Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 40.6886664449 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.222855425\) \(a_{3}=+1.405540984\) \(a_{4}=+0.495375391\) \(a_{5}=-0.017189610\)
\(a_{6}=+1.718773417\) \(a_{7}=+1.740353186\) \(a_{8}=-0.617082941\) \(a_{9}=+0.975545457\) \(a_{10}=-0.021020408\)
\(a_{11}=-0.313112474\) \(a_{12}=+0.696270414\) \(a_{13}=+1.020175592\) \(a_{14}=+2.128200335\) \(a_{15}=-0.024160702\)
\(a_{16}=-1.249978613\) \(a_{17}=+0.209571207\) \(a_{18}=+1.192951055\) \(a_{19}=+0.944406328\) \(a_{20}=-0.008515280\)
\(a_{21}=+2.446137729\) \(a_{22}=-0.382891287\) \(a_{23}=+1.283805769\) \(a_{24}=-0.867335364\) \(a_{25}=-0.999704517\)
\(a_{26}=+1.247527257\) \(a_{27}=-0.034371862\) \(a_{28}=+0.862128139\) \(a_{29}=+0.050699038\) \(a_{30}=-0.029545045\)
\(a_{31}=-0.949121723\) \(a_{32}=-0.911460187\) \(a_{33}=-0.440092414\) \(a_{34}=+0.256275288\) \(a_{35}=-0.029915993\)
\(a_{36}=+0.483261212\) \(a_{37}=+0.992038763\) \(a_{38}=+1.154872406\) \(a_{39}=+1.433898605\) \(a_{40}=+0.010607415\)
\(a_{41}=+0.047341976\) \(a_{42}=+2.991272792\) \(a_{43}=-0.658543373\) \(a_{44}=-0.155108214\) \(a_{45}=-0.016769246\)
\(a_{46}=+1.569908850\) \(a_{47}=+0.267037010\) \(a_{48}=-1.756896169\) \(a_{49}=+2.028829212\) \(a_{50}=-1.222494092\)
\(a_{51}=+0.294560921\) \(a_{52}=+0.505369882\) \(a_{53}=-0.109456557\) \(a_{54}=-0.042031818\) \(a_{55}=+0.005382281\)
\(a_{56}=-1.073942263\) \(a_{57}=+1.327401804\) \(a_{58}=+0.061997593\) \(a_{59}=-0.268763979\) \(a_{60}=-0.011968617\)
\(a_{61}=-0.204425901\) \(a_{62}=-1.160638647\) \(a_{63}=+1.697793645\) \(a_{64}=+0.135394574\) \(a_{65}=-0.017536408\)
\(a_{66}=-0.538169409\) \(a_{67}=-1.046859849\) \(a_{68}=+0.103816476\) \(a_{69}=+1.804441624\) \(a_{70}=-0.036582934\)
\(a_{71}=-0.888668323\) \(a_{72}=-0.601992460\) \(a_{73}=+0.267682471\) \(a_{74}=+1.213119983\) \(a_{75}=-1.405125671\)
\(a_{76}=+0.467835655\) \(a_{77}=-0.544926291\) \(a_{78}=+1.753450688\) \(a_{79}=-0.870257309\) \(a_{80}=+0.021486645\)
\(a_{81}=-1.023856518\) \(a_{82}=+0.057892392\) \(a_{83}=+0.259565478\) \(a_{84}=+1.211756433\) \(a_{85}=-0.003602447\)
\(a_{86}=-0.805303336\) \(a_{87}=+0.071259576\) \(a_{88}=+0.193216366\) \(a_{89}=-1.338973008\) \(a_{90}=-0.020506364\)
\(a_{91}=+1.775465841\) \(a_{92}=+0.635965784\) \(a_{93}=-1.334029481\) \(a_{94}=+0.326547657\) \(a_{95}=-0.016233977\)
\(a_{96}=-1.281094648\) \(a_{97}=-0.454767092\) \(a_{98}=+2.480964808\) \(a_{99}=-0.305455451\) \(a_{100}=-0.495229015\)

Showing 100 of 5000 available coefficients

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