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: \( 17.7385633811 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.765458057\) \(a_{3}=-0.977778907\) \(a_{4}=-0.414073964\) \(a_{5}=-1.015273523\)
\(a_{6}=+0.748448742\) \(a_{7}=+1.180820836\) \(a_{8}=+1.082414308\) \(a_{9}=-0.043948408\) \(a_{10}=+0.777149297\)
\(a_{11}=-0.620487725\) \(a_{12}=+0.404872781\) \(a_{13}=+0.265288699\) \(a_{14}=-0.903868822\) \(a_{15}=+0.992713036\)
\(a_{16}=-0.414468789\) \(a_{17}=-0.135740409\) \(a_{18}=+0.033640663\) \(a_{19}=+0.176971041\) \(a_{20}=+0.420398332\)
\(a_{21}=-1.154581707\) \(a_{22}=+0.474957329\) \(a_{23}=+1.001373356\) \(a_{24}=-1.058361880\) \(a_{25}=+0.030780326\)
\(a_{26}=-0.203067372\) \(a_{27}=+1.020750734\) \(a_{28}=-0.488947164\) \(a_{29}=-0.110159954\) \(a_{30}=-0.759880191\)
\(a_{31}=+1.275868489\) \(a_{32}=-0.765155834\) \(a_{33}=+0.606699811\) \(a_{34}=+0.103903589\) \(a_{35}=-1.198856129\)
\(a_{36}=+0.018197892\) \(a_{37}=+1.392318699\) \(a_{38}=-0.135463909\) \(a_{39}=-0.259393694\) \(a_{40}=-1.098946587\)
\(a_{41}=+0.344716239\) \(a_{42}=+0.883783869\) \(a_{43}=-0.351234617\) \(a_{44}=+0.256927812\) \(a_{45}=+0.044619655\)
\(a_{46}=-0.766509303\) \(a_{47}=-0.133377452\) \(a_{48}=+0.405258840\) \(a_{49}=+0.394337846\) \(a_{50}=-0.023561048\)
\(a_{51}=+0.132724108\) \(a_{52}=-0.109849143\) \(a_{53}=-0.535893732\) \(a_{54}=-0.781341874\) \(a_{55}=+0.629964760\)
\(a_{56}=+1.278137368\) \(a_{57}=-0.173038545\) \(a_{58}=+0.084322825\) \(a_{59}=-1.583035994\) \(a_{60}=-0.411056621\)
\(a_{61}=+1.968869689\) \(a_{62}=-0.976623814\) \(a_{63}=-0.051895196\) \(a_{64}=+1.000163487\) \(a_{65}=-0.269340592\)
\(a_{66}=-0.464403258\) \(a_{67}=-0.126274188\) \(a_{68}=+0.056206569\) \(a_{69}=-0.979121746\) \(a_{70}=+0.917674083\)
\(a_{71}=+0.660481656\) \(a_{72}=-0.047570386\) \(a_{73}=+0.424114180\) \(a_{74}=-1.065761565\) \(a_{75}=-0.030096353\)
\(a_{76}=-0.073279100\) \(a_{77}=-0.732684835\) \(a_{78}=+0.198554993\) \(a_{79}=+1.702569002\) \(a_{80}=+0.420799187\)
\(a_{81}=-0.954120129\) \(a_{82}=-0.263865823\) \(a_{83}=-0.938631333\) \(a_{84}=+0.478082224\) \(a_{85}=+0.137813643\)
\(a_{86}=+0.268855367\) \(a_{87}=+0.107712080\) \(a_{88}=-0.671624793\) \(a_{89}=+1.045259884\) \(a_{90}=-0.034154475\)
\(a_{91}=+0.313258423\) \(a_{92}=-0.414642634\) \(a_{93}=-1.247517297\) \(a_{94}=+0.102094844\) \(a_{95}=-0.179674012\)
\(a_{96}=+0.748153236\) \(a_{97}=+1.023748370\) \(a_{98}=-0.301849080\) \(a_{99}=+0.027269450\) \(a_{100}=-0.012745335\)

Showing 100 of 5000 available coefficients

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