Properties

Level $22$
Weight $0$
Character 22.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 4.21191805685 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.012736746\) \(a_{4}=+0.500000000\) \(a_{5}=-0.664040290\)
\(a_{6}=-0.716113021\) \(a_{7}=-1.036190429\) \(a_{8}=-0.353553391\) \(a_{9}=+0.025635718\) \(a_{10}=+0.469547392\)
\(a_{11}=-0.301511345\) \(a_{12}=+0.506368373\) \(a_{13}=-1.248419394\) \(a_{14}=+0.732697279\) \(a_{15}=-0.672498003\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.042883292\) \(a_{18}=-0.018127190\) \(a_{19}=+0.838108965\) \(a_{20}=-0.332020145\)
\(a_{21}=-1.049388124\) \(a_{22}=+0.213200716\) \(a_{23}=+1.020170654\) \(a_{24}=-0.358056510\) \(a_{25}=-0.559050493\)
\(a_{26}=+0.882765819\) \(a_{27}=-0.986774513\) \(a_{28}=-0.518095215\) \(a_{29}=+0.995888845\) \(a_{30}=+0.475527898\)
\(a_{31}=+0.427727840\) \(a_{32}=-0.176776695\) \(a_{33}=-0.305351618\) \(a_{34}=+0.737429848\) \(a_{35}=+0.688072193\)
\(a_{36}=+0.012817859\) \(a_{37}=+0.029374419\) \(a_{38}=-0.592632533\) \(a_{39}=-1.264320195\) \(a_{40}=+0.234773696\)
\(a_{41}=-0.637472730\) \(a_{42}=+0.742029459\) \(a_{43}=-1.799513861\) \(a_{44}=-0.150755672\) \(a_{45}=-0.017023149\)
\(a_{46}=-0.721369588\) \(a_{47}=+1.967483606\) \(a_{48}=+0.253184187\) \(a_{49}=+0.073690606\) \(a_{50}=+0.395308395\)
\(a_{51}=-1.056166233\) \(a_{52}=-0.624209697\) \(a_{53}=+0.798863814\) \(a_{54}=+0.697754950\) \(a_{55}=+0.200215681\)
\(a_{56}=+0.366348640\) \(a_{57}=+0.848783746\) \(a_{58}=-0.704199756\) \(a_{59}=+0.328891546\) \(a_{60}=-0.336249001\)
\(a_{61}=-0.024617604\) \(a_{62}=-0.302449256\) \(a_{63}=-0.026563485\) \(a_{64}=+0.125000000\) \(a_{65}=+0.829000776\)
\(a_{66}=+0.215916200\) \(a_{67}=+0.652121706\) \(a_{68}=-0.521441646\) \(a_{69}=+1.033164309\) \(a_{70}=-0.486540514\)
\(a_{71}=-1.753506293\) \(a_{72}=-0.009063595\) \(a_{73}=-1.843727414\) \(a_{74}=-0.020770851\) \(a_{75}=-0.566170978\)
\(a_{76}=+0.419054483\) \(a_{77}=+0.312423170\) \(a_{78}=+0.894009384\) \(a_{79}=-1.383659209\) \(a_{80}=-0.166010072\)
\(a_{81}=-1.024978528\) \(a_{82}=+0.450761290\) \(a_{83}=+0.084262928\) \(a_{84}=-0.524694062\) \(a_{85}=+0.692516524\)
\(a_{86}=+1.272448454\) \(a_{87}=+1.008573229\) \(a_{88}=+0.106600358\) \(a_{89}=+0.279742388\) \(a_{90}=+0.012037184\)
\(a_{91}=+1.293600228\) \(a_{92}=+0.510085327\) \(a_{93}=+0.433175701\) \(a_{94}=-1.391221000\) \(a_{95}=-0.556538120\)
\(a_{96}=-0.179028255\) \(a_{97}=+0.443254300\) \(a_{98}=-0.052107127\) \(a_{99}=-0.007729460\) \(a_{100}=-0.279525247\)

Showing 100 of 250 available coefficients

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