Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 24.0285125229 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577214066\) \(a_{4}=+0.500000000\) \(a_{5}=+0.239299219\)
\(a_{6}=-0.408151980\) \(a_{7}=-0.121257456\) \(a_{8}=-0.353553391\) \(a_{9}=-0.666823922\) \(a_{10}=-0.169210101\)
\(a_{11}=-0.879074557\) \(a_{12}=+0.288607033\) \(a_{13}=+1.652822998\) \(a_{14}=+0.085741969\) \(a_{15}=+0.138126875\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.116081089\) \(a_{18}=+0.471515717\) \(a_{19}=+1.460426654\) \(a_{20}=+0.119649610\)
\(a_{21}=-0.069991509\) \(a_{22}=+0.621599581\) \(a_{23}=-0.824702275\) \(a_{24}=-0.204075990\) \(a_{25}=-0.942735884\)
\(a_{26}=-1.168722350\) \(a_{27}=-0.962114214\) \(a_{28}=-0.060628728\) \(a_{29}=-0.729450867\) \(a_{30}=-0.097670450\)
\(a_{31}=-1.131832474\) \(a_{32}=-0.176776695\) \(a_{33}=-0.507414200\) \(a_{34}=+0.789188506\) \(a_{35}=-0.029016815\)
\(a_{36}=-0.333411961\) \(a_{37}=-0.280922215\) \(a_{38}=-1.032677590\) \(a_{39}=+0.954032683\) \(a_{40}=-0.084605050\)
\(a_{41}=+0.733492021\) \(a_{42}=+0.049491471\) \(a_{43}=-0.842864185\) \(a_{44}=-0.439537279\) \(a_{45}=-0.159570444\)
\(a_{46}=+0.583152571\) \(a_{47}=+0.628130224\) \(a_{48}=+0.144303517\) \(a_{49}=-0.985296629\) \(a_{50}=+0.666614936\)
\(a_{51}=-0.644217704\) \(a_{52}=+0.826411499\) \(a_{53}=-1.280556646\) \(a_{54}=+0.680317485\) \(a_{55}=-0.210361855\)
\(a_{56}=+0.042870985\) \(a_{57}=+0.842978807\) \(a_{58}=+0.515799655\) \(a_{59}=-1.024211537\) \(a_{60}=+0.069063438\)
\(a_{61}=-1.316498662\) \(a_{62}=+0.800326418\) \(a_{63}=+0.080857372\) \(a_{64}=+0.125000000\) \(a_{65}=+0.395519253\)
\(a_{66}=+0.358796022\) \(a_{67}=+0.326185533\) \(a_{68}=-0.558040545\) \(a_{69}=-0.476029754\) \(a_{70}=+0.020517986\)
\(a_{71}=-1.221702202\) \(a_{72}=+0.235757858\) \(a_{73}=+1.436736528\) \(a_{74}=+0.198642003\) \(a_{75}=-0.544160413\)
\(a_{76}=+0.730213327\) \(a_{77}=+0.106594345\) \(a_{78}=-0.674602980\) \(a_{79}=-0.618617827\) \(a_{80}=+0.059824805\)
\(a_{81}=+0.111478064\) \(a_{82}=-0.518657182\) \(a_{83}=+0.911063904\) \(a_{84}=-0.034995755\) \(a_{85}=-0.267077333\)
\(a_{86}=+0.595994981\) \(a_{87}=-0.421049301\) \(a_{88}=+0.310799790\) \(a_{89}=+0.166238835\) \(a_{90}=+0.112833343\)
\(a_{91}=-0.200417112\) \(a_{92}=-0.412351137\) \(a_{93}=-0.653309625\) \(a_{94}=-0.444155141\) \(a_{95}=+0.349478958\)
\(a_{96}=-0.102037995\) \(a_{97}=+1.060109902\) \(a_{98}=+0.696709928\) \(a_{99}=+0.586187944\) \(a_{100}=-0.471367942\)

Showing 100 of 1228 available coefficients

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