.319412256\) \(a_{28}=+0.518377697\) \(a_{29}=-0.977772824\) \(a_{30}=+0.066398492\)
\(a_{31}=-1.603516423\) \(a_{32}=+0.176776695\) \(a_{33}=+0.448698621\) \(a_{34}=-0.585047005\) \(a_{35}=-0.065418177\)
\(a_{36}=+0.607317489\) \(a_{37}=+1.463559990\) \(a_{38}=-0.432427477\) \(a_{39}=-0.520103162\) \(a_{40}=-0.022308848\)
\(a_{41}=-0.140371403\) \(a_{42}=-1.090968932\) \(a_{43}=-1.550572921\) \(a_{44}=-0.150755672\) \(a_{45}=-0.076642192\)
\(a_{46}=-0.299348243\) \(a_{47}=+1.560648423\) \(a_{48}=-0.372041243\) \(a_{49}=+0.074861747\) \(a_{50}=-0.704291451\)
\(a_{51}=+1.231280030\) \(a_{52}=+0.174746474\) \(a_{53}=-1.004906333\) \(a_{54}=-0.225858573\) \(a_{55}=+0.019025049\)
\(a_{56}=+0.366548385\) \(a_{57}=+0.910079552\) \(a_{58}=-0.691389794\) \(a_{59}=+1.470484561\) \(a_{60}=+0.046950824\)
\(a_{61}=-0.813697128\) \(a_{62}=-1.133857336\) \(a_{63}=+1.259279366\) \(a_{64}=+0.125000000\) \(a_{65}=-0.022052638\)
\(a_{66}=+0.317277838\) \(a_{67}=-1.164069475\) \(a_{68}=-0.413690705\) \(a_{69}=+0.630003249\) \(a_{70}=-0.046257637\)
\(a_{71}=-0.171481852\) \(a_{72}=+0.429438315\) \(a_{73}=-1.953190729\) \(a_{74}=+1.034893193\) \(a_{75}=+1.482239875\)
\(a_{76}=-0.305772401\) \(a_{77}=-0.312593513\) \(a_{78}=-0.367768472\) \(a_{79}=-0.517445905\) \(a_{80}=-0.015774738\)
\(a_{81}=-0.739296848\) \(a_{82}=-0.099257571\) \(a_{83}=+0.956665948\) \(a_{84}=-0.771431530\) \(a_{85}=+0.052206898\)
\(a_{86}=-1.096420627\) \(a_{87}=+1.455087266\) \(a_{88}=-0.106600358\) \(a_{89}=-1.313555384\) \(a_{90}=-0.054194214\)
\(a_{91}=+0.362338697\) \(a_{92}=-0.211671173\) \(a_{93}=+2.386296971\) \(a_{94}=+1.103545083\) \(a_{95}=+0.038587832\)
\(a_{96}=-0.263072885\) \(a_{97}=+1.724787600\) \(a_{98}=+0.052935249\) \(a_{99}=-0.366226226\) \(a_{100}=-0.498009261\)

Showing 100 of 268 available coefficients

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